Chemistry AP Study Notes 4 (Gases)

Thus far:
1. The Basics
2. Basic Chemical Reactions
3. Reactions in Solution

Chapter 5
Gases
Kinetic Molecular Theory, Part I

• 1) Gases are made up of very small particles, 
• 2) in constant, random motion, bouncing into their boundaries (which constitutes pressure), 
• 3) with lots of space between them, 
• 4) colliding randomly and elastically into each other, 
• 5) with the average kinetic energy being proportional to the Kelvin temperature.

Pressure, Volume, Temperature, Amount

• There are clear relationships between the pressure, volume, temperature, and amount of gas.
• Boyle's Law has to do with the relationship between pressure and volume when the temperature is constant. When the pressure goes up, the volume goes down. When the volume goes up, the pressure goes down. These are "inversely proportional." P x V is constant. Also P₁V₁ = P₂V₂.
• Pressure can be measured by a barometer or manometer. One "atmosphere" is sea level pressure. It would raise a column of mercury 760 mm (aka 760 torr-s). The pascal and pounds per square inch are other units of measuring pressure.
• Charles' Law has to do with the relationship between volume and temperature when the pressure is constant. When the temperature goes up, the volume goes up. When the temperature goes down, the volume goes down. These are "directly proportional." V/T is constant. Also V₁/T₁ = V₂/T₂.
• Temperature in such cases is in Kelvin. Kelvin is Celsius plus 273.15.
• Guy-Lussac's Law has to do with the relationship between pressure and temperature when the volume is held constant. When the pressure goes up, the temperature goes up. When the pressure goes down, the temperature goes down. Like volume and temperature, this is a directly proportional relationship. P₁/T₁ = P₂/T₂.
• Avogadro's Law has to do with the relationship between the amount of gas and the volume at a constant temperature and pressure. When the amount goes up, the volume has to go up for the temperature and pressure to stay the same, and vice versa. V₁/n₁ = V₂/n₂.
• We can add a constant and put all the above laws into a single ideal gas equation. The constant to make everything work out is R, the ideal gas constant (0.0821 L-atm/K-mol).

PV = nRT

• Johannes van der Waals made the ideal gas law a little more precise by adjusting the volume to take into account the fact that gas molecules do not have an infinite volume in which to move. He also adjusted the pressure part of the equation to take into account the attraction between molecules. His modified equation was:

(P + an²/V)(V - nb) = nRT

Kinetic Molecular Theory, Part II

• The average velocity of gas particles is the root mean square speed, u_rms.
• It is the square root of 3RT/M, where R is the ideal gas constant, T is the temperature in Kelvins, and M is the molar mass of the gas.
• The kinetic energy of each molecule is 3/2 RT.

Some More Laws

• Dalton's Law says the total pressure of a mixture of gases is just the sum of the individual "partial" pressures.
• You can figure out the partial pressure by multiplying the total pressure by the mole fraction of each gas.
• Graham's Law of Diffusion and Effusion states that the comparative rates of effusion (r1/r2, going through a tiny opening) are equal to the square root of the inverse ratio of the molar masses (M2/M1). Diffusion works similarly (mixing of gases due to their kinetic energy).

Other Details

• You can use the ideal gas law to answer stoichiometric questions. For example, you can find the number of moles of a gas released given the pressure, volume, and temperature. Then using the ratios of an equation, you can solve for grams of reactants and such.
• STP means "standard temperature and pressure."