 Gases

# Key Ideas

• Kinetic energy: the energy of all motion
• Elastic collision: the conservation of kinetic energy during collisions

# Kinetic Molecular Theory

Gases are in continuous, chaotic motion and, except during elastic collisions, are widely separated from each other

• Gases are widely separated with no intermolecular bonding between molecules
• Rapid, chaotic, random movement in straight lines until they collide with another particle or the wall of the container
• When gases collide, kinetic energy can be transferred from one particle to another, but no energy is lost

# Pressure

Pressure is the measure of the force exerted by the particles on the walls of the container during collisions.
Pressure $$=\frac{Force}{Area}$$ (The force per unit area of the container)

 Unit Symbol Conversion to kPa Kilopascal kPa 1 Pascal Pa 1000 Pa Atmosphere atm 0.987 atm Bar bar 1 bar Millimeters of Mercury mmHg 750 mmHg

# The Universal Gas Equation

For all gas equations, units must be kept constant

• P: Pressure is in kPa
• V: Volume is in L
• n: mol is in mol
• T: Temperature is in Kelvin ($$0K\approx -273^oC$$)
• R: The gas constant is $$=8.31\,J\,K^{-1}\,mol^{-1}$$

Volume and Pressure

• Given an amount of gas at a constant temperature, the volume will be inversely proportional to the pressure
• $$P\propto \frac{1}{V}$$
• $$P_1V_1=P_2V_2$$

Volume and Temperature

• Given an amount of gas at a constant pressure, the volume of the gas will be directly proportional to the temperature
• $$V\propto T$$
• $$\frac{V_1}{T_1}=\frac{V_2}{T_2}$$

Combined Gas Law

• $$\frac{P_1\times V_1}{n_1\times T_1}=\frac{P_2\times V_2}{n_2\times T_2}$$

Universal Gas Equation

• $$P\times V=n\times R\times T$$

Molar Volume of Gas

• If an amount of gas has a constant pressure and a constant temperature, the volume of the gas will be the same. If the gas is at SLC - Standard Laboratory Conditions ($$100kPa,\,25^oC$$) then $$1\,\text{mol}$$ of gas occupies $$24.8L$$

# Dalton's Law of Partial Pressure

The total pressure exerted by a mixture of gases is equal to the sun of all the partial pressures of the constituent gases

• $$P_{TOTAL}=P_1+P_2+P_3+P_{...}$$