The Gas Phase

Question 1

What are the 4 variables that are shown related to the Ideal Gas Law?

Answer 1

Pressure, Volume, concentration (moles), Temperature

• Formula: PV=nRT
  
  • R = ideal gas constant: 8.21 x 10^-2 (pressure units are atm) or 8.314 (only if using Pa for pressure units and m³ for volume units instead of L)

Question 2

What are the 4 units for pressure and what are the conversions between them? Designate which unit is the SI unit.

Answer 2

1. Pascals (Pa) *SI unit*
2. Millimeters of Mercury (mmHg)
3. Torrs
4. Atmospheres (atm)

• 1 atm = 760 mmHg = 760 torrs = 101.325 kPa

Question 3

What are the differences between STP conditions and Standard State conditions?

Answer 3

• STP conditions are 273 K (0ºC) at 1 atm
• Standard State conditions are 298 K (25ºC), 1 atm, 1 M concentrations

Question 4

What characteristics make the gas phase unique?

Answer 4

Gases are unique in relation to solids and liquids because they are compressible fluids with rapid molecular motion, large distances between molecules, and weak intermolecular forces.

Question 5

What is an ideal gas?

Answer 5

An ideal gas represents a hypothetical gas with molecules that have no intermolecular forces and occupy no volume.

• Real gases deviate from this ideal behavior at high pressures (low volumes) and low temperatures, but many compressed real gases demonstrate behavior that is close to ideal.

Question 6

At STP conditions, what volume does an ideal gas occupy?

Answer 6

A mole of an ideal gas occupies 22.4 L at STP conditions.

Question 7

How can the ideal gas law be utilized to calculate the density of any gas?

Answer 7

Density = mass / volume. In the ideal gas equation volume is already present on the left side of the equation. Mass is present on the right side because moles = mass / molar mass. So after manipulating the formula: density = (mass / volume) = { (Molar Mass (M) x Pressure) / (R x T) }

Question 8

What is the combined gas law?

Answer 8

The combined gas law compares the pressure, volume, and temperature of a gas at an initial and final state. Assuming the concentration (moles) of a gas stays the same the formula is:

Question 9

What is Avogadro’s Principle?

Answer 9

Avogadro’s principle states that the number of moles of a gas and the volume that gas occupies is directly proportional.

• Avogadro’s principle can be represented by two formulas:

n / V = k (a constant) or n₁ / V₁ = n₂/ V₂

Question 10

What is Boyle’s Law?

Answer 10

Boyle’s Law states that the volume of a gas is inversely proportional to the gas’ pressure given isothermal (constant temperature) conditions.

• Formula: P₁V₁ = P₂V₂

Question 11

What is Charle’s Law?

Answer 11

Charle’s law states that at a constant pressure, the volume of a gas is directly proportional to its temperature.

• Formula: V₁ / T₁ = V₂ / T₂

Question 12

What is Gay - Lussac’s Law?

Answer 12

Gay Lussac’s Law states that at constant volume and concentration, a gas’ pressure and temperature are directly proportional to each other.

• Formula: P₁ / T₁ = P₂ / T₂

Question 13

What is Dalton’s Law of Partial Pressures?

Answer 13

Dalton’s Laws of partial pressures describes that two or more gases that do not chemically interact will behave independently of the other gases. This means each gas will behave as if it were the only gas in the container. Therefore, the pressure exerted by each gas in the mixture will be equal to the pressure that the gas would exert if it were the only gas in the container.

P_T = P_A + P_B + … P_n

• P_A = X_AP_T where X_A = moles of gas A / total moles of gas

Question 14

What is vapor pressure?

Answer 14

Vapor pressure is the pressure exerted by evaporated particles above the surface of a liquid.

• Vapor pressure from the evaporated molecules forces some of the gas back into the liquid phase, and equilibrium is reached between evaporation and condensation.
  
  • Similar to diffusion but without a membrane (moving down a concentration gradient).

Question 15

What is the difference between diffusion and effusion?

Answer 15

Diffusion is the movement of molecules from a high concentration to low concentration through a medium (such as air or water). Effusion is the flow of gas particles under pressure from one compartment to another through a small opening.

• In both diffusion and effusion, the movement of particles down their concentration gradient will be slower for larger molecules.

Question 16

What are the 5 assumptions of the kinetic molecular theory?

Answer 16

The 5 assumptions made by the kinetic molecular theory are:

1. Gases are made up of particles with bolumes that are negligible compared to the container.
2. Gas atoms or molecules exhibit no intermolecular forces (do not attract or repel).
3. Gas particles are in continuous, random motion, undergoing collisions with other particles and the container walls.
4. Collisions between any two gas particles (or between particles and the container walls) are elastic.
   
   • Meaning that there is conservation of both momentum and kinetic energy.
5. The average kinetic energy of gas particles is directly proportional the absolute temperature of the gas.
   
   • True for all gases at a given temperature, irrespective of chemical identity or atomic mass.

Question 17

How do you calculate the KE of a gas particle based on absolute temperature of the gas?

Answer 17

KE = (3/2) x K_B x T

• K_B = Boltzmann constant = 1.38 x 10^-23 J/K

Question 18

What is Graham’s Law?

Answer 18

Graham’s law states that the rate at which two gases diffuse or effuse are inversely proportional to the square roots of their molar masses. Mathematically this is written:

Question 19

How do you calculate the average speed of a gas particle?

Answer 19

To calculate the average speed of a gas molecule, you use the root-mean-square speed equation: