STARODUB
CHEM. 2AP
UNIT 2-2:
#1
#2
#3
#4
#5
#6
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READ P. 179 – 214
ASSIGNMENTS:
UNIT 2-2
1
CH. 5: Gases
CH. 5 GASES
P. 7
P. 14
P. 17
P. 20
P. 22
P. 24
#1-12
#1-17
#1-12
#1-6
#1-4
#1-10
Pressure Problems
Gas Law Problems
Gas Density, Molar Mass, Stoichiometry
Graham’s Law
Partial Pressure Problems
KMT and Real Gases
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BASIC DEFINITIONS:
Avogadro’s hypothesis
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Equal volumes of gases under the same conditions of temperature and pressure have
equal numbers of particles. (All gases do the same thing under the same conditions.)
An apparatus used to measure atmospheric pressure.
Compressibility
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Barometer
The change in volume with change in pressure.
The total pressure of a mixture of gases is the sum of the pressures of the components
of the mixture.
Diffusion
The gradual mixing of the molecules of two or more substances by random molecular
motion.
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Dalton’s Law of Partial Pressures
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The movement of gas molecules through a membrane or other porous barrier by
random molecular motion.
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Effusion
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The proportionality constant in the ideal gas law.
Ideal gas law
A law that relates pressure, volume, number of moles, and temperature for an ideal
gas. PV = nRT
Mole fraction (X)
The ratio of the number of moles of one substance to the total number of moles in a
mixture of substances.
Partial pressure
The pressure exerted by one gas in a mixture of gases.
Pressure
The force exerted on an object divided by the area over which the force is exerted.
Root-mean-square (rms) speed
The square root of the average of the squares of the speeds of the molecules in a
sample.
Standard atmosphere (atm)
A unit of pressure: 1 atm = 760 mm Hg
Standard molar volume
The volume occupied by 1 mol of gas at standard temperature and pressure; 22.1 L
Standard temperature and pressure (STP)
A temperature of 0 °C and a pressure of exactly 1 atm.
torr
A unit of pressure equivalent to one millimeter of mercury
Van der Waals equation
A mathematical expression that describes the behavior of non-ideal gases.
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Gas constant ®
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10/16/2015
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CHEM. 2AP
UNIT 2-2
2
CH. 5: Gases
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General properties of gases and the basic gas laws
Matter exists as a solid, a liquid, or a gas. Atoms and molecules in gases have the lowest density of all the states of matter and the
weakest intermolecular forces.
Gases expand to fill the space available to them. They take the shape of their container and are evenly distributed within it. They mix
completely and uniformly with other gases when confined in the same space, providing no chemical reaction occurs.
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Expansion. Gases expand indefinitely to fill the space available to them.
Indefinite shape. Gases take the shape of their container.
Compressibility. Gases are the most compressible of the states of matter. They expand and contract easily with changes in
pressure. Solids and liquids do not.
Mixing. Two or more gases will mix evenly and completely when confined to the same container (air)
m
. gases have much lower densities than liquids and solids. They are about 1/1000th those of liquids and
Low density. D =
V
solids.
o Density of water = 1 g/mL, density of air = 0.00119 g/mL.
o Know the elements that exist as gases under normal temperature and pressure. (25 C. and 1 atmosphere pressure.
Atmosphere is a unit of pressure.)
o The state of a substance depends on its temperature and pressure. (Butane lighter – liquid under pressure; it is a gas
when released to the atmosphere)
Gases exert pressure.
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To describe the gaseous state, only 4 quantities are needed:
1. The quantity of gas, n (in moles),
2. The temperature of the gas, T (in kelvins). (Remember, K = C + 273)
3. The volume of gas, V (in liters),
4. The pressure of the gas P. Pressure is measured in:

atmospheres (atm),

mm of mercury (mm Hg), (1 mm Hg = 1 torr)

kilopascals (kPa).
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PRESSURE OF A GAS
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Air exerts pressure on us all the time due to a column of air extending all the way to the upper atmosphere. It pushes on us
from all directions all the time. These pushes equalize each other so we are unaware of them.
Gas pressure is the result of simultaneous collisions of billions of gas particles on an object. When no gas particles are
present, there is an empty space. There are no gas molecules to collide – no gas molecules, no collisions, no pressure.
This empty space is called a vacuum.
Air exerts pressure because gravity holds air molecules in the earth’s atmosphere.
Atmospheric pressure results from the collisions of gas molecules with objects. (An inflated car tire). It decreases with an
increase in elevation.
A gas is a substance that is in the gaseous state at ordinary temperature and pressure. A vapor is the gaseous form of any
substance that is a liquid or solid at normal temperatures and pressure. Water in the gas state is called water vapor.
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INTRODUCTION TO AIR PRESSURE (ATMOSPHERIC PRESSURE) AND THE
PRESSURE OF GASES
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The pressure of a gas is the force per unit area. A gas, such as our atmosphere exerts a pressure on every surface it contacts, no matter
what the direction of contact. The atoms and molecules of the gases in the atmosphere, like all other matter, are subject to Earth’s
gravitational pull. Therefore, the atmosphere is much denser near the surface of Earth than at high altitudes. The denser the air, the
greater the pressure it exerts. Atmospheric pressure is the pressure exerted by Earth’s atmosphere. The value of atmospheric pressure
depends on location, temperature, and weather conditions.
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10/16/2015
STARODUB
CHEM. 2AP
UNIT 2-2
3
CH. 5: Gases
HOW ATMOSPHERIC PRESSURE IS MEASURED
Atmospheric pressure is measured using a barometer.
A simple barometer consists of a long glass tube, close at one end and
filled with mercury. If the tube is carefully inverted in a dish of mercury
so that no air enters the tube some mercury will flow out of the tube into
the dish creating a vacuum at the top. The weight of the mercury remaining
in the tube is supported by atmospheric pressure acting on the surface of the
mercury in the dish. At sea level, the pressure of the atmosphere will support
a column of mercury 760 mm high. This is called STANDARD
ATMOSPHERIC PRESSURE. The pressure exerted by the mercury column
is balanced by the pressure at the bottom of the column of air above the dish –
a column of gas that extends to the top of the atmosphere. Other atmospheric
pressure units are torr, and kilopascals. On the top of Mt. Everest (6 miles
high) the air exerts enough pressure to support a column of mercury only 253 mm high.
h = 760 mm at sea level
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THE SIMPLE (TORICELLI) BAROMETER
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pool of Hg
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RELATIONSHIP OF PRESSURE UNITS:
STANDARD ATMOSPHERIC PRESSURE = 1 atm = 760 mm Hg = 760 torr = 101.325 kPa = 14.7 lb/in2 (psi)
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Any liquid can be used in a barometer. The height of the column depends on the density of the liquid. If it were water, the column
would be almost 34 feet high! WOW!! By using mercury in the barometer, a barometer is a useful practical size.
Barometers today are called ANEROID BAROMETERS. In these devices atmospheric pressure is related to the number of collisions
of air molecules with a sensitive metal diaphragm. The diaphragm controls the movement of a pointer that gives the pressure reading.
PRESSURE UNIT CONVERSIONS WORKSHEET
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Use the factor-label method for the unit conversions.
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“DO ‘EM IF YOU NEED ‘EM”
The atmospheric pressure in San Francisco on a certain day was 732 mm Hg. What was the pressure in kPa?
2.
The pressure inside a plane before pressurization is 688 mm Hg. What is this pressure in atmospheres?
3.
Convert a pressure of 645 mm Hg into its value in (a) atmospheres (b) kilopascals.
4.
Change the following temperatures from Celsius to kelvin:
(a) 20.5 C + 273 = 293.5 K (Treat 273 as a
constant with infinite sig figs. For this
course)
(97.6 kPa)
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1.
(0.905)
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(c) 27.86 K ________
(d) 100.0 K _____
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Convert to Celsius degrees
(a) 0 K ________
(b) 273 K ________
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(b) −272 C + 273 = 545 K
(c) 273 C ________
(d) −273 C ________
(e) –48.1 C ________
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10/16/2015
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CHEM. 2AP
UNIT 2-2
4
CH. 5: Gases
MEASURING PRESSURE OF GASES (OTHER THAN ATMOSPHERIC PRESSURE)
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The instrument used to measure pressure of gases other than air is called a manometer. A manometer will measure the pressure of a gas
in a container, like propane in the barbeque. There are many types of manometers and there are two of them in your textbook. I will
only discuss and expect you to know how an OPEN-END MANOMETER works.
An open-end manometer is made up of a U-tube that has mercury in it. If both sides of the U-tube are open to the air, the levels of the
mercury on both sides will be the same (atmospheric pressure of 760 mm Hg pushing on each side). SEE FIGURE 1 BELOW.
To make this device measure the pressure of a gas, a flask with a gas under pressure will be added to one side of the U-tube (left side in
figure 2 and 3 below). A valve will be opened that will allow the gas to go into the tube on the left side. The mercury will rise in the
side that has less pressure on it (think of a teeter-totter; in Americanized see-saw).
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ASSIGNMENT: Here are the three possibilities in determining the pressure of a gas. In each case, consider the atmospheric pressure
to be standard atmospheric pressure. Determine the pressure of each gas. Write down the relationship in symbols first as is shown in #1
below.
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10/16/2015
STARODUB
CHEM. 2AP
“DO ‘EM IF YOU NEED ‘EM”
UNIT 2-2
5
CH. 5: Gases
PRESSURE OF A GAS WORKSHEET
air pressure
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1.
What causes atmospheric pressure (explain fully)?
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2.
In the figure to the right:
(a) If the atmospheric pressure were to increase, in which direction would the mercury
move in the open arm?
(b) If the atmospheric pressure were to change so that the levels of mercury were the
same in both arms of the manometer, how would the pressure in the container
change?
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Draw a sketch showing what a mercury manometer would look like when it is hooked
up to a flask containing a gas sample at 90 kPa on a day when the atmospheric pressure
is 100 kPa. Label the arrows you use to show the pressure at various points in the
manometer. Write the pressure at each arrow.
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3.
In a simple barometer, how does the height of a column of mercury at sea level compare with the height on a mountain top?
5.
An open-end manometer, similar to the one in the diagram above, is attached to a container of gas that is exerting a pressure of
104.5 kPa.
(a) When the valve is opened, will the mercury in the open arm of the U-tube move up or down?
(b) After the mercury in the U-tube stops moving, what will be the difference in height of the mercury levels in the arms of the
tube?
(24 mm)
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STANDARD TEMPERATURE AND PRESSURE (S.T.P.)
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Standard temperature is 0 C and standard pressure is 1 atmosphere. These conditions are referred to as STP.
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MOLAR VOLUME (Gases only)
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Molar volume is the volume occupied by 1 mole of a gaseous substance. It applies to gases only. Molar volumes vary from substance
to substance for solids and liquids therefore we do not study the molar volumes of solids and liquids. IT IS IMPORTANT TO NOTE
THAT MOLAR VOLUMES ARE IDENTICAL FOR ALL GASES.
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It doesn’t matter what the gas is; equal moles of any gas at the same temperature and pressure occupy equal volumes.
OR
Equal volumes of any gas at the same temperature and pressure have the same number of moles.
For example, if 2 moles of CO2 at STP occupies 44.8 liters of volume, then 2 moles of O2, or H2, or N2O4(g) will occupy the same
volume: 44.8 liters (at the same temperature).
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AT STP, 1 MOLE OF ANY GAS OCCUPIES A VOLUME OF 22.4 LITERS. 22.4 L is known as the molar volume of a gas.
Therefore, 22.4 L of any gas at STP contains 6.022 x 1023 particles of that gas.
STP means standard temperature of 0C and a pressure of 1 atmosphere (atm). At sea level, a column of air above you will exert a
pressure of 1 atmosphere due to the weight of the column of air due to gravity.
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22.4 L of one gas does not have the same mass as 22.4 L of another gas because 1 mole of a gas (22.4 L)
has a mass equal to the molar mass.
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AVOGADRO’S HYPOTHESIS: EQUAL VOLUMES OF DIFFERENT GASES AT THE SAME
TEMPERATURE AND PRESSURE CONTAIN AN EQUAL NUMBER OF MOLES THEREFORE
EQUAL NUMBERS OF PARTICLES.
In other words, all gases do the same thing!! It doesn’t matter what the gas is. They all exert the same
pressure at the same temperature if they occupy the same volume and contain the same number of moles.
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 1 mole of O2 gas occupies 22.4 L at STP (molar volume) has a mass of 32.00 g (molar mass), and contains 6.022 x 1023 molecules
of O2.
 1 mole of He gas occupies 22.4 L at STP, has a mass of 4.00 grams, and contains 6.022 x 1023 He atoms.
 1 mole of NH3(g) occupies 22.4 L at STP, has a mass of 18.02 g, and contains 6.022 x 1023 NH3 molecules.
STARODUB
CHEM. 2AP
UNIT 2-2
6
CH. 5: Gases
EQUAL MOLES OF ANY GAS AT THE SAME TEMPERATURE EXERT THE SAME PRESSURE IF THEY ARE IN THE
SAME CONTAINER OR CONTAINERS WITH EQUAL VOLUMES.
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Suppose there is 1 mole of N2 in a rigid steel container and it exerts a pressure of 4 atm.
 If there was 1 mole of CO2 in the same container at the same temperature, then the CO2 would also exert a pressure of 4 atm.
EQUAL MOLES EXERT EQUAL PRESSURES AT THE SAME TEMP AND PRESSURE
 All gases do the same thing regardless of what gas it is. 1 mole of any gas under these conditions will exert the same
pressure.
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If the number of moles of N2 was doubled from 1 to 2, then the pressure exerted by the N2 gas would double. By doubling the
number of moles of any gas, the pressure will double
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If you had a container with 5 times as many moles of CO2 then there is N2, then the pressure exerted by the CO2 gas would be 5
times that of the N2.
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There is an important relationship between the pressures of gases and their number of moles.
EQUAL MOLES OF GASES EXERT EQUAL PRESSURES. 5 MOLES OF A GAS WILL EXERT 5 TIMES THE PRESSURE
OF 1 MOLE OF ANY OTHER GAS.
COMPARISON OF MOLES OF A GAS TO RATIOS OF THEIR PRESSURES
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0.082
25°C
CO2
0.164
25°C
pressure
exerted
moles CO 2
moles N 2
1.0 L
2 atm
0.164
2
=
0.082
1
1.0 L
Comparison of ratios
presssure CO 2
pressure N 2
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4 atm
2
=
2 atm
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The ratio of the moles of
gas is equal to ratio of the
pressures.
4 atm
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N2
Volume
(rigid steel
container)
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Temp.
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moles
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gas
Formula:
(can be derived from the Combined Gas Law; just like the other gas laws)
“DO ‘EM IF YOU NEED ‘EM”
1.
MOLAR VOLUME PRACTICE QUESTIONS
(a) Determine the volume in liters of 0.600 moles of SO2 gas at STP.
(b) Would your answer change if the gas were carbon monoxide? Explain your answer.
What is the volume (at STP) of 0.0291 moles of hydrogen gas?
5.
How many moles of gas are in 572 liters of nitrogen gas at STP?
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(0.652 L)
(25.5)
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(2.06 x 1024)
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How many molecules are there in 58.3 grams of ammonia gas at STP?
(1.61 x 1023)
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(a) How many molecules are in a 6.00 L balloon at STP filled with carbon dioxide?
(13.4)
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(b) What would the volume be if the gas were N2O5 gas?
2.
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n1
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= 1
n2
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THE RATIO OF THE PRESSURES IS EQUAL TO THE RATIO OF THE MOLES OF GAS.
You could put this into formula form but it is not necessary.
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What is the volume occupied by 3.3 x 10 grams of carbon dioxide at STP?
(1.7 x 10 )
7.
What is the mass of 0.245 L of N2(g) at STP?
(0.306)
8.
A sample of HCl gas at STP has a mass of 25.5 grams. What is the volume occupied by this mass of HCl?
(15.7)
9.
What is the volume at STP of 6.50 moles of sulfur dioxide gas?
(146)
(162)
11. If we measure the densities of helium and neon gas at STP, we obtain values of 0.1786 g/L and 0.901 g/L respectively. What is
the volume occupied by exactly one mole of each of these noble gases at STP
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10. What is the mass of 44.8 liters of hydrogen bromide gas at STP?
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6.
STARODUB
DO ASSIGNMENT #1
CHEM. 2AP
UNIT 2-2
PRESSURE PROBLEMS
7
CH. 5: Gases
P. 7
#1-12
ASSIGNMENT #1 PRESSURE PROBLEMS
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1.
Do the following unit conversions:
(a) 725 mm Hg to kilopascals
(b) 1.87 atm to mm Hg
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Use the properties of gases to explain the following observations. Each can be explained in about 2 or 3 sentences.
(a) Aerosol cans will explode if heated.
(b) You can drink through a soda straw.
(c) A thin-walled can will collapse when the air inside is removed by a vacuum pump.
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Freon-12 (CF2Cl2) is commonly used as the refrigerant in central home air conditions. The system is initially charged to a pressure
of 4.8 atm. Express this pressure in each of the following units:
(4.9 x 105, 3.6 x 103, 71 and one answer twice)
(a) mm Hg
(b) torr
(c) Pa
(d) psi
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3.
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The following two questions deal with 2 different manometers, one is a sealed-tube manometer and the other is an open-tube
manometer. Read the questions carefully.
A sealed-tube manometer (as shown to the right) can be used to measure
pressures below atmospheric pressure. The tube above the mercury is
evacuated. When there is a vacuum in the flask, the mercury levels in both
arms of the U-tube are equal. If a gaseous sample is introduced into the
flask, the mercury levels are different. The difference h is a measure of the
pressure of the gas inside the flask. If h is equal to 6.5 cm. calculate the
pressure in the flask in mmHg, torr, pascals, and atmospheres.
(answers in order: 65, 65, 8.7 x 103, 0.086)
5.
A diagram for an open-end or open-tube manometer is shown to the right. If the flask is open to
the atmosphere, the mercury levels are equal. For each of the two situations (a and b below) where
a gas is contained in the flask, calculate the pressure in the flask in torr, atmospheres, and pascals.
(answers not in order: 975, 1.28, 0.845, 642, 8.56 x 104, 1.30 x 105)
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(517, 850)
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(c) Calculate the pressures in the flask in parts a and b (in torr) if the atmospheric pressure is 635 torr.
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What is the relationship between atmospheric pressure and altitude?
The density of a gaseous compound of carbon and oxygen is 1.964 g/L at STP. Determine the molar mass of the compound.
(43.99)
8. What is the molar mass of a gas that has a volume of 100.0 liters and a mass of 143.1 grams at STP?
(32.05 g/mole)
9. Calculate the density (in g/L) of hydrogen gas at STP.
(9.02 x 102 g/L)
10. Find the mass of 1 molecule of aspirin, C9H8O4 (in grams).
(2.9919 x 10−22)
11. The density of a gaseous element at STP is 5.86 g/L. Determine the molar mass of the element and identify it.
(xenon)
12. How many molecules of carbon dioxide gas are there in a volume 11.2 liters of gas at STP?
(3.01 x 1023)
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7.
STARODUB
CHEM. 2AP
UNIT 2-2
8
CH. 5: Gases
REAL VS. IDEAL GASES: THE GAS LAWS
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We will explore various gas laws that deal with and predict the behavior of gases. To describe the gaseous state, only 4
quantities are needed:
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The quantity of gas, n (in moles),

The temperature of the gas, T (in kelvins),

The volume of gas, V (in liters),

The pressure of the gas, P (in atm, kPa, or mm Hg).
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In using the gas laws, we will assume that we are dealing with IDEAL GASES. Ideal gases don’t really exist. There is no such
thing as an ideal gas, only real gases. Real gases can, however act as an ideal gas under the right conditions. Consider these
fundamental properties of gases:

As the pressure of a gas increases, the volume decreases (as P, V).

As the temperature of a gas increases, the volume increases (as T, V).
An ideal gas is one that will follow these relationships and gas laws under all conditions of pressure and temperature.
A real gas does not work this way. The reason any gas is not an ideal gas is because you cannot study gases at very low
temperatures and high pressures.
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GASES ARE IDEAL ONLY AT HIGH TEMPERATURES AND LOW PRESSURES.
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AT LOW TEMPERATURES AND HIGH PRESSURES, ALL GASES BECOME LIQUIDS SO YOU CANNOT STUDY
THEM AS GASES ANY MORE.
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Also, as you increase pressure, the volume of an ideal gas would eventually become zero. This is impossible because the gas
cannot be compressed to zero volume. (Law of Conservation of Mass)
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Temperatures are ALWAYS in Kelvin. Kelvin = C + 273 Treat “273” as a constant that has infinite sig. figs.
Cancel all units.
In all problems, isolate and identify each quantity with symbols (pressure P, volume V, moles n). Get rid of the words!
Gases will change conditions so use subscripts to indicate those conditions: “1” for initial conditions and “2” for final
conditions (P1 = 3 atm, and P2 = 6 atm).
When a condition such as temperature is held “constant”, it has no effect on the gas. When a condition is constant, it is
not a variable in the study of the gas.
You will be learning many new formulas in this section. When you use a formula, write it down, manipulate the formulas
to the form required, substitute numbers with units, and solve. ALL WORK MUST BE SHOWN TO OBTAIN FULL
CREDIT. If you try to substitute in your head while remembering the formula, you will make mistakes. Do these
problems the way I tell you to do them.
To solve problems using the formulas for the gas laws, rearrange the formula first, then plug in the numbers with units. In
this way, the units will cancel.
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IMPORTANT HINTS IN WORKING WITH GAS LAWS
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5 different gas laws:
1. Boyle’s Law: (relationship of pressure and volume; temperature constant)
2. Charles’ Law: (relationship of volume and temperature; pressure constant)
3. Gay-Lussac’s Law: (relationship of pressure and temperature; volume constant)
4. Combined Gas Law: combines the above three laws.
5. Ideal Gas Law: (when moles are involved).
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THE GAS LAWS
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Gas Laws 1 through 4 inclusive are used when conditions of pressure, temperature, and/or volume change. Gas Law #5 is to solve
for one variable when conditions of a gas are not changing.
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STARODUB
CHEM. 2AP
UNIT 2-2
9
CH. 5: Gases
BOYLE’S LAW
This law illustrates the relationship between the pressure and volume of a gas when temperature is held constant.
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Boyle’s Law: At a constant temperature, the volume of a fixed amount of a gas is inversely proportional to its pressure.
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P1V1 = P2V2
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The product of the initial pressure P1, and the initial volume V1 will be equal to the product of the new pressure P2 and the new
volume V2.
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Ex. 1: A gas is collected in a 242-cm3 container. The pressure of the gas in the container is measured and determined to be
87.6 kPa. What is the volume of this gas at standard temperature and pressure?
(209)
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Ex. 2: Here’s a problem to show you how to line up the data so that your units cancel.
216 mL of a gas is collected at a temperature of 73C. What is the volume of the gas if the pressure changes to 86.7 kPa
from 2.20 atm?
(555)
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CHEM. 2AP
UNIT 2-2
10
CH. 5: Gases
CHARLES’ LAW:
E
P
This law illustrates the relationship between volume and temperature, as pressure is held constant. When a gas is heated, it
expands. An inflated balloon immersed in a pan of boiling water will increase in size and may even burst.
=
R
E
T
Charles’ Law: At a constant pressure, the volume of a fixed amount of gas is directly proportional to its Kelvin
temperature.
S
T
V1 is the volume of the gas at a temperature T1 and V2 is the volume of the gas at a second temperature T2.
B
U
D
O
R
A
A
-P
Volume (L)
S
LO
E
V
D
R
Temperature
S
E
Ex. 1: A balloon inflated in an air-conditioned room at 27 C has a volume of 4.00 liters. It is heated to a temperature of 57
C. What is the new volume of the balloon if the pressure remains constant?
(4.40)
LA
U
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IN
N
E
P
H
IG
H
Ex. 2: Carbon dioxide produced by yeast in bread dough causes the dough to rise, even before baking. During baking, the
carbon dioxide expands. Predict the final volume of 0.100 liters of carbon dioxide in bread dough that is heated from 25 C
to 98 C.
(0.124 )
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CHEM. 2AP
UNIT 2-2
11
CH. 5: Gases
GAY-LUSSAC’S LAW
GAY-LUSSAC’S LAW: At constant volume, the pressure of a fixed mass of any gas is directly proportional to its
Kelvin temperature.
=
R
E
T
E
P
This law illustrates the relationship between pressure and temperature with volume held constant. If a gas is contained in a
vessel that cannot expand such as a steel cylinder or an automobile tire, as the temperature is increased the pressure will
increase.
S
T
Ex 1:
O
R
A
Where P1 and P2 represent the pressure of the gas at the temperatures T1 and T2. You must use Kelvin temperatures.
B
U
D
A steel cylinder with a volume of 450 mL contains a gas at a pressure of 520 kPa at 25 C. If the cylinder is heated
to 410. C, what will the new pressure be?
(1200 kPa)
A
-P
A glass vessel that can only withstand a maximum internal pressure of 225 kPa is filled with gas at 21 C and 100.
kPa and then heated. At what temperature (in °C) would the vessel burst?
(389)
S
LO
Ex. 2:
D
R
E
V
S
E
THE COMBINED GAS LAW
Combined Gas Law:
=
LA
U
S
IN
N
E
P
In each of the 3 gas laws discussed above, one of the variables (pressure, volume, or temperature) was held constant. In practice,
we often find that all three variables change. For example, when a weather balloon is released, the temperature, volume, and
pressure of the gas inside the balloon all change as the balloon ascends into the atmosphere. We can calculate the new value of any
one of the three variables, provided that the new values of the other two are known by using the combined gas law. It is a
combination of Boyle’s, Charles’, and Gay-Lussac’s Law. Each of these laws can be derived from the Combined Gas Law by
eliminating the variable that is held constant. NOTE: n = moles and can be entered into the Combined Gas Law as well. You
probably didn’t have “moles” in this law in Honors Chemistry.
IG
H
An 11.2-L sample of gas is determined to contain 0.50 mol of N2. At the same temperature and pressure, how
many moles of gas would there be in a 20.0-L sample? ?
(0.89)
Ex. 2:
A weather balloon with a volume of 55.0 L is filled with hydrogen gas at a pressure of 98.5 kPa and a temperature
of 13 C. When the balloon is released, it rises to the stratosphere where the temperature is –48 C and the
pressure is 19.7 kPa. What is the volume of the balloon under these conditions?
(216)
H
Ex. 1:
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10/16/2015
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CHEM. 2AP
“DO ‘EM IF YOU NEED ‘EM”
UNIT 2-2
12
CH. 5: Gases
COMBINED GAS LAW PROBLEMS
A sample of gas has a volume of 152 cm3 when its temperature is 18 C. If its temperature is increased to 32 C, what will its
volume become, assuming the pressure remains constant throughout?
