Study Guides
Big Picture
Gases are all around us. They are in the air we breathe, the sodas we drink, and the tires in your bike. The kinetic
molecular theory states that gases are made up of small particles in constant random motion. As a result, gas particles
theoretically have no shape or volume. They expand to fit their container and are easily compressible. In addition, all
gases behave the same when temperature, pressure, or volume changes are applied to them. As a result, calculations
with gases can be easily generalized, allowing us to predict and understand their behavior.
Key Terms
Chemistry
Gases
Gas: A substance in a phase with high energy, that has no definite shape or volume.
Kinetic Energy: The energy an object has from being in motion. Kinetic energy = ½ mv2
Ideal Gas: A theoretical gas where gas particles have no volume and do not interact with each other. Calculations are
typically done by assuming ideal gas.
Real Gas: All gases are real gases. A real gas at low pressure and high temperature is most like an ideal gas.
Universal Gas Constant: R = 8.31 J/mol•K, 8.31 L•kPa/mol•K, or 0.0821 L•atm/mol•K.
Absolute Zero: 0 kelvin. Lowest possible temperature.
Pressure: The amount of force exerted per unit area. Various methods of measuring pressure below:
mm Hg (Torr): Pressure can be measured in millimeters of mercury. The higher the pressure, the higher a column
of mercury will be pushed upwards, and the greater the number of millimeters of Hg. 1 mm Hg = 1 Torr
Atmosphere (atm): One atmosphere is equal to the pressure at sea level. 1 atm = 760 mm Hg
Pascal (Pa): SI unit of pressure.
. Since the pascal is so small, pressure is typically measured in
kilopascals (kPa), where 101.325 kPa = 1 atm.
Barometer: Device that measures atmospheric pressure by measuring the height of mercury in an inverted column.
Manometer: Device that measures the pressure of a gas.
STP (Standard Temperature and Pressure): At STP, temperature = 273 K and pressure = 1 atm.
Vapor Pressure: The pressure a vapor has within a liquid. Substances with high vapor pressures are called volatile.
Vapor pressure increases as temperature increases, due to increased particle mobility that pushes against the
surface of a liquid. As the surface tension is disrupted, gases are more likely to enter the gas phase until the vapor
pressure reaches the atmospheric pressure, where the mixture reaches its boiling point.
Kinetic Theory
A gas is mostly empty space – at room temperature, the distance between particles in an enclosed space is about 10
times the diameter of the particle.
The kinetic theory of gases: Gas is composed of particles (molecules or atoms) that move rapidly in constant random
motion.
Assumptions – ideal gas behavior:
• Particles take up no space.
• Particles neither attract nor repulse each other (non-interacting).
• Particles move in random, straight-line motion.
The particles are constantly colliding with surfaces or other particles.
In reality, real gas particles take up a small amount of space, and there can be slight attractions among the particles.
• The behavior of real gases differ from the behavior of ideal gases at low temperatures and high pressures.
Notes
This guide was created by Steven Lai, Rory Runser, and Jin Yu. To learn more
about the student authors, visit http://www.ck12.org/about/about-us/team/
interns.
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v1.1.12.2012
Disclaimer: this study guide was not created to replace
your textbook and is for classroom or individual use only.
• Collisions are perfectly elastic – kinetic energy is transferred without loss from one particle to another.
• The average kinetic energy for a gas depends on the temperature.
Chemistry
Gases
cont .
Kinetic Energy & Temperature
Temperature reflects the kinetic energy of a particle.
• Velocity
of the particles is greater at higher
temperatures and lower at lower temperatures.
• The particles in a gas (and in any collection of atoms
or molecules) have a range of kinetic energy. A
few particles will have either very low or very high
kinetic energy, while many particles will have an
intermediate kinetic energy.
• The temperature of a gas reflects the average kinetic
energy.
• states that the average kinetic
energy of gas particles is directly related to the
temperature, where R is the universal gas
constant.
Image Credit: Jin, CC-BY-NC-SA 3.0
Make sure to use the correct gas constant when doing calculations. Choose the value that matches units, or
convert units to match the other units in your calculations.
