Ideal Gases

Question 1

Boyle’s Law

Answer 1

Pressure exerted by a fixed mass is indirectly proportional to its volume, provided that temperature is constant

p ∝ 1/v

p1v1 = p2V2

Question 2

Charles Law

Answer 2

V is directly proportional to T

• pressure is constant

Question 3

Pressure Law

Answer 3

P is directly proportional to T

• volume is constant

Question 4

Combining all the equations

Answer 4

pV = NT

N is the number of molecules

the greater number of molecules, the greater the pressure

Question 5

The two equations of Ideal Gases

Answer 5

pV = NkT

pV = nRT

Question 6

N = ???
n = ???

Answer 6

N = number of molecules
n = number of moles

Question 7

Avogardo Constant (1 mole)

Answer 7

the number of atoms of carbon-12 = 6.02x10^23 molecules

Question 8

Equation linking N, n and Na (Avogardo’s constant)

Answer 8

n = N / Na

number of moles = number of molecules / Avogardo constant

Question 9

Assumptions of Gases

Answer 9

R - random motion
A - attraction of gas molecules is none
V - volume of gas negligible
E - elastic collision // Ek is conserved
D - duration of collision is negligible

Question 10

Kinetic theory of gases equation

Answer 10

P = 1/3Nm<c^2>

Question 11

Derivation of Kinetic theory of gases equation

Answer 11

Consider a box of gas:
x = length
y = width
z = height

c = speed of the molecule
t = time taken for the particle to travel forward AND backward

P = F/A
F = 2mc / t
t = 2x / c
F = 2mc / (2x / c )
P = (mc^2 / x ) / xyz

P = mc^2 / V —— (1)

Since it’s a box, gas movements are in 3D. The (1) equation only considers 2D. Therefore we use the 3D Pythagoras Theorem to calculate the mean speed.

c^2 = cx^2 + cy^2 + cz^2
<cx^2> = <cy^2> = <cz^2>
<cx^2> = 1/3 <c^2> —— (2)

Substitute (2) to (1):

P = 1/3Nm<c^2> / V
V = xyz

Final equation:
pV = 1/3Nm<c^2>

Question 12

Definition of mole

Answer 12

the SI base unit of an amount of substance. it is the amount containing as many particles as there are atoms in 12g of carbon-12

Question 13

Definition of molar mass

Answer 13

the mass of 1 mole

Question 14

Explain what happens to the pressure inside a box with moving gas particles

Answer 14

• a gas exerts pressure on any surface with which it comes into contact
• when an air molecule collides with the surface of the box, it exerts a small force on the box
• the pressure inside the box is a result of the forces exerted by a vast number of molecules in the box

Question 15

Factors that affect the pressure that gas exerts

Answer 15

• number of molecules that hit the box in one second
• the force with which a molecule collides with the wall

Question 16

The average speed of molecules

Answer 16

400 ms^-1

Question 17

Explain pressure when gas molecules hit a wall in relation to momentum

Answer 17

If a molecule of mass m hits the wall with speed v, it will rebound with speed v at the opposite direction

Hence change in momentum = 2mv

Since force is equal to rate of change of momentum, the higher the speed of the molecule, the greater the force it exerts when colliding the wall; the pressure on the wall increases.

Question 18

Properties of gases to measure

Answer 18

• pressure
• temperature
• volume
• mass

Question 19

Changing degrees Celsius to Kelvin

Answer 19

θ°C + 273.15

Question 20

Pressure in ideal gases

Answer 20

The frequency of collisions of the gas molecules per unit area of the container

Question 21

Mass in ideal gases

Answer 21

the amount of gas measured in moles

Question 22

Mass of a proton / neutron (1u)

Answer 22

1.66 x 10^-23

Question 23

According to Boyle’s law, if gas is compressed at constant temperature…

Answer 23

… its pressure increases, and volume decreases.

volume decrease because there are more particles per unit volume and more collisions per second of the particles with unit area of the wall

constant temperature = speed doesn’t change

each collision with the wall involves the same change in momentum, but with more collisions per second on unit area of the wall there is a greater rate of change of momentum and, therefore, a larger pressure on the wall.

Question 24

How does Charles Law prove absolute zero?

Answer 24

• graph of Charles Law
• gradient is constant
• the graph does show that there is a temperature at which the volume of a gas does, in principle, shrink to zero.
• Looking at the lower temperature scale on the graph, where temperatures are shown in kelvin (K), we can see that this temperature is 0 K, or absolute zero.

Question 25

R (constant of proportionality) value

Answer 25

R = 8.31 J mol−1 K−1

Question 26

What does the equation pV = 1/3Nm<c^2> suggest?

Answer 26

• pressure is proportional to the number of molecules
• the greater the mass of the molecule, the greater force it will exert in collision
• pressure is proportional to the average value speed squared
• pressure is inversely proportional to volume (Boyles law)

Question 27

Combining equations pV = 1/3Nm<c^2> and pV = nRT

Answer 27

nRT = 1/3Nm<c^2>
3nRT/N = m<c^2>
m<c^2> = 3RT / Na

KE = 1/2mv^2
KE = 1/2m<c^2>

1/2M<c^2> = 3RT / Na

k = R / Na (Boltzmann constant)

1/2 m<c^2> = 3/2kT

KE = 3/2kT -> the kinetic energy of only one molecule of gas

Question 28

What does KE = 3/2kT suggest

Answer 28

the mean kinetic energy of an ideal gas molecule is proportional to its thermodynamic temperature

Question 29

definition of translational kinetic energy

Answer 29

the energy a molecule has as it moves from one point to another

Question 30

Calculating root mean squared speed

Answer 30

Imagine three molecules with speeds 10, 20 and 30 m s−1

mean speed <c> = 10+ 20 + 30 / 3 = 20ms^-1</c>

mean square speeds = 10^2 + 10^2 + 30^2 / 3 = 467 ms^-1

√ <c^2> = √ 467 = 22ms^-1