(159)
2.
A gas confined in a rigid container exerts a pressure of 33.5 kPa at a temperature of 17.0 C. what will the pressure of this gas
be if it is cooled to a temperature of –23.0 C?
(28.9)
R
E
T
E
P
1.
If a gas is confined in a rigid container and then heated, what will happen to the pressure exerted by the gas?
S
3.
T
Show how Charles’ Law can be derived from the combined gas law.
A
4.
A gas has a volume of 844 mL at a pressure of 98.5 kPa. Correct this volume to standard atmospheric conditions.
6.
A container with an initial volume of 1.00 liters is occupied by a gas at a pressure of 1.5 atm at 25C. By changing the
volume, the pressure of the gas increases to 6.0 atm as the temperature is raised to 100.C. What is the new volume? (0.31 L)
7.
A cylinder of compressed oxygen gas has a volume of 30.0 liters and 100. atm pressure at 27C. The cylinder is cooled until
the pressure is 5.0 atm. What is the new temperature of the gas in the cylinder (in C)?
(258)
8.
Assume that you place some octane in the cylinder of an automobile engine. The cylinder has a volume of 250. cm3, and the
pressure of gaseous octane is 3.50 atm in the hot engine (250C). What would be the pressure in the cylinder if you lower the
temperature of the automobile engine to room temperature (25C) and change the volume of the cylinder to 500. cm3? (0.997)
B
U
D
O
R
5.
A
-P
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V
R
E
THE IDEAL GAS LAW
D
You used the combined gas law (including Boyle’s, Charles’ and Gay-Lussac’s) in problems that involved changing conditions of
P, V and T.
An ideal gas is a hypothetical gas whose pressure-volume-temperature behavior can be completely accounted for by the ideal gas
equation. Although there is no such thing in nature as an ideal gas, discrepancies in the behavior of real gases over reasonable
temperature and pressure ranges do not significantly affect calculations. Thus we can safely use the ideal gas equation to solve
many gas problems. The ideal gas law has great importance in the study of gases. It does not contain information that is
characteristic of any particular gas. Rather, it is a generalization applicable to most gases, at pressures up to about 10 atm, and at
temperatures above 0C. An ideal gas is one whose behavior agrees with that predicted by the ideal gas law. Although ideal gases
do not exist, as long as we avoid low temperatures and high pressures, most gases behave as if they were ideal.
The ideal gas law is used when a gas is under fixed conditions and you are trying to find the P, V, T, or n (number of moles) of the
gas.
S
E
where
P = pressure (in atm)
V = volume (in L)
n = moles
T = temperature (Kelvin)
R = Ideal Gas constant
LA
PV = nRT
U
S
IN
N
E
P
IDEAL GAS LAW:
•
H
If you have a 150. L tank of gaseous nitrogen and the gas exerts a pressure of 41.8 mmHg at 25C, how many
moles of nitrogen are in the tank?
(0.337)
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Ex. 1:
•
IG
H
= 0.0821
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CHEM. 2AP
UNIT 2-2
“DO ‘EM IF YOU NEED ‘EM”
13
CH. 5: Gases
IDEAL GAS LAW PROBLEMS
1.
What is the pressure exerted by 4.50 moles of gas in a 198 L container at a temperature of 8C?
(0.524)
2.
What volume would be occupied by 3.22 moles of gas at a temperature of 35C and a pressure of 93.2 kPa?
(88.5)
How many moles of gas can be contained in a 1.4 L flask at 32 C and 93.5 kPa?
(0.052)
R
E
T
E
P
**In solving Ideal Gas Law problems, use the value of R given above using pressure units of atm. If pressure is given to you
in kPa or mm Hg, change them to atm in the problem. Do it as one step in the factor label method.
S
3.
T
A certain sample of gas occupies a volume of 20.0 L at a temperature of 21C and a pressure of 94.2 kPa.
(a) How many moles are there in the sample?
(b) If the temperature is increased to 85C and the volume is changed to 35.0 L, what is the pressure?
5.
D
O
R
A
4.
What pressure is exerted by 0.622 moles of gas contained in a 9.22 L vessel at 16C?
(0.771)
(0.647)
(1.60)
B
U
A
-P
S
LO
D
R
E
V
S
E
LA
U
S
IN
N
E
P
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IG
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GAS LAW PROBLEMS
P. 14
#1-17
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10/16/2015
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CHEM. 2AP
ASSIGNMENT #2
UNIT 2-2
14
CH. 5: Gases
GAS LAW PROBLEMS
A particular balloon is designed by its manufacturer to be inflated to a volume of no more than 2.5 L. If the balloon is filled
with 2.0 L of helium at sea level, is released, and rises to an altitude at which the atmospheric pressure is only 500. mm Hg,
will the balloon burst? (Assume temperature is constant.)
(3.0)
2.
As temperature decreases, at constant pressure, at what point will a gas cease to obey Charles’ Law?
R
E
T
E
P
1.
3.
S
A sample of oxygen gas has a volume of 205 cm3 when its temperature is 22.0 C and its pressure is 30.8 kPa. What volume
will the gas occupy at STP?
(57.7)
T
4.
O
R
A
A rigid metal container contains hydrogen gas. The volume of the container is 2.0 liters. If 10.0 moles of the gas exert a
pressure of 6.00 atm at 28°C, how many moles of gas would have to be released at 28°C so the pressure in the tank is 2.00
atm?
(3.33 is a partial answer)
Suppose that 2 quantities A and B are related to each other by inverse proportion. If the value of A becomes 5 times greater
than it was, what will happen to the value of B?
6.
Imagine that you live in a small cabin with an interior volume of 150. m3. On a cold morning the indoor temperature is 10.C
but by afternoon the sun has warmed the cabin air to 18C. Because air expands (to maintain a constant pressure) as the
temperature increases, and because the cabin is not sealed, some of the air has leaked out of the cabin. How many cubic
meters of air have been forced out of the cabin by the sun’s warming? How many liters?
(154, 1.54 x 105)
7.
A 12.5-liter bulb contains a gas at 3.6 atm pressure. If it is connected to an empty 3.6-Liter bulb. What is the new pressure of
the gas?
(2.8)
8.
What temperature in C is a gas if 2.31 moles of it occupy 61.0 L at a pressure of 94.6 kPa?
9.
When can the Ideal Gas Law not be used?
B
U
D
5.
A
-P
S
LO
(27)
R
E
V
D
10. When a rigid hollow sphere containing 680. L of helium gas is heated from 300 K to 600 K, the pressure of the gas increases
to 18.0 atm. How many moles of helium does the sphere contain?
(249)
S
E
E
P
11. A 2.50 L container is filled with sulfur dioxide gas at a pressure of 120.0 kPa at a temperature of 27C. Calculate the mass of
sulfur dioxide gas in the container.
(7.70)
12. Find the volume of 1.00 g of water in the gas phase at its boiling point (100 C) and standard pressure.
(1.68)
S
IN
N
 N2O4(g)
If 25.0 mL of NO2 gas is
13. Consider the following chemical equation:
2 NO2(g) 
completely converted to N2O4 gas under the same conditions, what volume will the N2O4 occupy?
(12.5)
U
14. What volume is occupied by 2.0 g of He at 25°C and a pressure of 775 mmHg?
(12)
LA
IG
H
15. A hot-air balloon is filled with air to a volume of 4.00 x 103 m3 at 745 torr and 21°C. The air in the balloon is then heated to
62°C, causing the balloon to expand to a volume of 4.20 x 103 m3. What is the ratio of the number of moles of air in the heated
balloon to the original number of moles of air in the balloon? (Hint: Openings in the balloon allow air to flow in and out.
Thus the pressure in the balloon is always the same as that of the atmosphere.)
(0.921/1)
H
16. A compressed gas cylinder contains 1.00 x 103 g of argon gas. The pressure inside the cylinder is 2050. psi (pounds per square
inch) at a temperature of 18°C. How much gas remains in the cylinder if the pressure is decreased to 650. psi at a temperature
of 26°C?
(309)
Container B
Contents: Unknown gas
Pressure = PB
Moles of gas = 2.0 mol
Volume = 2.0 L
Temperature = 287°C
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How is the pressure in container B related to the pressure in
container A?
(twice)
Container A
Contents: SO2(g)
Pressure = PA
Moles of gas = 1.0 mol
Volume = 1.0 L
Temperature = 7°C
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17. Consider two separate gas containers at the following
conditions (see table to the right).
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CHEM. 2AP
UNIT 2-2
15
CH. 5: Gases
GAS STOICHIOMETRY
In the reaction to produce ammonia NH3:
R
E
T
E
P
According to Avogadro’s Law, equal volumes of all gases at the same temperature and pressure contain the same number of
moles. Because of this, the coefficients in a balanced equation apply to molecules, moles, and volume units as shown below. The
volume units can be in L, mL, or any volume units.