Kelvin
The Kelvin temperature scale is a measure of the absolute, average kinetic energy of the gases in a system.
• Substances at 0 K have zero kinetic energy.
• A temperature interval of 1 kelvin is equal to a temperature interval of 1 °C.
• 0 K is absolute zero, which corresponds to zero kinetic energy. 0 K=-273 °C
Properties of Gases
Gases can be characterized by four physical properties:
Property
Type
Property
Units
Pressure (P)
Pa, atm, Torr
intensive
Volume (V)
cm3, L
extensive
Temperature (T)
K, °C
intensive
Moles (n)
mol
extensive
• Atmospheric
pressure results from air molecules
colliding with objects
• A
barometer measures atmospheric pressure
by measuring the height of a mercury column in
an inverted column. Low pressure
lower
height in the column; high pressure
higher
height in the column
• In a manometer, the difference in mercury col-
• Gas
pressure is the result of particles colliding with
a surface – increasing the number of collisions
increases the pressure
umn heights equals the gas pressure
Gas Laws
Gas laws relate the volume, pressure, temperature, and quantity of gas present.
• Determined from years of experimentation
• Can be derived by examining the definitions of pressure, volume, and temperature
Boyle's law:
• States that the pressure and volume of a gas are inversely related
Charles's law:
• States that temperature and volume of a gas are directly related
Gay-Lussac's law:
• States that pressure and temperature of a gas are directly related
Combined gas law:
• Combination of the first three gas laws
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cont .
Gas Laws (cont.)
Avogadro's law
• States that equal volumes of gases at the same temperature and pressure contain the same number of moles of
gas
Ideal gas law:
• Combination of all the other gas laws
Many gas laws equations are assumed to be at STP to make for easier conversions.
• At STP, 1 mole of gas will equal 22.4 L of volume.
Mixture of Gases
In a mixture of gases, each component exerts a pressure called the partial pressure.
• Dalton's law of partial pressures: The sum of the partial pressures of a mixture of gases must equal the total
pressure of the gas mixture.
Diffusion
Gases spread and occupy all available space. The spreading out and mixing of a substance is called diffusion. If there
is a tiny hole in a container, gas can escape by effusion.
Graham's law of effusion:
where v is velocity of the particles and M is the molar mass
Note that the rates are inversely related to the square roots of molar masses.
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Chemistry
Gases
Chemistry
Gases Problem Guide
Equations
P = pressure, V = volume, T = temperature, n = number of particles (in moles), R = universal gas constant, 8.31 J/
mol•K
• Boyle's Law:
• Charles's Law:
• Gay-Lussac's Law:
• Combined Gas Law:
• Ideal Gas Law:
• Graham's Law of Diffusion:
where v is velocity of the particles and M is the molar mass of the substance
• Common Problems
It's important to be able to understand how
changes in an environment affect a gas.
Advanced Problems
Basic Problems
room would it take up if the pressure is increased to 2 atm and temperature is decreased to 200 K?
Example: If a gas exerts a pressure of 700
mm Hg at 30 °C, how much pressure will it
exert when the temperature drops to 0 °C?
1.Convert temperature to Kelvin.
30 °C + 273 = 303 K, 0 °C + 273 = 273 K
Always convert all temperatures to
Kelvin when dealing with gas laws.
2.Use the appropriate gas law. In this case,
use Gay-Lussac's Law,
700 mm Hg/303 K = P2/273 K
3. P2 = 630 mm Hg
Example: If a gas takes up 1 L at 0.5 atm and 300 K, how much
1.Use the appropriate gas law. In this case, use the combined gas
law
.
2. Plug in the numbers.
.
3. Solve. V2 = 0.2 L
Example: How many grams of oxygen will fill a 2.0 liter container
at STP?
1.Use the ideal gas law: PV = nRT.
101.3 kPa • 2.0 L = n • 8.31 (L•kPa)/(mol•K) • 273 K
n = 0.089 mol
2.Use the molar mass to convert to grams.
molar mass of O2 = 32.00 g/mol • 0.089 mol = 2.85 g = 2.9
grams of oxygen.
