Thursday

Stoichiometry and PV = nRT

Partial Pressures

Dalton’s Law

Idea: sum of pressures of a mix of gases = total pressure of gas mix

Mathematically: P_t = p₁ + p₂ + p₃ + …

Derivation from PV = nRT

Microscopically:

Example Problem:

Mole Fraction:

Idea: fraction of gas in moles / total # of moles

Symbol: X

Mathematically: X =

How does this relate to PV = nRT:

Example Problems:

1. As an anesthesiologist, you want to mix oxygen with halothane (the anesthetic) to administer to your patient during an operation. You mix 23.5 g of O₂ and 15.0 g of halothane together to a total pressure of 855 mm Hg. What is the partial pressure of each gas in your mixture?

2. You place your gas mixture from #1 into a 5.00 L tank at 25 C. What is the total pressure of the gases in the tank? What are the partial pressures of each gas?

Kinetic-Molecular Theory of Gases

Why can you smell Perfume?

DEMO

Key points of demo:

1. Molecules moving randomly

2. Molecules had different speeds

3. Molecules have different energies

4. Molecules hit other molecules

5. Molecules can transfer energy to each other through collisions

6. Big (heavier) molecules move slower than smaller (lighter) ones.

How this translates to Kinetic-Molecule Theory:

1. Gases consist of molecules whose separation is much greater than the size of the molecules themselves.

2. The molecules of a gas hare in continual, random, and rapid motion.

3. The average kinetic energy of gas molecules is proportional to the gas temperature. All gases, regardless of their molecular mass, have the same average kinetic energy at the same temperature. (KE = ½ mv²)

4. Gas molecules collide with one another and with the walls of their container, but they do so without loss of energy.

Graph:

T1 and T2

More Kinetic-Molecular Theory of Gases

Relationship to PV=nRT

Pressure à collisions w/ container

Micro view

Temperature à Kinetic Energy

More collisions per second

Micro view

# atoms increases à increase # of collisions à increase pressure

# atoms increases à increased volume

increased force (pressure)

Diffusion & Effusion

Definitions:

Diffusion: mixing of molecules of 2 or more gases due to their molecular motions

Example: perfume bottle

Micro drawing

Effusion: the movement of gas through a tiny opening in a container into another container where the pressure is very low.

Example: DEMO

Micro drawing

Graham’s Law:

Idea: heavier molecules effuse slower than faster ones.

Mathematically:

Example problems:

1. ²³⁵U effuses at a rate of 8.9 x 10^-7 mol/hour. What is the rate of effusion of ²³⁸U?

 

2. C₂F₄ effuses through a barrier at 4.6 x 10^-6 mol/h. An unknown gas made of B and H effuses at 5.8 x 10^-6 mol/h. What is the molar mass of the unknown gas?

Non-ideal gas behavior

Assumptions of Ideal Gas:

1. Volume of gas molecules << volume of container

2. No IMF’s b/w particles

Real-world:

Non-ideal behavior @ high pressure or low temperature