S
+
3 H2(g)
N2(g)
2 NH3(g)
1 molecule
1 mole
1 volume
(liters)
O
R
A
T
3 molecules
3 moles
3 volumes
(liters)
2 molecules
2 moles
2 volumes
(liters)
Gas Stoichiometry
B
U
D
Therefore, 3 L of H2 combines with 1 L N2 to produce 2 L of NH3; the same relationship as moles. You don’t have to change
volume to moles in stoichiometry problems. Use volume units just like you use moles. ** This works only if both substances are in
the gas phase. It cannot be used if one of the substances is either a solid or a liquid.
A
-P
Ex. 1: Calculate the mass in grams of hydrogen chloride produced when 5.6 L of molecular hydrogen measured at STP
react with an excess of molecular chorine gas.
(18)
S
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E
V
DO THIS ONE!!
Ex. 2:The discovery of oxygen resulted from the decomposition of mercury (II) oxide.
D
R
2 HgO(s)  2 Hg(s) + O2(g)
(a) What volume of oxygen will be produced by the decomposition of 25.2 grams of the oxide if the gas produced is
measured at 20. °C and 2.30 atm?
(0.608)
S
E
S
IN
N
E
P
(b) How many grams of mercury (II) oxide must be decomposed to yield 10.8 L of O2 at 1 atm and 298 K?
(191)
LA
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CHEM. 2AP
UNIT 2-2
16
CH. 5: Gases
MOLAR MASS OF A GAS
R
E
T
E
P
A very important use of the ideal gas law is in the calculation of the molar mass (molecular weight) of a gas from its measured
density. By using the ideal gas law, a formula for the density and also the molar mass of a gas can be derived to give the formula
below. Memorize these 2 formulas together.
PV = nRT
Ideal Gas Law Formula:
S
PMM = dRT
B
U
D
O
R
A
T
Formula for molar mass and density
PMM = dRT
dRT
P
1.95 g 0.0821 L atm
)(300.K)
(
)(
mole K
L
=
1.50 atm
LO
MM =
S
g
L
P = 1.50 atm
T = 27 °C = 300.K
MM = ?
d = 1.95
A
-P
ex. 1: The density of a gas was measured at 1.50 atm and 27C and found to be 1.95 g/L. Calculate the molar mass of the
gas.
(32.0 g/mol)
Method 1 (using the formula)
E
V
D
R
= 32.0 g/mole
S
E
The density of 1.95
indicates a mass of 1.95 g in
a volume of exactly 1 L;
therefore
m = 1.95 g
V=1L
LA
U
(1.50 atm)(1 L)
=
0.0821 L atm
(
)(300.K)
mol K
S
IN
N
= 0.0609 0 mol
IG
H
g
1.95 g
=
mole
0.0609 0 mol
PV = nRT
PV
n =
RT
E
g
L
P = 1.50 atm
T = 27 °C = 300.K
g
= ?
mole
d = 1.95
P
Method 2 (using PV = nRT) Memorizing the formulas above is unnecessary!!
Remember: when finding molar mass, you are being asked to find the unit g/mole.
H
= 32.0 g/mole
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P. 17
#1-12
GAS DENSITY, MOLAR MASS, AND REACTION STOICHIOMETRY
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CHEM. 2AP
UNIT 2-2
17
CH. 5: Gases
ASSIGNMENT #3 GAS DENSITY, MOLAR MASS, AND REACTION STOICHIOMETRY
Sodium azide decomposes according to the equation.
2 NaN3(s) 
at 1.1 atm and 50°C will be produced by the decomposition of 5.0 g of NaN3?
2.
Assume that you take 355 L of H2 gas at 25C and 542 mmHg and combine it with excess N2 gas. What is the theoretical
yield (in moles) of NH3 gas?
(6.87)
3.
Consider the reaction of 20.0 g calcium oxide with carbon dioxide
CaO(s) + CO2(g)  CaCO3(s)
If you have 5.5 L of CO2 at 7.50 atm and 22°C, will you have enough carbon dioxide to react with all the CaO? (Support your
answer with full calculations.)
R
E
T
E
P
1.
2 Na(s) + 3 N2(g) What volume of N2
(2.8 L)
S
A
T
A gas consisting of only carbon and hydrogen has an empirical formula of CH2. The gas has a density of 1.65 g/L at 27C and
734 torr. Determine the molar mass and molecular formula of the gas.
(42.1 g/mol C3H6)
5.
A student adds 4.00 g of dry ice (solid CO2) to an empty balloon. What will be the volume of the balloon at STP after all the
(2.04)
dry ice sublimes (converts to gaseous CO2)?
6.
The method used by Joseph Priestley to obtain oxygen made use of the thermal decomposition of mercuric oxide:
B
U
D
O
R
4.
A
-P
heat
 2 Hg(l) + O2(g)
2 HgO(s) 
What volume of oxygen gas, measured at 30.°C and 725 torr can be produced from the complete decomposition of 4.10 g
mercuric oxide?
(0.247)
LO
7.
S
Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap.
This causes sodium azide NaN3 to decompose explosively according to the following reaction:
V
 2 Na(s) + 3 N2(g)
2 NaN3(s) 
What mass of NaN3(s) must be reacted in order to inflate an air bag to 70.0 L at STP?
E
Urea H2NCONH2 is used extensively as a nitrogen source in fertilizers. It is produced commercially from the reaction of
ammonia and carbon dioxide:
S
E
heat
pressure
D
R
8.
(135)
Methanol, CH3OH, can be produced by the following reaction:
S
IN
N
9.
E
P
 H2NCONH2(s) + H2O(g)
2 NH3(g) + CO2(g)  
Ammonia gas at 223°C and 90. atm flows into a reactor at a rate of 500. L/min. What mass of urea is produced per minute by
this reaction assuming 100% yield?
(3.3 x 104)
 CH3OH(g)
CO(g) + 2 H2(g) 
Hydrogen at STP flows into a reactor at a rate of 16.0 L/min. carbon monoxide at STP flows into the reactor at a rate of 25.0
L/min. If 5.30 g of methanol is produced per minute, what is the percent yield of the reaction?
(46.5)
U
(0.578)
H
11. Calculate the density of ammonia gas at 27°C and 635 torr.
LA
10. A compound has the empirical formula CHCl. A 256-mL flask at 373 K and 750. torr, contains 0.800 g of the gaseous
compound. Give the molecular formula.
(C2H2Cl2)
H
IG
12. Suppose you are given two flasks at the same temperature, one of volume exactly 2 L and the other of exact volume 3 L. The
2-L flask contains 4.8 g of gas, and the gas pressure is X atm. The 3-L flask contains 0.36 g of gas and the gas pressure is
0.1X.
(a) Do the two gases have the same molar mass?
(b) If not, which contains the gas of higher molar mass?
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CHEM. 2AP
UNIT 2-2
18
CH. 5: Gases
DALTON’S LAW OF PARTIAL PRESSURE
R
E
T
E
P
Molecules of a gas do not attract or repel one another. Because there is no attraction, the pressure exerted by one type of molecule
is unaffected by the presence of another gas. This leads to Dalton’s Law of Partial Pressure that states:
IN A MIXTURE OF GASES, THE TOTAL PRESSURE OF A MIXTURE OF GASES IS EQUAL TO THE SUM OF THE
PRESSURES THAT EACH GAS WOULD EXERT IF IT WERE PRESENT ALONE.
For example: suppose that you have 1 L of oxygen at a pressure of 200 kPa and 1L of nitrogen also at 150 kPa. You now transfer
one of the gases into the container occupied by the other. You will find that the total pressure is now 350 kPa. Each gas is
occupying the same volume of 1L (although they are mixed). Each gas is therefore exerting its original pressure. Within the single
volume of 1L, the two pressures combine to produce a total of 350 kPa
S
Where P1, P2, PN are partial pressures.
D
O
R
A
T
PTOTAL = P1 + P2 + P3 +…….+ PN.
B
U
FINDING THE PARTIAL PRESSURE WHEN MOLES OF EACH GAS IS GIVEN
where Pi = partial pressure of gas 1
Χ = mole fraction of gas 1
PT = total pressure of all gases
mole fraction (X)
=
S
LO
P1 = Χ PT
A
-P
Partial pressure refers to the pressure of each individual gas in the mixture. When you are given the amount (in moles) of each gas
in the mixture, you are able to find the mole fraction (χ) of each gas. Once you have the mole fraction of each gas and you know
the total pressure, you can find the partial pressure of each gas by the formula below:
V
D
R
E
Ex. 1: Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium if the partial pressures of
the gases are: Poxygen = 150 mm Hg, Pnitrogen = 350 mm Hg, Phelium = 200 mm Hg.
S
E
U
S
IN
N
E
P
LA
Ex. 2: Air contains oxygen, nitrogen, carbon dioxide and trace amounts of other gases. At a pressure of 1 atm, what is the
partial pressure of oxygen if the partial pressure of nitrogen is 593.4 mm Hg, carbon dioxide 0.3 mm Hg, and the pressure
of other gases = 7.1 mm Hg?
H
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CHEM. 2AP
UNIT 2-2
19
CH. 5: Gases
THE COLLECTION OF GASES OVER WATER
R
E
T
E
P
In the laboratory preparation of gases that are lighter than air such as hydrogen and oxygen, the gas
is usually collected by the displacement of water. This process is useful for collecting many gases
but the gas must be practically insoluble in water. When the collection is finished, water vapor is
present in the container along with the gas collected. The pressure in the container actually is the
sum of the partial pressures of the gas and the water vapor. (Dalton’s Law of Partial Pressures.)
