Chapter 15 - Ideal Gases

Question 1

15.1

What is the definition of one mole?

Answer 1

The amount of substance that contains as many elementary entities as there are atoms in 12 grams of Carbon-12

Question 2

15.1

What is the Avogadro constant?

Answer 2

Na, 6.02 x 10^23, the number of atoms in 12 grams of Carbon-12

Question 3

15.1

What is the formula to work out the total number of atoms or molecules in a substance?

Answer 3

N = n x Na

N - Total number of atoms in a substance
n - Number of moles
Na - Avogadro constant

Question 4

15.1

What is the formula to work out the mass of a sample of a substance?

Answer 4

m = n x M

m - The total mass of a sample of a substance
n - The number of moles in a substance
M - Molar mass

Question 5

15.1

What is the molar mass of a substance?

Answer 5

M, The mass of one mole of a substance

Question 6

15.1

What assumptions are made about an ideal gas in the kinetic model?

Answer 6

• The gas contains a very large number of atoms or molecules that move in random directions and speeds
• The atoms or molecules of the gas occupy a negligible volume compared with the volume of the gas
• The collisions with each other or the walls of the container are perfectly elastic
• The time during collisions of atoms or molecules is negligible compared to time between collisions
• Electrostatic forces between atoms or molecules are negligible except during collisions

Question 7

15.1

How does an ideal gas cause pressure?

Answer 7

• When atoms collide with the walls of the container, the container exerts a force on them, changing their momentum as they bounce off
• When a single atom collides with the container wall elastically, it’s speed doesn’t change, but it’s velocity changes from mu to -mu, the total change is -2mu
• The atoms frequently collide with the container walls, according to newtons’s second law the force on the atom is f = p/t
  with p being -2mu
• A large number of atoms collide with the walls of the container, p= f/a

Question 8

15.2

What is Boyle’s law?

Answer 8

Boyle’s law is the relationship between the pressure and volume of an ideal gas

The relationship is that Pressure is inversely proportional to the volume

Question 9

15.2

If a fixed mass of gas is kept in a sealed box, what happens if you half the volume of the box?

Answer 9

If you half the volume of the box, then the pressure will double

Question 10

15.2
Charles’s law:
What is the relationship between pressure and temperature?

Answer 10

If the volume and mass of a gas remain constant, the pressure of an ideal gas is directly proportional to its absolute temperature in Kelvin

Question 11

15.2

If a fixed mass of gas is kept in a sealed box and the temperature is doubled what happens to the pressure of the gas?

Answer 11

If the temperature is doubled the pressure of the gas is also doubled

Question 12

15.2

What is the pressure of a gas at absolute zero?

Answer 12

At absolute zero, the particles aren’t moving (as internal energy is at its minimum), so the pressure must be zero

Question 13

15.2

Using a graph how would you estimate absolute zero?

Answer 13

• Plotting a graph of pressure against temperature (in Celsius)
• It will give you a line that can be extrapolated to a point where the pressure is zero

Question 14

15.2
Gay - Lassac’s law:
By combining the two gas laws, how do you work out the conditions from initial to final?

Answer 14

P1 V1 P2 V2
—————— = ———————
T1 T2

Question 15

15.2
What is the molar gas constant?
Its symbol?
Its value?

Answer 15

• The molar mass constant is the constant from pV/T
• R
• 8.31 JK^-1mol^-1

Question 16

15.2

What is the ‘Equation of state of an ideal gas’?

Answer 16

pV/T = nR or pV = nRT

Question 17

15.2

For a graph of pV against T what would be each part of the graph?

Answer 17

pV = NR . T + 0

y = m . x + C

Question 18

15.3

What is R.M.S Speed?

Answer 18

R.M.S speed is the root mean squared speed is how we describe the speed of motion of particles in a gas

Question 19

15.3

Why is R.M.S speed used over velocity?

Answer 19

Velocity is a vector and if we averaged all the directions velocities it would be 0. So we use R.M.S speed

Question 20

15.3

How do you determine the R.M.S speed of a gas?

Answer 20

• The velocity of each atom in the gas is squared (C^2)
• Then you take an average of them, (ĉ^2)
• Then you square root to give the R.M.S speed

Question 21

15.3

What is the equation to work out pressure with the root mean squared speed?

Answer 21

pV = 1/3 Nmĉ^2

p - Pressure
V - Volume 
N - Total number of particles 
m - mass
ĉ - RMS speed

Question 22

15.3 How do you derive the equation:

pV = 1/3 Nmĉ^2

Answer 22

For a single atom:
- The force exerted on the wall is: F = P/t
- The momentum: P = 2mc
- The time: t= 2L/c
Force = 2mc x mc/2L
F = mc^2/L

For multiple atoms:
p = mĉ^2/ L x N x 1/3 = Nmĉ/3L
p = Nmĉ/3L x 1/L^2 = Nmĉ/3L^3 = Nmĉ^2/3V

pV = 1/3 x N x m x ĉ^2

Question 23

15.3

What is the Maxwell - Boltzmann constant?

Answer 23

The range of speeds of the particles at a given temperature

Question 24

15.3

How does changing the temperature of the gas change the distribution?

Answer 24

The hotter the gas, the greater the range of speeds

Question 25

15.4
What is the Boltzmann constant?
What is it’s symbol?
What is it’s value?

Answer 25

The Boltzmann constant is the Molar gas (R) constant divided by the Avogadro constant (Na)
It’s symbol is k
It’s value is 1.38 x 10^-23

Question 26

15.4

What equation links the pressure and the Boltzmann constant?

Answer 26

pV = NKT

Question 27

15.4

What is the relationship between K.E and temperature?

Answer 27

K.E is directly proportional to temperature

Question 28

15.4

What is the mean average Kinetic energy?

Answer 28

1/2mĉ^2

Question 29

15.4

When does the relationship between temperature and Pressure apply?

Answer 29

When temperature is in Kelvin

Question 30

15.4

Why is temperature directly proportional to internal energy in an ideal gas?

Answer 30

Internal energy is K.E and P.E
P.E is negligible since electrostatic forces in an ideal gas are negligible
So temp is directly proportional to K.E which is directly proportional to Internal energy