Name: _________________________________
Unit 10- Gas Laws
Day
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Description
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9 – 10
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17 – 20
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21 – 23
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Warm-up
Kinetic Molecular Theory
Notes
Kinetic Molecular Theory
and Pressure Worksheet
Gas Law Notes
Boyle’s Law Problems
Charles’ Law Problems
Gas Laws Practice
Gas Laws Lab Quest
Ideal Gas Law and Dalton’s
Law Notes
Ideal Gas Laws Practice
The Molar Relationship
involving mass and volume
lab
Unit 10 Test Review
Unit 10 Test
7
X
Mole Project
1
Due
Date
Completed
IC
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HW
In class March 15 and 16
Mole Projects are Due March 19
and 20
Warm-up
Day 1
1. What is the difference between a theory and a law? (yes, I’m asking you again, an d I
hope you’ve finally learned the answer)
Day 2
1. Convert 843 mmHg to atm
2. Convert 32 830 Pa to mmHg
Day 4
1. If a 5.0 L balloon at a pressure of 0.98 atm is moved to a room with a pressure of 120
kPa, what is the new volume?
Day 5
1. If you are given 5.00 g of oxygen gas at 298 K and 101.3 kPa, what is the volume?
2
Kinetic Molecular Theory Notes
• The observable properties of gas (
,
,
)
are the consequence of the actions of the molecules making up the gas
• To understand the behavior of a gas, we must look at the gas particles
themselves
• The particles in a gas are considered to be __________________________
____________________________________________________________.
• Gases are spread far apart, with empty space between molecules
• The motion of the particles in a gas is _________________________ ,
______________________________, and _________________________.
o Gas takes the shape of its container and can spread out into space
without limit
o Particles change direction only when they rebound from collisions
• All collisions between particles in a gas are perfectly __________________.
o No attractive or repulsive forces
o No transfer of Kinetic Energy
o The average Kinetic Energy is dependent only on _____________
3
• As the Temperature increases, the average kinetic energy (measured by
speed), ______________________________
• The distribution broadens Maxwell Distribution
• Diffusion- is the process in which a gas enters a container with another gas
and the two mix to form a uniform mixture.
• Effusion- when a gas moves through a small hole in its current container
into another container.
Pressure
• Gas particles are in constant, rapid, random motion and exert pressure as
they collide with the walls of their containers
• How strong is Atmospheric Pressure?
1atm=760mmHg=760 torr=101.3kPa
4
• Atmospheric pressure is
measured using a
_________________________.
• The pressure of a gas is measured using a __________________________.
o A Manometer is a device to measure the pressure of an enclosed gas
sample. A common simple manometer consists of a U shaped tube
of glass filled with some liquid. Typically the liquid is mercury
because of its high density.
5
6
Kinetic Molecular Theory and Pressure Worksheet
1.
The word “gas” comes from the Greek word chaos, which means unpredictable
randomness, or disorder. Why do you think this makes sense when you think about gas
particles?
2.
The word kinetic comes from a Greek word that means “to move.” The kinetic
molecular theory is based upon the assumption that particles of matter (atoms or molecules)
are in constant
3.
Of the three states of matter, which one has
the most kinetic energy?
4.
Which state of matter has particles that are
separated by the largest distance?
A scientific theory is an explanation of some type of natural phenomena. Theories are
normally developed from careful study of the way the world behaves. Let’s look at how gases
behave and see if the kinetic molecular theory makes sense.
5.
Compared to liquids and solids, gases tend to have
________ ______ densities.
This can be explained because the particles of gas are
6.
If you apply pressure to a sample of gas, it is fairly easy to
.
________
its volume (think about what would happen to a balloon if you squeeze it gently). This can be
explained because there is a lot of
_______
between gas
particles.
7.
If someone sprays perfume in one corner of the room, eventually a person on the other
side of the room can smell it. This can be explained because gas particles move
and
. In general, we would expect lighter gas particles to travel
than heavier gas particles.
7
8.
When two gases mix together or move through each other, this process is known as
. When gas particles escape out of a tiny hole in a
. You should
container, this process is known as
know the difference between these two words so you can avoid any confusion!
9.
Kinetic molecular theory can be summarized as follows:
•
Gas particles are in constant
.
•
Gas particles are separated by relatively
•
When gas particles collide, they
distances.
kinetic energy.
•
Gas particles have
attractive or repulsive forces between them.
•
The kinetic energy of a gas is dependent on the
of the gas.
10.
Pressure can be defined as
௙௢௥௖௘
௔௥௘௔
. When do gas particles exert pressure?