Molar Mass and Density
Molar mass = grams/mol or M = g/n, so n = g/M. This can be substituted into the ideal gas law: PV = nRT
gRT/M.
PV =
Example: 15 grams of a gas occupy 6.0 liters at STP. What is the molar mass of the gas?
1.Use the derived molar mass gas law.
101.3 kPa • 6.0 L = (15 g • 8.31 (L • kPa)/(mol • K) • 273 K)/M
2.Solve: M = 55.99 grams/mol = 60. grams/mol
Density (ρ) is equal to mass per unit volume, or g/V. The molar mass gas law PV = gRT/M is rewritten as M = gRT/
PV, and ρ is substituted for g/V, giving M = pRT/P.
Example: What is the density of argon gas at STP?
1.Find the molar mass of argon.
M = 39.95 g/mol
2.Plug into equation M = pRT/P.
39.95 g/mol = (ρ • 8.31 (L • kPa)/(mol • K) • 273 K)/101.3 kPa
3. ρ=1.78 g/L
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Chemistry
Gases Problem Guide
Reading Manometers
Manometers are used to read the pressure of a
gas. There are two types: open-ended and closedended.
A closed-ended manometer contains mercury and
a vacuum, with a gas on the other side. The height
difference equals the pressure of the gas, and the
higher side of the mercury will be on the outside.
1. In manometer A, the height difference is 0, so
the pressure of the gas is 0 mm Hg. In other
words, there is no gas in manometer A.
2.Manometer B is filled with a gas at a pressure of
760 mm Hg, or 1 atm.
3.Manometer C is filled with a gas at a pressure
of 200 mm Hg.
In an open-ended manometer, the atmospheric
pressure is allowed to push down on the mercury.
Thus, an even mercury level means that the
pressure of the gas equals the atmospheric
pressure. Thus, you must know the atmospheric
pressure (which is not always 1.0 atm) to use an
open-ended manometer.
1.In manometer A, the mercury levels are
the same, so the gas pressure equals the
atmospheric pressure.
2.In manometer B, the gas is 760 mm Hg
greater than the atmospheric pressure.
3.In manometer C, the gas is 200 mm Hg less
than the atmospheric pressure.
Dalton’s Law of
Partial Pressures
Image Credit: CK-12 Foundation, CC-BY-NC-SA 3.0
If the excess gas is on the outside, the pressure of the
gas is greater than atmospheric pressure. If the excess
gas is on the inside, it is less than atmospheric pressure.
Graham’s Law of Diffusion
Remember that this law states
that the total pressure in a closed
system equals the sum of the partial
pressures of each gas within it.
Remember that under identical conditions, gases have the same kinetic
energy, but larger gases move more slowly than small gases.
Example: Suppose a container is
Example: A flask of HCl gas is uncorked, and after 10.0 seconds, it reaches
filled with nitrogen and oxygen.
If the nitrogen exerts a pressure of
0.5 atm, and the total pressure in the
system is 0.7 atm, what is the partial
pressure of oxygen?
1. Ptotal = Pnitrogen + Poxygen
The way to compare two gases' speeds is given by
.
your nose and you can smell it. How long will it take for a flask of ammonia
gas (NH3) to reach your nose if it is uncorked from the same position?
1.Find the molar masses of both compounds
HCl = 35.42 g/mol + 1.01 g/mol = 36.43 g/mol
NH3 = 14.01 g/mol + 3 • 1.01 g/mol = 17.04 g/mol
2.Plug into the equation:
2. 0.7 atm = 0.5 atm + Poxygen
3. Poxygen = 0.2 atm
= 0.6839
3.The ratio of speeds between HCl and ammonia is 0.6839. In other words,
HCl will travel 0.6839 times slower than ammonia, going 0.6839 times
as far as ammonia in the same amount of time. Since HCl takes 10.0
seconds to reach your nose, ammonia takes 10.0 s • 0.6839 = 6.84
seconds to reach your nose.
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