We know that each of the gases exerts the same pressure it would if it were present alone in the
container. Therefore, if we subtract the value for water vapor pressure from the total pressure, the
result will be the pressure of the collected gas alone (the “dry” gas). The vapor pressure of water at
various temperatures has been measured and is contained in a table of Vapor Pressures of Water at
various temperatures.
S
B
U
D
O
R
A
T
A
-P
S
LO
E
V
Table: Pressure of Water
Vapor at
Various Temperatures
Temperature
Water
(°C)
Vapor
Pressure
(mm Hg)
4.58
0
5
6.54
9.21
10
12.79
15
20
17.54
23.76
25
31.82
30
35
42.18
55.32
40
71.88
45
92.51
50
118.04
55
149.38
60
187.54
65
70
233.7
289.1
75
355.2
80
433.6
85
525.76
90
633.90
95
760.00
100
D
R
In all types of gases law problems you have been doing so far, you have been dealing with
DRY GASES only. You will now have to watch out for gases that are collected over water. If
they are, you must subtract the vapor pressure of water to get the pressure of the dry gas alone. You will recognize these
gas problems because they will indicate that the gas has been collected “over water” or collected by “water displacement”.
Vapor pressure changes with a change of temperature.
S
E
P
S
IN
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Ex. 1: A quantity of gas is collected over water at 10C. The pressure of gas over the water was found to be 675 mmHg.
(a) What is the pressure of the collected dry gas only? (**Use the vapor pressure of water table).
(b) What volume would the dry gas occupy at standard pressure if originally collected in a 353-cm3 vessel?
(309)
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Ex. 2: 500.0 mL of oxygen is collected over water at 23 C and 748 mm Hg. Calculate the volume of the oxygen gas at 10.C
and 700. mm Hg. The vapor pressure of water at 23 C is 21.1 mm Hg)
(496 mL)
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DO ASSIGNMENT #4
P. 20
#1-6
PARTIAL PRESSURE PROBLEMS
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CHEM. 2AP
ASSIGNMENT #4
UNIT 2-2
20
CH. 5: Gases
PARTIAL PRESSURE PROBLEMS
2. Consider the flasks diagramed at the right. What are the final partial
pressures of H2 and N2 after the stopcock between the two flasks is
opened? What is the total pressure in torr?
(317, 50.7, 368)
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1. A mixture of 1.00 g of H2 and 1.00 g of He is placed in a 1.00-L container at 27°C. Calculate the partial pressure of each gas
and the total pressure.
(M.F.: 0.333, 0.667)
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3. At 0°C a 1.0-L flask contains 5.0 x 10−2 mol of N2, 1.5 x 102 mg O2,
and 5.0 x 1021 molecules of NH3. What is the partial pressure of each
gas, and what is the total pressure in the flask?(1.4, 1.1, 0.18, 0.10)
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4. Helium is collected over water at 25°C and 1.00 atm total pressure. What total volume of gas must be collected to obtain 0.586
g of helium? (At 25°C the vapor pressure of water is 23.8 torr.)
(3.69)
5. The oxides of Group 2A metals (symbolized by M here) react with carbon dioxide according to the following reaction:
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MO(s) + CO2(g) 
 MCO3(s)
A 2.85-g sample containing only MgO and CuO is placed in a 3.00-L container. The container is filled with CO2 to a pressure
of 740. torr at 20.°C. After the reaction has gone to completion, the pressure inside the flask is 390. torr at 20.°C. What is the
mass percent of MgO in the mixture? Assume that only the MgO reacts with CO2.
(81.4)
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Small quantities of hydrogen gas can be prepared in the laboratory by the addition of aqueous hydrochloric acid to metallic
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zinc. The reaction is:
Zn(s) + 2 HCl(aq) 
 ZnCl2(aq) + H2(g)
Typically, the hydrogen gas is bubbled through water for collection and becomes saturated with water vapor. Suppose 240.
mL of hydrogen gas is collected at 30.°C and has a total pressure of 1.032 atm by this process. What is the partial pressure of
hydrogen gas in the sample? How many grams of zinc must have reacted to produce this quantity of hydrogen? (The vapor
pressure of water is 32 torr at 30°C.)
(0.990 atm, 0.625 g)
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THE MEANING OF TEMPERATURE
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K.E.avg =
RT
where:
R = 8.3145
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T = Kelvin temperature
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The exact relationship between temperature and average kinetic energy of gas molecules is
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This is a very important relationship. It summarizes the meaning of the Kelvin temperature of a gas. The kelvin temperature is an
index of the random motions of the particles of a gas, with higher temperature meaning greater motion and therefore greater kinetic
energy. THEREFORE, THE AVERAGE KINETIC ENERGY OF DIFFERENT GASES IS THE SAME AT THE SAME
TEMPERATURE. THE AVERAGE KINETIC ENERGY OF A GAS DEPENDS ONLY ON THE TEMPERATURE!
You would think that heavier molecules would have more energy because of their larger mass. The relationship in the formula is
true because the lighter molecules move faster and the heavier molecules move slower therefore they have the same average kinetic
energy.
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IN THE AP EXAM YOU WILL NEVER BE ASKED A CALCULATION QUESTION REGARDING
KINETIC ENERY. JUST KNOW THAT THE AVERAGE KINETIC ENERGY OF ALL GAS
MOLECULES IS THE SAME AND DEPENDS ONLY ON TEMPERATURE.
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UNIT 2-2
21
CH. 5: Gases
SPEED OF MOLECULES
ROOT-MEAN-SPEED: urms =
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How fast does a molecule move on the average at any temperature T? One way to estimate molecular speed is to calculate the rootmean-square (rms) speed (urms) which is an average molecular speed. The heavier a gas is, the slower the molecules move. As the
Kelvin temperature increases, all molecules of any gas increase their root-mean-speed. The rms of a molecule can be determined
using the following formula:
3RT
MM
where
R = ideal gas constant = 8.3145
J
K  mole
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T = temp. in Kelvin
MM = molar mass (in kg/mole)
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The unit of root-mean-speed that you will end up with is m/s. In using this formula, you must also know this relationship:
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1 Joule (J) = 1
kg  m 2
s2
Ex. 1: Place the following gases in order of increasing average molecular speed at 25C: CO, SF6, H2S, Cl2, HI.
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Ex .2: Calculate the root-mean-square speed of the nitrogen molecule in m/s at 25C.
(515 m/s)
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NOTE: The speed of different gas molecules is not the same. The speed of a gas molecule is
dependent on molar mass and temperature.
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However, the average kinetic energy of all gas molecules is the same and is dependent only on
the temperature. Lighter molecules move faster and heavier molecules move slower so that the
average kinetic energy of all gas molecules is the same.
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UNIT 2-2
22
CH. 5: Gases
EFFUSION, DIFFUSION AND GRAHAM’S LAW
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Because gas molecules are in rapid motion, one gas can mix with another. Gases move from where there is a high concentration to
where there is a low concentration. The ability of a gas to move from one place to another is called diffusion. Diffusion is usually a
slow process. The rate of diffusion is the rate of mixing gases.
Effusion is the term used to describe the passage of a gas through a tiny opening in a membrane (air passing through the pores of a
balloon). The rate of effusion measures the speed at which a gas is transferred through a membrane.
Different gases travel at different rates because heavier gases move slower than light gases. The heavier the gas, the slower it
moves. Ammonia molar mass of 17 g/mole moves faster than does hydrogen chloride HCl at 36.5 g/mole.
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Graham’s Law of Effusion: Graham developed a law that states that the effusion rate of a gas is inversely proportional to the
square root of its molar mass. His law compares the velocity or speed of 2 molecules and the formula yields a ratio of how fast one
molecule is compared to another.
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GRAHAM’S LAW OF EFFUSION: The rates of effusion of gases at the same temperature and pressure are inversely
proportional to the square roots of their molar masses.
MM 2
MM 1
where
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u
r1
= 1 =
r2
u2
MM = molar mass
u = root mean speed (or just speed)
r = rate of effusion
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Ex. 1: The rate of diffusion of an unknown gas is four times faster than the rate of oxygen gas. Calculate the molar mass of
the unknown gas and identify it.
(hydrogen)
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(1.069)
DO ASSIGNMENT #5 GRAHAM’S LAW
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Ex. 2: Calculate the ratio of the effusion rates of N2 and O2,, that is: rN2/rO2.
P. 22
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GRAHAM’S LAW PROBLEMS
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ASMT #5
1.
What is the ratio of the rates of effusion of hydrogen gas to ethane gas, C2H6?
2.
If a molecule of neon gas travels at an average of 400. m/s at a given temperature, estimate the average speed of a molecule of
(235 m/s)
butane gas C4H10 at the same temperature.
3.
At a certain temperature and pressure, chlorine molecules have an average velocity of 0.0380m/s. What is the average
velocity of sulfur dioxide molecules under the same conditions?
