15 - Ideal Gasses

Question 1

What is the SI unit for the amount of a substance?

Answer 1

Mole (mol)

Question 2

Define the mole.

Answer 2

The amount of a substance that contains as many elementary entities as there are atoms in 12g (0.012kg) of carbon-12.

The Avogadro constant.

Question 3

What is the sign for the Avogadro constant?

Also what is it?

Answer 3

Nₐ

6.02x10²³

Question 4

What does one mole of any substance contain?

Answer 4

The Avogadro constant of individual molecules.

Question 5

How do you calculate the number of molecules in a substance?

Answer 5

N = n x Nₐ

Question 6

What is the molar mass of a substance?

Answer 6

The mass of a single mole of the substance.

M

Question 7

How do we calculate the mass of a substance from the molar mass?

Answer 7

m = n x M

Question 8

What is the kinetic theory of gases?

Answer 8

A model used to describe the behaviour of the atoms / molecules in an ideal gas.

Question 9

Why do we use the kinetic theory of gases?

Answer 9

Because real gases have complex behaviour which we must simplify.

Question 10

What are the assumptions made in the kinetic theory of gases?

Answer 10

• Very large number of molecules moving in random directions with random speeds
• Molecules occupy a negligible volume compared to the volume of the gas
• Collision of molecules and sides of container are perfectly elastic
• Time of colisions is negligible compared to time between collisions
• Electrostatic forces between molecules are negligible except during collisions

Question 11

What is the relationship between the volume of a container and the pressure inside it?

(What are the other conditions for this to be true?)

Answer 11

P ∝ 1/v

If temperature and mass of gas remains constant

Question 12

What is Boyle’s law?

Answer 12

P ∝ 1/v

If temperature and mass of gas remains constant

Question 13

What is the relationship between the pressure of an ideal gas and the temperature?

(What are the other conditions for this to be true?)

Answer 13

P ∝ T

If volume and mass of gas remain constant

Question 14

How does the relationship between the pressure of an ideal gas and the temperature help us find the value of absolute zero.

Answer 14

Plot graph of pressure against temperature.

Extrapolate backwards to where pressure = 0.

Question 15

How do we combine the relationships between pressure and volume and pressure and temperature?

Answer 15

PV / T = Constant

Question 16

What is the molar gas constant?

What is its symbol?

Answer 16

The constant from the equation PV / T for one mole of gas.

R

Question 17

What is the equation of state of an ideal gas?

Answer 17

PV = nRT

P = Pressure
V = Volume
n = number of moles
R = molar gas constant
T = Temperature

Question 18

What is the SI unit of temperatute?

Answer 18

Kelvin

K

Question 19

What is the SI unit for pressure?

Answer 19

Pascal

Pa

Question 20

What is the SI unit for volume?

Answer 20

m³

Question 21

On a graph of PV against T, what does the gradient represent?

Answer 21

nR

y = mx + c

Pv = (nR)T + 0

Question 22

How do we calculate root mean square speed?

Answer 22

Square all velocity values
Find mean of squared values
Square root mean

Question 23

Why do we use root mean square speed?

Answer 23

Because velocities are vectors and just the mean would cancel out to equal 0.

Squaring the velocities removes the negative.

Question 24

What is the Maxwell-Boltzmann distribution?

Answer 24

The range of speeds of particles in a gas at a constant temperature.

Question 25

Where is the most probable speed on the Maxwell-Boltzmann distribution curve?

Answer 25

At the peak

Question 26

Where is the mean speed on the Maxwell-Boltzmann distribution curve?

Answer 26

Slightly to the right of the peak,

Between the peak and the RMS.

Question 27

Where is the root mean square speed on the Maxwell-Boltzmann distribution curve?

Answer 27

Further right of the peak.

Right of the mean speed.

Question 28

How does changing the temperature affect the Maxwell-Boltzmann distribution?

Answer 28

It becomes more spread out.

All three speed values become larger.

Question 29

Define the Boltzmann constant.

Answer 29

Molar gas constant divided by the Avogadro constant.

k = R / Nₐ

Question 30

What is the symbol of the Boltzmann constant?

Answer 30

k

LOWERCASE

Question 31

How can the Boltzmann constant be incorporated into the equation of state of an ideal gas?

Answer 31

PV = nRT (equation of state of an ideal gas)

R = kNₐ (Rearrange formula for Boltzmann constant)

PV = knNₐT (Sub in formula above)

n x Nₐ = N (number of moles x Avogadro = number of molecules)

PV = NkT

Question 32

What does the symbol “k” represent?

Answer 32

Boltzmann constant

Question 33

What does the symbol “R” represent?

Answer 33

Molar gas constant

Question 34

What does the symbol “Nₐ” represent?

Answer 34

Avogadro constant

Question 35

What is the derivation of the equation:
(1/2)mc̅ ²kT = (3/2)kt?

Probably use paper

Answer 35

1/3 Nmc̅ ² = NkT
1/3mc̅ ² = kT (Cancel N)

REWRITE LHS

(2/3)(1/2mc̅ ²) = kt

1/2mc̅ ² = 3/2kt

Question 36

What does the equation 1/2mc̅ ² equal?

Answer 36

The mean average kinetic energy of the particles in the gas.

1/2 mv²

Question 37

What is the relationship between the mean kinetic energy of particles in the gas and the temperature of the gas?

Answer 37

Eₖ ∝ T

Question 38

What is the internal energy of an ideal gas and why?

Answer 38

A sum of the kinetic and potential energies of the particles in the gas.

Ee assume that the electrostatic forces between particles are negligible.

Internal energy of ideal gas = kinetic energy of all of the particles.

Question 39

What would happen to the internal energy of an ideal gas if you doubled the temperature?

Answer 39

It would also double.

Eₖ ∝ T
THEREFORE
Internal E ∝ T