Lec 11 - November 14 2025

Dalton’s Law of Partial Pressures

The total pressure of a mixture of gases is the sum to the partial pressures of the mixture

Dalton’s Law of Partial Pressure Equation 

The total pressure is the sum of partial ones

If the temperature and volume of the mixture of 2 gases are the same, we can use this equation

Mole fraction, X

Partial pressure of a gas equation using mole fractions

What happens when a gas is collected over water?

there is a water vapour present (P_H2O)

P_H2O equation for P_total

P_H2O equation for P_H2

T/F Vapour pressure of water is constant

False

T/F: Vapour pressure of water varies with the temperature

True

Kinetic molecular theory

Average kinetic energy (1/2mv²) of the particles is proportional to the temperature in K

Boyle: At constant temperature and moles

Pressure is inversely proportional to volume

• volume increases, pressure decreases, collisions decrease

Charles: At constant pressure and moles

Volume is proportional to Temperature

• Temperature increases, volume increases, collisions increase

Avogadro: At constant pressure and moles

Volume is proportional to moles

• moles increase, volume increases, collisions increase

Dalton: At constant volume and temperature

P_^tot= P_a + P_b + … P_n

Average kinetic energy of gas particles is proportional to the ___________

gas temperature

gas particles have the same average kinetic energy at the ________

same temperature

Kinetic energy of a single molecule equation

If gas particles have the same kinetic energy but different masses, then they must also have:

different velocities

Root mean square velocity (u_rms)

Average kinetic energy equation in terms of root mean square velocity

Average kinetic energy equation in terms of temperature

root mean square velocity equation using gas constant 

this equation is proportional to molar mass and temperature

Diffusion

migration of molecules due to random molecular motion

Rate of diffusion is proportional to:

average molecular speed

average molecular speed is proportional to:

molecular weight

Effusion

the escape of molecules through a tiny hole

Rate of effusion is inversely proportional to:

molecular mass

Graham’s Law definition

the rate of effusion is inversely proportional to molecular mass

Graham’s Law equation

In Graham’s Law, how do you determine which effusion rate for a gas goes in the numerator and which goes in the denominator

The lighter gas (molar mass) goes on top and the heavier gas goes on the bottom

Non-Ideal gases

gases that deviate from the gas laws

At high pressure and low temperature, the ideal gas model fails. Why might this be?

two assumptions are violated 

• volume of gas is negligible 

• there are no forces interacting on particles

Volume corrections

• ideal gas law assumes gases take up zero volume

• need to account for the actual volume gas occupies

• the more gas, the more subtraction needed

• the larger the gas molecules, the more volume will be occupied

Volume correction calculation

V-nb

When is the volume correction between ideal gases and real gases most needed?

at high pressures, small volumes, or near the condensation point

Pressure corrections

• ideal gas law assumes gases don’t interact 

• need to include factor that accounts for intermolecular forces

• real gas exerts less pressure than an ideal gas at low pressure

• at high pressure repulsive forces are dominant

• the more gas, the more adding is required

When is the pressure correction between ideal and real gases most needed?

at low pressures or near the condensation point

Pressure correction calculation

P + an²/V²

Van Der Waals equation

Polar species have a _____ value of a (from equation) since they are more “sticky”

higher

Species with a _______ volume have a _______ volume of b

larger, larger