(0.0400 m/s)
4.
The diffusion rate of an unknown gas is measured and found to be 31.50 mL/min. under identical experimental conditions, the
diffusion rate of O2 is found to be 30.50 mL/min. If the choices are CH4, CO, NO, CO2, and NO2, what is the identity of the
unknown gas?
(NO)
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(3.86/1)
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UNIT 2-2
23
CH. 5: Gases
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INTERESTING STUFF: Earth unlike Jupiter does not have a lot of hydrogen or helium in its atmosphere. Because Earth is
smaller than Jupiter, Earth has a weaker gravitation attraction for the lighter molecules. To escape Earth’s gravity, a molecule
must possess an escape velocity equal to or greater than 11,000 m/s. Because the average speed of helium is considerably
greater than that of molecular nitrogen or molecular oxygen, more helium atoms escape from Earth’s atmosphere into outer
space. Therefore, only a trace amount of helium is present in our atmosphere. Jupiter, with a mass about 320 times greater than
that of Earth retains both heavy and light gases in its atmosphere. WOW
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THE KINETIC MOLECULAR THEORY
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Gas laws help us to predict the behavior of gases, but they do not explain what happens at the level of the molecules to
cause the changes observed in the world, for example, why does a gas expand upon heating?
The physical properties of gases can be explained in terms of the motion of individual molecules. This molecular
movement is a form of energy, which is the capacity to produce change or to do work. Molecules have kinetic energy. The word
kinetic means moving so kinetic energy is the type of energy expended by a moving object or the energy of motion.
Generalizations about gas behavior can be made and are contained in the KINETIC MOLECULAR THEORY OF
GASES which contains the following assumptions:
1. A gas is composed of very tiny molecules very widely separated. These molecules are separated from each other by distances
far greater than their own dimensions. The molecules possess mass but have negligible volume.
2. The molecules are in rapid, random, straight-line motion.
3. The molecules collide frequently with each other and with the walls of the container but the collisions are perfectly elastic. This
means that they do not lose any speed after a collision.
4. All gases at the same temperature and pressure have the same number of molecules per unit volume. For example, 22.4 L of
any gas at STP contains one mole.
5. IMPORTANT: The average kinetic energy of all molecules is directly proportional to the temperature of the gas (only the
temperature!) Any 2 gases at the same temperature will have the same average kinetic energy. As temperature increases, the
kinetic energy increases. The absolute temperature (K) is a measure of the average kinetic energy of the molecules. In other
words, the absolute temperature is an index of the random motion of the molecules − the higher the temperature, the more
energetic the molecules. The warmer the gas, the more energy the molecules have. Individual molecules may possess differing
amounts of energy because a few may be a little faster or a little slower than all the others. Notice in the formula below,
absolute temperature is the only variable on which the energy of the molecules depends.
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The average kinetic energy of a molecule is given by:
3
RT KE depends only on temperature.
2
Average KE of all gas molecules is the same
KEave =
=
3 RT
MM
The speed of a gas molecule is dependent on temperature
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speed = urms
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The speed of a gas molecule
and molar mass. Gas molecules travel at different speed.
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Because hydrogen molecules are lighter than oxygen molecules, they move faster than hydrogen molecules (at the same
temperature.)
However, the energy of oxygen and hydrogen molecules is the same because they are at the same temperature.
Therefore, for different gas molecules at the same temperature:
The speed is different but the kinetic energy is the same.
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APPLICATION OF THE KINETIC MOLECULAR THEORY
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Ex. 2: Use the Kinetic Molecular Theory to explain temperature.
Absolute temperature is a measure of the average kinetic energy of the molecules. Higher temperatures are determined by more
movement of the molecules hitting each other and creating friction. Friction causes heat. The higher the temperature, the more
energetic the molecules. The more energetic the molecules the more often they will hit each other and therefore more heat will be
produced thereby raising the temperature.
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Ex. 1: Use the Kinetic Molecular Theory to explain the cause of gas pressure.
Gas pressure is caused by collisions between molecules and the walls of their container. The frequency of collisions and how hard
the molecules hit the walls determines how much pressure is exerted by the gas. If more molecules hit the wall, then the pressure is
higher. If the molecules hit harder, then the pressure increases.
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CHEM. 2AP
UNIT 2-2
24
CH. 5: Gases
P. 24
#1-10
KINETIC MOLEULAR THEORY AND REAL GASES
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ASSIGNMENT #6
Calculate the average kinetic energy of N2 molecules in a sample of N2 gas at 273 K and 546 K.
(3.40 x 103, 6.81 x 103)
Do all the molecules in a 1-mol sample of CH4(g) have the same velocity at 546 K? Explain your answer.
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KINETIC MOLECULAR THEORY AND REAL GASES
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Consider a 1.0-L container of neon gas at STP. Will the average kinetic energy, average velocity, and frequency of collisions
of gas molecules with the walls of the container increase, decrease, or remain the same under each of the following
conditions?
(a) The temperature is increased to 100° C.
(b) The temperature is decreased to −50° C.
(c) The volume is decreased to 0.5 L.
(d) The number of moles of neon is doubled.
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3.
Consider separate 1.0-L gaseous samples of H2, Xe, Cl2 and O2 all at STP.
(a) Rank the gases in order of increasing average kinetic energy.
(b) Rank the gases in order of increasing average velocity.
(c) How can separate 1.0-L samples of O2 and H2 each have the same average velocity?
5.
The rate of effusion of a particular gas was measured and found to be 24.0 mL/min. Under the same conditions, the rate of
effusion of pure methane (CH4) gas is 47.8 mL/min. What is the molar mass of the unknown gas?
(63.7)
6.
It took 4.5 min for 1.0 L of helium to effuse through a porous barrier. How long will it take for 1.0 L of Cl2 gas to effuse under
identical conditions?
(19 min)
7.
Use the Kinetic Molecular Theory to explain the following observations.
(a) Aerosol cans will explode if heated.
(b) You can drink through a soda straw.
(c) A thin-walled can will collapse when the air inside is removed by a vacuum pump.
(d) Manufacturers produce different types of tennis balls for high and low elevations.
8.
Consider the three flasks in the diagram on the right. Assuming
the connecting tubes have negligible volume, what is the partial
pressure of each gas and the total pressure when all the
stopcocks are opened? (Give your answer in torr.)
(224.7, 45.0, 85.9, 93.8)
9.
An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only 0.355 times that of oxygen gas at
the same temperature. What is the identity of the unknown gas?
(I2)
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10. A sample of pure methane CH4 is found to effuse through a porous barrier in 1.50 min. under the same conditions, an equal
number of molecules of an unknown gas effuse through the barrier in 4.73 min. What is the molar mass of the unknown gas?
(159)
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UNIT 2-2
25
CH. 5: Gases
PRACTICE TEST– GAS LAWS
MULTIPLE CHOICE
The pressure of 3.00 moles of neon in a flask is 2.50 atmospheres. The pressure rises to 4.60 atmospheres when 1.00 mol of
hydrogen and some oxygen are added. How many moles of oxygen are added?
(A) 1.52
(B) 3.04
(C) 5.52
(D) 2.52
(E) 4.52
2.
A certain gas has a density of 1.11 grams per liter at 2.50 atmospheres of pressure and at a temperature of 165°C. What is
the most probable identity of this gas?
(A) oxygen
(B) nitrogen
(C) methane
(D) carbon dioxide
(E) water
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Which of the following is FALSE about an ideal gas?
(A) One-half mole will occupy 11.2 L at STP.
(B) Each atom is assumed to have no volume.
(C) Attractive forces keep ideal gas molecules in the
container.
A
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4.
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(D) The kinetic energy of all ideal gases is the same at STP.
(E) The average velocity of a helium atom will be twice that
of a CH4 molecule.
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The kinetic molecular theory predicts that at a given temperature
(A) All gas molecules have the same kinetic energy
(B) All gas molecules have the same average velocity
(C) Only real gas molecules collide with each other
(D) On the average, heavier molecules move more slowly
(E) Elastic collisions result in the loss of energy
The effect of increasing the temperature on the pressure may be explained by the kinetic molecular theory as due to
(A) The increase in force with which the gas molecules collide with the container walls
(B) The increase in rotational energy of the gas molecules
(C) The increase in average velocity of the gas molecules, which causes a corresponding increase in the rate of collision
with the container walls
(D) A decrease in the attractive forces between gas molecules
(E) A combination of A and C
6.
A rigid metal tank contains oxygen gas. Which of the following applies to the gas in the tank when additional oxygen is
added at constant temperature?
(A) The volume of the gas increases.
(D) The total number of gas molecules remains the same.
(E) The average distance between the gas molecules
(B) The pressure of the gas decreases.
increases.
(C) The average speed of the gas molecules remains the
same.
7.
Gases W and X react in a closed, rigid vessel to form gases Y and Z according to the equation:
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8.
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W(g) + X(g) 
 Y(g) + Z(g)
The initial pressure of W(g) is 1.20 atm and that of X(g) is 1.60 atm. No Y(g) or Z(g) is initially present. The experiment is
carried out at constant temperature. What is the partial pressure of Z(g) when the partial pressure of W(g) has decreased to
1.0 atm?
