Gas Laws

Question 1

The mole

Answer 1

The primary counting unit for atoms
- really just a number like dozen

Question 2

Unfamiliar equations

Answer 2

one atom of something when mass of a mole is known: m = m/Np

Question 3

Ideal gas assumptions

Answer 3

• large # of identical molecules
• volume of molecules is negligible
• motion is random
• no forces between molecules
• all collisions are elastic

**described in terms of the kinetic theory

Question 4

The gas is no longer ideal when…

Answer 4

• it is compressed (molecules close together)
• close to phase change (all internal energy is from Ek)
• low temperatures and high pressures

Question 5

Boyle’s law

Answer 5

• Volume and Pressure are inversely proportional
  the graph is curvy line starting on top ending on bottom
• air travels from high to low pressures

Question 6

Pressure law

Answer 6

• Temperature and pressure are directly proportional
  graph: straight line (bottom to top)

Question 7

Charles’ law

Answer 7

• Temperature and volume are directly proportional
  graph: straight line (bottom to top)

Question 8

Ideal gas Law

Answer 8

pV = nRT
p - [Pa]
V - [m3]
n - [mol]
T [K]

R = 8.31 J K-1 mol-1

Question 9

Related constants

Answer 9

R/kb (Stefan Boltzmann’s constant) = 6.02 x 1023 mol-1

So,
Ek = 3/2kbT = 3/2(R/Na)T
- labeled as U in the data booklet

Question 10

Suggest why only the average kinetic energy of the molecules of an ideal gas is related to the internal energy of the gas.

Answer 10

• The number of molecules in a gas is extremely large.
• The molecules have a range of velocities, resulting in a distribution of kinetic energies.
• the equipartition theorem states that energy is equally partitioned among all degrees of freedom, and for an ideal gas, only translational kinetic energy is considered
• the molecules do NOT have potential energy

This assumption of zero potential energy is what allows us to directly relate the temperature of an ideal gas to the average kinetic energy of its molecules, as expressed in the equation:

(1/2)mv² = (3/2)kT

Question 11

Waiting for some time before measuring the pressure after each reduction in volume is necessary because…

Answer 11

To achieve steady-state conditions: When the volume is reduced, the air molecules need time to redistribute and reach equilibrium. This process ensures that the pressure reading accurately reflects the new state of the system.

To minimize dynamic measurement errors: Rapid changes in pressure can lead to temporary fluctuations that do not represent the true static pressure. Waiting allows these transient effects to dissipate, reducing dynamic measurement error

Question 12

Standard pressure (assumed)

Answer 12

1.01 x 10^5 kPa

Question 13

Relationship between average kinetic energy and temperature

Answer 13

• directly proportional
• 2 bodies of different mass but at same temperature will have the same kinetic energy

Question 14

Volume scales in 3D spaces

Answer 14

e.g:
The density of the gas is 1000 times less than in the liquid state, meaning the same mass occupies 1000 times more volume. Since molecules are distributed in 3D space, the average separation between them scales with the cube root of the volume increase. The cube root of 1000 is 10, so the average distance between molecules in the gas state is 10 times the molecular diameter. Thus, the correct answer is
10𝑑/

Question 15

Kinetic molecular theory

Answer 15

• explains the states of matter, and is based on the idea that matter is composed of tiny particles that are always in motion. This theory helps explain observable properties and behaviors of solids, liquids, and gases.