Gases Study Guide

Properties of a Gas

A gas is a state of matter. The particles that make up a gas can range from individual atoms to complex molecules. Some other general information involving gases:

• Gases assume the shape and volume of their container.
• Gases have lower densities than their solid or liquid phases.
• Gases are more easily compressed than their solid or liquid phases.
• Gases will mix completely and evenly when confined to the same volume.
• All elements in Group VIII are gases. These gases are known as the noble gases.
• Elements that are gases at room temperature and normal pressure are all nonmetals.

Pressure

Pressure is a measure of the amount of force per unit area. The pressure of a gas is the amount of force the gas exerts on a surface within its volume. Gases with high pressure exert more force than gas with low pressure.
The SI unit of pressure is the pascal (Symbol Pa). The pascal is equal to the force of 1 newton per square meter. This unit is not very useful when dealing with gases in real world conditions, but it is a standard that can be measured and reproduced. Many other pressure units have developed over time, mostly dealing with the gas we're most familiar with: air. The problem with air, the pressure isn't constant. Air pressure depends on the altitude above sea-level and many other factors. Many units for pressure were originally based on an average air pressure at sea-level, but have become standardized.

Temperature

Temperature is a property of matter related to the amount of energy of the component particles.
Several temperature scales have been developed to measure this amount of energy, but the SI standard scale is the Kelvin temperature scale. Two other common temperature scales are the Fahrenheit (°F) and Celsius (°C) scales.
The Kelvin scale is an absolute temperature scale and used in nearly all gas calculations. It is important when working with gas problems to convert the temperature readings to Kelvin.
Conversion formulas between temperature scales:
K = °C + 273.15
°C = 5/9(°F - 32)
°F = 9/5°C + 32

STP - Standard Temperature and Pressure

STP means standard temperature and pressure. It refers to the conditions at 1 atmosphere of pressure at 273 K (0 °C). STP is commonly used in calculations involved with the density of gases or in other cases involving standard state conditions.
At STP, a mole of an ideal gas will occupy a volume of 22.4 L.

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Gases - General Properties of Gases

By Anne Marie Helmenstine, Ph.D.

Dalton's Law of Partial Pressures

Dalton's law states the total pressure of a mixture of gases is equal to the sum of all the individual pressures of the component gases alone.
P_total = P_{Gas 1} + P_{Gas 2} + P_{Gas 3} + ...
The individual pressure of the component gas is known as the partial pressure of the gas. Partial pressure is calculated by the formula
P_i = X_iP_total
where
P_i = partial pressure of the individual gas
P_total = total pressure
X_i = mole fraction of the individual gas
The mole fraction, X_i, is calculated by dividing the number of moles of the individual gas by the total number of moles of the mixed gas.

Avogadro's Gas Law

Avogadro's law states the volume of a gas is directly proportional to the number of moles of gas when pressure and temperature remain constant. Basically: Gas has volume. Add more gas, gas takes up more volume if pressure and temperature do not change.
V = kn
where
V = volume k = constant n = number of moles
Avogadro's law can also be expressed as
V_i/n_i = V_f/n_f
where
V_i and V_f are initial and final volumes
n_i and n_f are initial and final number of moles

Boyle's Gas Law

Boyle's gas law states the volume of a gas is inversely proportional to the pressure when the temperature is held constant.
P = k/V
where
P = pressure
k = constant
V = volume
Boyle's law can also be expressed as
P_iV_i = P_fV_f
where P_i and P_f are the initial and final pressures V_i and V_f are the initial and final pressures
As volume increases, pressure decreases or as volume decreases, pressure will increase.

Charles' Gas Law

Charles' gas law states the volume of a gas is proportional to its absolute temperature when pressure is held constant.
V = kT
where
V = volume
k = constant
T = absolute temperature
Charles' law can also be expressed as
V_i/T_i = V_f/T_i
where V_i and V_f are the initial and final volumes
T_i and T_f are the initial and final absolute temperatures
If pressure is held constant and the temperature increases, the volume of the gas will increase. As the gas cools, the volume will decrease.

Guy-Lussac's Gas Law

Guy-Lussac's gas law states the pressure of a gas is proportional to its absolute temperature when the volume is held constant.
P = kT
where
P = pressure
k = constant
T = absolute temperature
Guy-Lussac's law can also be expressed as
P_i/T_i = P_f/T_i
where P_i and P_f are the initial and final pressures
T_i and T_f are the initial and final absolute temperatures
If the temperature increases, the pressure of the gas will increase if the volume is held constant. As the gas cools, the pressure will decrease.

Ideal Gas Law or Combined Gas Law

The ideal gas law, also known as the combined gas law, is a combination of all the variables in the previous gas laws. The ideal gas law is expressed by the formula
PV = nRT
where
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = absolute temperature
The value of R depends on the units of pressure, volume and temperature.
R = 0.0821 liter·atm/mol·K (P = atm, V = L and T = K)
R = 8.3145 J/mol·K (Pressure x Volume is energy, T = K)
R = 8.2057 m³·atm/mol·K (P = atm, V = cubic meters and T = K)
R = 62.3637 L·Torr/mol·K or L·mmHg/mol·K (P = torr or mmHg, V = L and T = K)
The ideal gas law works well for gases under normal conditions. Unfavorable conditions include high pressures and very low temperatures.

Kinetic Theory of Gases

Kinetic Theory of Gases is a model to explain the properties of an ideal gas. The model makes four basic assumptions:

1. The volume of the individual particles making up the gas is assumed to be negligible when compared to the volume of the gas.
2. The particles are constantly in motion. Collisions between particles and the borders of the container cause the pressure of the gas.
3. The individual gas particles do not exert any forces on each other.
4. The average kinetic energy of the gas is directly proportional to the absolute temperature of the gas. The gases in a mixture of gases at a particular temperature will have the same average kinetic energy.

The average kinetic energy of a gas is expressed by the formula:
KE_ave = 3RT/2
where
KE_ave = average kinetic energy R = ideal gas constant
T = absolute temperature
The average velocity or root mean square velocity of individual gas particles can be found using the formula
v_rms = [3RT/M]^1/2
where
v_rms = average or root mean square velocity
R = ideal gas constant
T = absolute temperature
M = molar mass

Density of a Gas

The density of an ideal gas can be calculated using the formula
ρ = PM/RT
where
ρ = density
P = pressure
M = molar mass
R = ideal gas constant
T = absolute temperature

Graham's Law of Diffusion and Effusion

Graham's law atates the rate of diffusion or effusion for a gas is inversely proportional to the square root of the molar mass of the gas.
r(M)^1/2 = constant
where
r = rate of diffusion or effusion
M = molar mass
The rates of two gases can be compared to each other using the formula
r₁/r₂ = (M₂)^1/2/(M₁)^1/2

Real Gases

The ideal gas law is a good approximation for the behavior of real gases. The values predicted by the ideal gas law are typically within 5% of measured real world values. The ideal gas law fails when the pressure of the gas is very high or the temperature is very low. The van der Waals equation contains two modifications to the ideal gas law and is used to more closely predict the behavior of real gases.
The van der Waals equation is
(P + an²/V²)(V - nb) = nRT
where
P = pressure
V = volume
a = pressure correction constant unique to the gas
b = volume correction constant unique to the gas
n = the number of moles of gas
T = absolute temperature
The van der Waals equation includes a pressure and volume correction to take into account the interactions between molecules. Unlike ideal gases, the individual particles of a real gas have interactions with each other and have definite volume. Since each gas is different, each gas has their own corrections or values for a and b in the van der Waals equation.

Practice Worksheet and Test

Test what you've learned. Try these printable gas laws worksheets:
Gas Laws Worksheet
Gas Laws Worksheet with Answers
Gas Laws Worksheet with Answers and Shown Work
There is also a gas law practice test with answers available.