The Earth is surrounded by a blanket of gases that is called the atmosphere. Atmospheric
pressure is something that is very real. However, we often take it for granted because we can’t
see the air molecules all around us.
11.
In the 17th century a simple device invented by Torricelli to measure air pressure was
called a
. It consisted of a thin glass tube that was
closed at one end. It was filled with liquid
and the open end
was covered so that no air could get in. Then it was placed upside down in a dish of mercury.
The open end of the tube was below the surface of mercury in the dish. The height of the
mercury fell down to about 30 inches, or
mm. Since the air molecules on the
outside of the tube “push” down on the pool of mercury, the height of the mercury is equal to
the measurement that we call “air pressure.”
12.
Today we define standard atmospheric pressure (at sea level) as
This is equal to 760 mmHg (millimeters of mercury) or 760 torr (this unit was named to honor
Torricelli) 1 atm =
kPa (kilopascals)
8
13.
Another instrument used to measure gas pressure is called a
,
which consists of a flask connected to a U
U-shaped
shaped tube. There is mercury in the U-bend
U
of the
tube. In an open-ended
ended manometer, when the two levels of mercury are equal, the pressure of
the gas in the flask is
. When the mercury levels are different, we
can use the difference in the height of mercury to calculate the gas pressure in the flask (by
either adding or subtracting).
14.
Calculate the pressure inside
nside each flask, given an atmospheric pressure of 760 mmHg.
The gas in the flask has a higher pressure than
The gas in the flask has a lower pressure than
760 mmHg. The pressure is
760 mmHg. The pressure is
.
.
1 atm = 760 mmHg = 760 torr = 101.3 kPa
15.
Consider the pressure units shown above. Use dimensional analysis to convert from one
unit to another for each problem given.
a.
Convert 593 mmHg into atm
c.
Convert 1.08 atm into kPa
b.
Convert 0.45 atm into mmHg
d.
Convert 215 kPa into atm
9
Gas Laws Notes
•
Gay-Lussac's Law
•
o Temperature always in Kelvin Scale
Charles' Law
•
o Lower temperature leads to a lower volume
o Higher temperature leads to a higher volume
o Directly proportional
o Temperature must be converted to Kelvin
Boyle's Law
•
•
o As the pressure decreases, the volume increases.
o Indirectly proportional
A gas occupies 12.3L at a pressure of 40.0 mmHg. What is the volume when the
pressure is increased to 60.0mmHg?
o Step 1: Write everything you are given in the problem.
o Step 2: Which law do you want to use?
o Step 3: Do your units match? If not, convert. (Temperature must always be in
Kelvin)
o Step 4: Plug in your values and solve.
Calculate the final temperature when 2.00L at 20.0°C is compressed to 1.00L.
10
•
Calculate the final pressure when the temperature of a flask at 0.50 atm is reduced
from 350. K to 200.0K
•
The Combined Gas Law
•
Remember Avogadro’s Law
11
Boyle’s Law Problems
1) A chemist collects 59.0 mL of sulfur dioxide gas on a day when the atmospheric pressure
is 0.989 atm. On the next day, the pressure has changed to 0.967 atm. What will the
volume of the SO2 gas be on the second day?
2) 2.2 L of hydrogen at 6.5 atm pressure is used to fill a balloon at a final pressure of 1.15
atm. What is its final volume?
3) A sample of gas occupies 20 L under a pressure of 1 atm. What will its volume be if the
pressure is increased to 2 atm? Assume the temperature of the gas sample does not
change.
4) A sample of oxygen occupies 10.0 L under a pressure of 105 kPa. At what pressure will it
occupy 13.4 L if the temperature does not change?
5) A student collects 400 mL of oxygen at 4 atm. If the temperature remains constant,
what volume would this gas occupy at 670 torr? *watch pressure units, they have to
match!!!
6) An unknown sample of gas has a new volume of 45 L with a pressure of 780 atm. It’s
original pressure was 890 atm, what was it’s original volume?
12
Charles’ Law Worksheets
1. A can contains a gas with a volume of 56 mL and 20 °C. What is the volume in the can if
it is heated to 50 °C?
2. At a winter carnival, a balloon is filled with 5.00 L of helium at a temperature of 273 K.
What will be the volume of the balloon when it is brought into a warm house at 295 K?
3. A balloon is inflated to 665 mL volume at 27 °C. It is immersed in a dry-ice bath at 78.5°C. What is its volume, assuming the pressure remains constant?
4. Helium gas in a balloon occupies 2.5 L at 300.0 K. The balloon is dipped into liquid
nitrogen that is at a temperature of 80.0 K. What will the volume of the helium in the
balloon at the lower temperature be?
