15 : Ideal gases

Question 1

Define a mole

Answer 1

• The amount of substance that contains as many elementary entities as there are atoms in 0.012kg of carbon-12
• this is avogadro constant

Question 2

Total number of molecules in a substance equation

Answer 2

N = n x Na
Total number of molecules in a substance = number of moles of the substance x avogadro constant

Question 3

amount of matter equation

Answer 3

m = n x M
Amount of matter = molar mass x number of moles

Question 4

Assumptions

Answer 4

• very large number of molecules moving in random directions at random speeds
• occupy negligible volume compared to volume of container
• collisions are perfectly elastic
• electrostatic forces are negligible apart from during collisions

Question 5

total change in momentum

Answer 5

when a single atom collides with container wall elastically peed does not change goes from +mu to -mu so total change is -2mu

Question 6

pressure and volume

Answer 6

• temperature and mass remain constant
• pressure is inversely proportional to volume

Question 7

pressure and temperature

Answer 7

• volume and mass remain constant
• pressure is directly proportional to temerpature
• T in kelvin

Question 8

estimating absolute zero

Answer 8

• extrapolate p/T graph x-axis intercept is absolute zero
• T in celsius

Question 9

Maxwell-Boltzmann distribution

Answer 9

• at any temperature the random motion and collision of particles means some are travelling very fast whilst others are barely moving.
• the range of speeds at a given temp is the distribution

Question 10

temperature and distribution

Answer 10

Changing temperature of the gas changes the distribution. the hotter the gas the greater range of speeds. the modal speed nd the r.m.s speed increase and the distribution becomes more spread out

Question 11

Boltzmann constant

Answer 11

molar gas constant divided by avogadro constant

Question 12

particle speeds at same temperatures

Answer 12

• at a given temperature the molecules of different gases have the same average kinetic energy
• the molecules have different masses
• higher masses = smaller speeds

Question 13

why is helium not in earth’s atmosphere

Answer 13

• small mass and therefore high speed
• when molecule has a greater speed than the r.m.s speed
• higher speed then escape velocity of 11kms-1 so can escape earths atmosphere

Question 14

internal energy of an ideal gas

Answer 14

• sum of kinetic and potential energies
• assumption - electrostatic forces are negligible except during collisions.
• thus no electrical potential energy in an ideal gas
• internal energy is just kinetic energy

Question 15

Temp increases, oven isn’t sealed show that internal energy stays the same

Answer 15

• The atmospheric pressure of the oven is constant at 1E5
• since p=F/A force exerted on the walls which is equal to rate of change in momentum
• higher oven temperature means higher average kinetic energy leading to more frequent collisions with greater momentum leading to a greater force
• number of molecules in oven must decrease to keep pressure constant
• pV=NkT thus T = (Pv)/(Nk)
• total internal energy is given by 3NkT/2 thus T=2E/(3Nk)
• rearrange E=3pV/2
• showing that the internal energy E depends on pressure and volume only and therefore is independent of temperature.

Question 16

Newtons law and pressure

Answer 16

• free to move with constant random motion wih no forces of attraction = 1st law move with constant velocity
• particles collide with the walls it exerts a force on the wall = newtons 3rd law wall exerts an eual and opposite force on particle
• size of force = 2nd law f=rate of change in momentum = 2mu
• significant number of particles all colliding at any given moment