THERMO2

Question 1

Ideal Gas Equation

Answer 1

PV = nRT

P = pressure
V = volume
n = number of moles
R = molar gas constant
T = temperature

Question 2

Assumptions of Kinetic Gas Theory

Answer 2

1. Gas contains many molecules
2. Molecules are well separated
3. Direction of motion of molecules is random
4. Molecules exert no force on each other except during collisions
5. Collisions between molecules and with walls are elastic

Question 3

Ideal Gas Constant

Answer 3

R = PV/nT = 8.31

Question 4

When do real gases behave as ideal gases?

Answer 4

Real gases behave as ideal gases when molecules are well separated i.e. at high temperatures and low pressures

Question 5

Units of Pressure

1 pascal

Answer 5

1Pa = 1 N/m^2

Question 6

Units of Pressure

1 bar

Answer 6

1 bar = 10^5 Pa

Question 7

Units of Pressure

1 atmosphere

Answer 7

1 atm = 1013millibar = 1.013x10^5 Pa

Question 8

Standard Temperature and Pressure (STP)

Answer 8

0C = 273.15K
1atm = 1.013x10^5 Pa

Question 9

How does kinetic gas theory explain pressure?

Answer 9

Collisions of molecules with the walls of the container

Change in momentum

Question 10

Pressure Equation

Answer 10

P = (1/3) * Nm/V * (v^2)av

Question 11

Kinetic Energy per Molecule

Answer 11

(1/2)mv^2 = (3/2)kT

Question 12

Dalton’s Law of Partial Pressures

Answer 12

Ptotal = P1 + P2

Pt =RT/V (n1 + n2)

Question 13

Pressure in a Fluid

Answer 13

P = ρhg

Question 14

Kinetic Energy per Mole

Answer 14

(1/2)Mv^2 = (3/2)RT

Question 15

Number of Molecules and Moles Equation

Answer 15

N = n*Na

N = number of molecules
n = number of Moles
Na = advogadros constant

Question 16

Mass of Molecules and Moles Equation

Answer 16

M = m*Na

M = mass of a mole
m =mass of a molecule
Na = advogadros Constant

Question 17

Relationship between advogadros Constant, the molar Gas Constant and Boltzmann Constant

Answer 17

R = k*Na

Question 18

Root Mean Square Speed Equation

Answer 18

Vrms = √(Vav^2) = √(3kT/m)

Question 19

Mean Free Path

Definition

Answer 19

The average distance travelled by a Molecule between collisions

Question 20

Mean Free Path

Equation

Answer 20

λ = 1/(√2nvπ*d²)

λ = mean free path
nv = number density
d = diameter of a molecule

Question 21

What does mean free path depend on?

Answer 21

• size of molecules
• particle density of the gas
• doesn’t depend on speed
• depends on geometric factors

Question 22

Collision Time

Definition

Answer 22

The average time between collisions

Question 23

Collision Time

Equation

Answer 23

λ = Vav * τ

τ = collision Time
λ = mean free path
Vav = average velocity

Question 24

What does collision time depend on?

Answer 24

• mean free path

- speed of molecules

Question 25

NND

Answer 25

Nearest Neighbour Distance ``` NND = ∛(volume per molecule) NND = ∛(1/nv) = ∛(V/N) = ∛(kT/P) ```

Question 26

Maxwell Boltzmann Distribution | Description of Graph

Answer 26

- bell curve - steeper on left hand side - doesn't touch the y axis - theoretically the Graph continues to x=∞ - speed on X axis - fraction of molecules on y axis

Question 27

Maxwell Boltzmann Distribution | Vmax

Answer 27

Vmax is the speed that the highest proportion of molecules have I.e. The maxima of the Graph To find it differentiate the Graph equation and set it equal to zero Vmax = √(2RT/M)

Question 28

Maxwell Boltzmann Distribution | Vrms

Answer 28

The square root of the average of the speeds squared Calculated using an integral Vrms = √(3kT/m) = √(3RT/M)

Question 29

Maxwell Boltzmann Distribution | Vav

Answer 29

Average of the velocities of each molecule so accounts for direction Calculated using an integral Vav = √(8kT/πm) = √(8RT/πM)

Question 30

Relationship Between Vmax, Vrms and Vav

Answer 30

Vmax < Vav < Vrms

Question 31

Maxwell Boltzmann Distribution | Change With Temperature

Answer 31

For a fixed mass of gas, an increase in temperature results in: - Vmax increases - peak moves to the right - height decreases - area under graph remains constant as the number of molecules has not changed

Question 32

Maxwell Boltzmann Distribution | Change With Molar Mass

Answer 32

Temperature remains constant but molar mass is increased results in: - Vmax decreased - height of graph increases - area under graph remains constant as the number of molecules has not changed

Question 33

Maxwell Boltzmann Distribution | Evaporative Cooling - Change With Loss of Fast Molecules

Answer 33

- the fastest molecules are lost - once thermal equilibrium is achieved again after the initial loss, the graph: - Vmax decreased - height decreased and area under the graph has decreased as there are fewer molecules than their were before the evaporative Cooling