5. A sample of neon gas has a volume of 752 mL at 25.0 °C. What will the volume at 50.0
°C be if pressure is constant?
6. The volume of gas in a syringe is 15.0 mL at 23.5 °C, what will the volume of the gas be
at 72.5 °C if the pressure is held constant?
13
Gas Laws Practice
1. A gas with a volume of 4.0L at a pressure of 90. kPa is allowed to expand until the pressure
drops to 20. kPa. What is the new volume?
2. A given mass of air has a volume of 6.0L at 100.kPa. What volume will it occupy at a
pressure of 25kPa if the temperature does not change?
3. The pressure in an automobile tire is 200. kPa at a temperature of 25°C. At the end of a
journey on a hot sunny day the pressure has risen to 223 kPa. What is the temperature of the
air in the tire?
4. The gas in a container has a pressure of 300.kPa at 27°C. What will the pressure be if the
temperature is lowered to –173°C?
5. A certain amount of gas will occupy a volume of 8.50L at a temperature of 35.0°C. What
temperature will change the volume to 15.5L?
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6. A sample of Nitrogen gas will occupy a volume of 79.8L at 50.0°C. If the temperature is
changed to 135°C, what volume will the gas occupy?
7. A 12.0L sample of gas has a pressure of 3.50 atm and a temperature of -12.0°C. If the
temperature changes to 20.0°C and the pressure changes to 2.75 atm, what volume will the gas
occupy?
8. A 5.0 L air sample at a temperature of –50°C has a pressure of 107 kPa. What will be the
new pressure if the temperature is raised to 100.°C and the volume expands to 7.0L?
9. A 3.50L gas sample at 20°C and a pressure of 86.7 kPa is allowed to expand to a volume of
8.00L. The final pressure of the gas is 56.7 kPa. What is the final temperature?
15
Ideal Gas Law and Dalton’s Law Notes
•
Ideal Gas Law
R = 0.0821
•
௔௧௠‫כ‬௅
= 8.315
௞௉௔‫כ‬௅
= 62.4
௠௠ு௚‫כ‬௅
௠௢௟‫כ‬௄
௠௢௟‫כ‬௄
௠௢௟‫כ‬௄
o To determine which R value to use, look at your unit of ____________________
o If gases follow the Kinetic Molecular Theory, they are said to be ideal gases.
o Although there is no such thing as an ideal gas, the theory still provides a good
model to explain gas properties (P,V, T)
A balloon has a volume of 2.34L, and is at 47.5°C, at 98.2kPa. How many grams of
Helium are contained in the balloon?
•
Calculate the volume of 32.0 g of dinitrogen tetroxide at 45.0°C and 3.4 atm.
•
Dalton’s Law of Partial Pressures
o The total pressure exerted by a mixture of gases is the sum of the individual of
each gas
o Each individual gas behaves as if it were independent of the others.
•
o For example, if two gases such as oxygen and nitrogen are present in a flask and
Pnitrogen = 250 mmHg and Poxygen = 3.0*102 mmHg, then the total pressure is 550
mmHg.
o Mole Fraction (X) – the ratio of the number of moles of a given component in a
mixture to the total number of moles in the mixture.
o At constant volume and temperature, mole ratios and pressure ratios mean the
same thing.
o The partial pressure of oxygen was observed to be 156 torr in the air with an
atmospheric pressure of 743 torr. Calculate the mole fraction of oxygen
present.
Kinetic Energy- KE = ½ mv2
o If the temperature is constant, the kinetic energy is constant
o As mass lowers, the velocity will increase
o As mass increases, the velocity will decrease
16
Ideal Gas Law Practice
1) The air in a person’s lungs consists of 0.177 mol of gas particles at 310 K and 101.3 kPa
pressure. What is the volume of the air?
2) How many moles of gas are contained in 22.41 liters at 101.325 kPa and 0°C?
3) How many moles of gases are contained in a can with a volume of 555 mL and a
pressure of 600.0 atm at 20 °C?
4) Calculate the pressure exerted by 43 mol of nitrogen in a 65 L cylinder at 5 °C.
5) What is the volume of 45 grams of Argon gas at a pressure of 85.6 kPa and 26.0 °C?
6) How many moles of air molecules are contained in a 2.00 L flask at 98.9 atm and 245 K?
17
The Molar Relationship Involving Mass and Volume
Both solids and gases must often be handled in the same experiment. The amount of solid used of
produced can be determined by measuring the mass of the material on a balance. It is difficult,
however, to find the mass of a gas. For convenience the chemist measures gas volume and uses this
value to calculate the mass of the gas. Therefore, it is necessary for the chemist to know the
quantitative relationship between the molar mass and the molar volume of a gas. Avogadro’s
hypothesis explains the relationship between the molar volume, the molecular mass, and the actual
mass of a sample gas. This hypothesis states that equal volumes of gases under the same temperature
and pressure contain equal numbers of molecules. Also, the volume occupied by one mole of any gas at
standard temperature and pressure equals 22.4 L.
In this experiment you will investigate the chemical significance of Avogadro’s hypothesis. You will
determine the volume of hydrogen gas evolved in a reaction between magnesium metal and
hydrochloric acid, and from your results determine the mass of H2 produced. Your experimental results
will then be compared to the results predicted by Avogadro’s hypothesis. You will need to convert room
temperature and pressure to standard conditions (STP) in order to compare your results.
Objectives
•
•
•
measure the mass of a piece of magnesium ribbon
react the magnesium with HCl(aq) and collect the gaseous product, measure the volume of the
gas collected and convert the volume to standard conditions (STP), and
calculate the molar relationship between the solid magnesium consumed and the gas produced.
Equipment
•
•
•
•
•
•
•
•
•
•
•
Goggles and apron
Milk jug
Thermometer
Barometer
Balance
Cu wire
Ring stand
Utility Clamp
Gas measuring tube (50 mL)
One hole rubber stopper (to fit tube)
Battery jab (2 or 3 mL)
Pre-lab
1. Write a balanced equation for the reaction. What is the mole ratio between magnesium and
hydrogen?
18
2. Calculate the volume of gas you would expect to be evolved if X mol of magnesium were reacted
with an excess of HCL at standard conditions (STP).
3. If 1.00 meter of Mg ribbon has a mass of 0.900 grams, what is the mass of 5.0 cm of Mg ribbon?
4. Read procedure steps 8 and 9, how will you be collecting the gas? What adjustments to
pressure will need to be made?
5. a)
Will this lab be conducted at STP?
b)
Identify the entries in your data table that will correspond to the following
measurements:
P1
V1
T1
c)
Explain how you can convert these values to STP.
Procedure
1. On entering the lab, obtain a milk jug filled with room temperature water.
2. Record the temperature of the room, the barometric pressure, and the precise mass of 1.00
meter of magnesium ribbon (from your teacher). Safety goggles and lab apron must be worn for
this experiment.
3. Cut a piece of magnesium ribbon about 2.5 cm long. Make sure you cut the ends of the ribbon
squarely. Carefully measure the length of your sample of ribbon to the nearest millimeter (0.1
cm). Record the length on your data table.
4. Obtain a stopper with a piece of copper wire attached and tie it to the magnesium ribbon which
has been folded to a size that will fit inside the gas-measuring tube.
5. Prepare a ring stand with a utility clamp to support the gas-measuring tube.
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6. Slowly pour about 5 mL of 6M HCl into the gas tube. CAUTION: Dilute HCl will stain, cause mild
burns, and irritate lungs and eyes. Avoid contact and inhalation. Rinse spills with plenty of
water.
7. Incline the tube slightly so the air may escape and slowly fill it with tap water from the beaker.
Pour the water slowly down the side of the tube so the water and acid mix as little as possible.
Fill the tube completely. Refill the beaker three-fourths full of water.
8. With the tube completely full of water, insert the stopper with the copper wire attached and the
magnesium ribbon securely tied to the copper wire. The stopper should force water and all air
bubbles out of the tube and should hold the thread or wire suspending the magnesium in place.
9. With your finger over the hole in the stopper (make sure there is no air in the hole of the
stopper), invert stoppered end of the tube in the beaker of water. Clamp the tube in place so
that the bottom of the rubber stopper is slightly above the bottom of the milk carton. The
reaction will not start immediately because it takes time for the acid to diffuse down through
the column of water to the metal.
10. When the magnesium has reacted completely and evolution of gas has stopped, tap the tube
with your finger to dislodge any bubbles you see attached to the side of the tube.
11. Place your finger over the hole in the stopper and remove the tube from the milk carton. Lower
the tube into the large graduated cylinder filled with water and remove your finger. Raise or
lower the tube until the level of the water inside the tube is the same as the level of water
outside the tube. This equalizes the pressure. Read the scale on the tube as accurately as
possible (to the nearest 0.1 mL). This reading will give the volume of the gases (hydrogen and
water vapor) in the tube. Record the volume.