(D) 1.2 atm
(E) 1.4 atm
(A) 0.20 atm
(B) 0.40 atm
(C) 1.0atm
A 0.03 mol sample of NH4NO3(s) is placed in a 1 L evacuated flask, which is then sealed and heated. The NH4NO3(s)
9.
(E) 0.03 atm
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decomposes completely according to the balanced equation:
NH4NO3(s) 
 N2O(g) + 2 H2O(g)
The total pressure in the flask measured at 400 K is closest to which of the following?
(A) 3 atm
(B) 1 atm
(C) 0.5 atm
(D) 0.1 atm
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10. Samples of F2 gas and Xe gas are mixed in a container of fixed volume. The initial partial pressure of the F2 gas is 8.0
atmospheres and that of the Xe gas is 1.7 atmospheres. When all of the Xe gas reacted, forming a solid compound, the
pressure of the unreacted F2 gas was 4.6 atmospheres. The temperature remained constant. What is the formula of the
compound?
(A) XeF
(B) XeF2
(C) XeF4
(D) XeF6
(E) XeF8
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A sample of nitrogen gas is placed into a closed container. The volume is held constant while the temperature is increased
from 200 K to 400 K. Given these conditions, which of the choices below is true?
(A) The density of the gas doubles.
(D) The number of nitrogen gas molecules increases.
(B) The pressure of the gas doubles.
(E) The potential energy of the gas molecules doubles.
(C) The average velocity of the gas molecules doubles.
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CH. 5: Gases
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11. A sample of an ideal gas is cooled from 50.0° C to 25.0° C in a sealed container of constant volume. Which of the following
values for the gas will decrease?
(I) The average molecular mass of the gas.
(II) The average distance between the molecules.
(III) The average speed of the molecules.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
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12. A gaseous mixture containing 7.0 moles of nitrogen, 2.5 moles of oxygen and 0.50 moles of helium exerts a total pressure of
0.90 atmospheres. What is the partial pressure of the nitrogen?
(A) 0.13 atm
(B) 0.27 atm
(C) 0.63 atm
(D) 0.90 atm
(E) 6.3 atm
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13. As the temperature is raised from 20° C to 40° C, the average kinetic energy of neon atoms changes by a factor of
(D) 2
(E) 4
1
313
313
(A)
(C)
(B)
2
293
293
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14. If a barometer were built using water instead of Hg, how high would the column of water be if the pressure were 1 atm,
knowing that the density of water is 13.6 times lower than that of mercury?
(A) 10.3 m
(B) 3.17 m
(C) 20.0 m
(D) 33.0 m
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15. A 50-mL sample of gas is collected over water. What will be the effect on the calculated molar mass of the gas if the effect
of the water vapor is ignored? It will be
(A) high because of the mass of water in the collection flask.
(B) high because of omitting the vapor pressure of the water in the calculation.
(C) low because of the mass of water in the collection flask.
(D) low because of omitting the vapor pressure of the water in the calculation.
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16. Which of the following are postulates of the kinetic-molecular theory of gases?
(I)
The distance between gas molecules is large in comparison to their size.
(II)
Gas molecules are in constant, random motion.
(III) The kinetic energy of a gas molecule is inversely proportional to its temperature.
(C) III only
(D) I and II
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(B) II only
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(A) I only
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18. The average velocity of a gas molecule is
(A) inversely proportional to its kinetic energy.
(B) directly proportional to the gas constant, R.
(C) directly proportional to the square root of its temperature in k.
(D) inversely proportional to the square of its mass.
(E) directly proportional to the square root of its mass.
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17. If the volume of a confined gas is quadrupled while its temperature remains constant, what change will be observed?
(A) The pressure of the gas will decrease to ¼ it original value.
(B) The pressure of the gas will quadruple.
(C) The density of the gas will decrease to ½ its original value.
(D) The average velocity of the molecules will quadruple.
(E) The average velocity of the molecules will double.
C,C,C,A,D,
D,A,C,A)
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(Answers: A,C,C,A,E,
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19. One way in which real gases differ from ideal gases is that the molecules of a real gas
(A) are attracted to each other.
(D) move in circles rather than straight paths.
(B) are liquids or solids above 273 K.
(E) have no kinetic energy.
(C) are always polar.
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CH. 5: Gases
FREE RESPONSE QUESTIONS
20. Why is the density of a gas much lower than that of a solid or liquid?
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21. For each of the following properties state whether it is characteristic of all gases, some gases, or no gases
(a) odorless
(b) follows Boyles law at 100 atm and 20°C..
(c) follows Boyles law at 1 atm and 200°C.
(d) more compressible than water.
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22. Which has more molecules: a) 1.0 L of O2 gas at 20°C and 2.0 atm or b) 1.0 L of SF4 gas at 20°C and 2.0 atm? Which one
has more mass?
23. How does kinetic molecular theory explain Charles's law?
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24. Compare the average kinetic energy of Xe molecules to that of He molecules at the same temperature.
25. Compare the average speed of Xe molecules to that of He molecules at the same temperature.
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26. Determine the molar mass of chloroform gas if a sample weighing 0.495 g is collected as a vapor (gas) in a flask of volume
127 cm3 at 98°C. The pressure of the chloroform vapor at this temperature in the flask was determined to be 754 mm Hg.
(120)
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27. A sample of nitrogen gas is bubbled through liquid water at 25°C and then collected in a volume of 750 cm3. The total
pressure of the gas, which is saturated with water vapor, is found to be 740 mm Hg at 25°C. The vapor pressure of water at
this temperature is 24 mm Hg. How many moles of nitrogen are in the sample?
(0.0289 mol N2)
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28. If the root-mean-square speed of an N2 molecule is 475 m/s at 25°C, what is the root-mean-square speed of a He molecule at
25°C?
(1260)
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29. A novel energy storage system involves storing air under high pressure. (Energy is released when the air is allowed to
expand.) How many cubic feet of air, measured at standard atmospheric pressure of 14.7 lb/in2, can be compressed into a 19(1.4 x 109)
million-ft3 underground cavern at a pressure of 1070 lb/in2?
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30. How many grams of gas must be released from a 45.2-L sample of N2(g) at STP to reduce the volume of 45.0 L at STP?
(0.3)
31. What increase in the Celsius temperature will produce a 5.0% increase in the volume of a sample of gas originally at 25.0° C
if the gas pressure is held constant?
(15)
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32. Without doing detailed calculations, determine which of the following samples contains the greatest number of molecules.
(a) 5.0 g H2
(b) 50 L SF6(g) at STP
(c) 1.0x 1024 molecules of CO2
(d) 67 L of a gaseous hydrocarbon at STP
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33. At 25° C, the pressure in a gas cylinder containing 8.00 mol O2 is 5.05 atm. To maintain a constant pressure of 5.05 atm,
(3.31)
how many moles of O2(g) should be released when the temperature is raised to 235° C?
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34. A hyperbaric chamber is an enclosure containing oxygen at higher-than-normal pressures used in the treatment of certain
heart and circulatory conditions. What volume of O2(g) from a cylinder at 25° C and 151 atm is required to fill a 4.20 x 103
L hyperbaric chamber to a pressure of 2.50 atm at 17° C?
(71.5)
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36. What volume of nitrogen gas can be produced from the decomposition of 37.6 L of ammonia, with both gases measured at
725° C and 5.05 atm pressure.
(18.8)
O
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35. Calculate the molar mass of a liquid that, when vaporized at 98° C and 756 torr, gives 139 mL of vapor with a mass of 0.808
grams.
(178)
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CHEM. 2AP
UNIT 2-2
28
CH. 5: Gases
37. The density of sulfur vapor at 445° C and 755 mm Hg is 4.33 g/L. What is the molecular formula of sulfur vapor?
(S8)
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38. How many liters of CO2(g) can be produced in the reaction of 5.24 L of CO(g) and 2.65 L of O2(g) if all three gases are
measured at the same temperature and pressure?
(5.24)
40. How many liters of O2(g) measured at 22° C and 763 mm Hg are consumed in the complete combustion of 2.55 L of
dimethyl ether measured at 25° C and 748 mm Hg?
(7.42)
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39. How many milligrams of magnesium metal must react with excess HCl(aq) to produce 28.50 mL of H2(g) measured at 26°C
and 758 torr?
(28.2)
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 CO2(g) + H2O(l) (not balanced)
CH3OCH3(g) + O2(g) 
A
41. Elodea is a green plant that carries out photosynthesis under water
B
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 C6H12O6(aq) + 6 O2(g)
6 CO2(g) + 6 H2O(l) 
In an experiment, some Elodea produce 122 mL of O2(g), collected over water at 743 torr and 21° C. What mass of oxygen
(0.154, 0.145)
is produced? What mass of glucose (C6H12O6) is produced concurrently?
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42. Suppose you have two 1-L flasks, one containing N2 at STP, the other containing CH4 at STP. How do these systems
compare with respect to
(a) Number of molecules
(b) Density
(c) Average kinetic energy of the molecules
(d) Rate of effusion through a pinhole leak?
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