12. Empty the contents of the tube into the sink, and rinse with tap water.
Data Table
Mass of 1 meter Mg ribbon
g
Length of Mg ribbon
cm
Moles of Mg ribbon used
mol
Room temperature
K
Barometric pressure
kPa
Volume of gas collected
mL
Corrected pressure of dry H2 gas
(PH2 = Proom – PH2O)
Volume of H2 gas at STP
kPa
mL
Volume of H2 from 1 mole of Mg at STP
mL
Analysis
1. Complete the data table with the calculations you perform below. Use 1 kPa = 7.50 mmHg.
20
2. Calculate the mass of magnesium by using the known mass per meter of ribbon. Assume the
magnesium ribbon was of uniform thickness and width. Calculate the moles of magnesium in
the sample. Show your work.
3. Calculate the partial pressure of hydrogen gas in the hydrogen gas-water vapor mixture.
Remember that the total pressure of a gas mixture is equal to the sum of the partial pressures of
each gas:
Ptotal = PH2O + PH2
4. Use the gas laws to calculate the volume that would be occupied by the gas at standard
temperature, 273 K, and standard pressure, 101.3 kPa. Use the volume of hydrogen gas (from
your experiment) at the corrected pressure (Calculation 3) and room temperature.
5. From your calculations, a fractional part of a mole of magnesium gave an experimentally
determined volume of H2 gas at STP. Use this information to calculate the volume of H2 gas that
could be produced if one mole of magnesium were reacted with excess HCl at STP.
Conclusions
1. The reactants in this experiment are known. One of the products is hydrogen gas. If the water
in the tube is evaporated, the other product, a white salt remains. Write the balanced chemical
equation for this reaction. What is the molar relationship between the solid Mg and the H2 gas?
2. Calculate the volume of gas you would expect to be evolved if X mol of magnesium were reacted
with an excess of HCl at standard conditions.
3. From your experimental results, predict the volume occupied by one mole of hydrogen gas
(molar volume) at STP. Compare this value to the theoretical value for the volume of one mole
of H2 at STP. Calculate your percentage error. What were your major sources of error?
21
Unit 10 Test Review
1) A gas has a volume of 3.4 L at 25 °C, what is the final temperature if the volume
increases to 4.7 L?
2) The initial pressure of a gas is 457 mm Hg, the final volume is 750 mL with a final
pressure of 650 mm Hg. What is the initial volume of the gas?
3) A gas of 3.4 moles occupies a volume of 40.6 mL at 298 K, what is the pressure of the
gas?
4) A gas of 1 mole has a temperature and volume at STP, the temperature of the gas is
increased to 311 K.
5) In an air tight box the total pressure is 1.3 atm. Determine the partial pressure of argon
in the box, if oxygen has a pressure of 0.32 atm and carbon dioxide has a pressure of
550 mm Hg? *watch your units!!!
6) At 18 °C , 34.7 grams of carbon dioxide gas creates a pressure of 613 mm Hg, what is the
volume of the gas? Hint: get into the correct units before you start.
22
7) A 3.00 L pocket of air at sea level has a pressure of 100 atm. Suppose the air pockets
rise in the atmosphere to a certain height and expands to a volume of 10.0 L. What is
the pressure of the air at the new volume?
8) The gas in a balloon occupies 3.50 L at 300. K. At which temperature will the balloon
expand to 8.50 L?
9) A gas is collected by water, it contains 78.5 atm of nitrogen, 998.7 atm of oxygen and
324.1 atm of hydrogen. Determine the total pressure of this gas.
10) How many moles of argon are there in 20.0 L, at 25 °C and 96.8 kPa?
11) What volume will 2.00 mol of oxygen gas occupy at STP?
12) A weather balloon has a volume of 1750 L at 103 kPa. The balloon is released to the
atmosphere. At the highest point above the ground, the pressure on the balloon is 35.0
kPa. What is the new volume of the balloon at this height?
23
13) A balloon filled with helium has a volume of 2.30 L on a warm day at 311 K. It is brought
into an air-conditioned room where the temperature is 295 K. What is its new volume?
14) A .589 mole of nitrogen is sealed in a 6.00 L container and heated to a temperature of
327 °C. What is the pressure of the gas?
15) A sample of gas is released into the atmosphere, it contains 789 mm Hg carbon dioxide
and 998 mm Hg of nitrogen. What is the total pressure of the sample?
16) A sample of nitrogen occupies a volume of 350 mL at 25 °C. What volume will it take to
occupy at 87 °C?
17) A 7.00 L sample of gas is contained in a jar, how many moles are presented at STP?
18) A ball has a volume of 5.00 L at a pressure of 100 kPa at the surface of the ocean. What
is the volume of the ball if the pressure decreases to 9.80 kPa?
24