Ideal gases

Question 1

Mole

Answer 1

Measurement of the amount of substance(number of atoms/molecules)
One mole = the amount of substance that contains as many elementary entities as there are atoms in 12g of carbon 12

Question 2

Avagadro’s constant

Answer 2

N/n (number of particles/number of moles) = 6.02 x10^23

Question 3

Molar mass

Answer 3

mass of one mole of a substance
M=m/n
molar mass= mass number (grams)

Question 4

Assumptions in kinetic model for an ideal gas

Answer 4

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

Question 5

Pressure when atoms collides with wall

Answer 5

F=change in momentum/t
F=2mu/time between collisions
The atom exerts an equal and opposite force on the wall
P=F/A

Question 6

Ideal gas laws

Answer 6

p is proportional to 1/v
p is proportional to T
pV/T = constant
pV= nRT
R=molar gas constant = 8.31

Question 7

Root mean square speed

Answer 7

square root of mean of velocity of each atom squared

Question 8

Derrivation of rms pressure equation

Answer 8

Considering one single particle in a cube LxLxL travelling at velocity c, mass m
change in momentum = 2mc
change in time = 2L/c
F= mc^2/L
For N particles - each particle exerts F of mc^2/L
1/3 hit each pair of walls
F= 1/3 (Nmc^2)/L
P= F/A = F/L^2 = 1/3 (Nmc^2)/L^3 = 1/3(Nmc^2)/v

pV= 1/3 Nm c^2

Question 9

Maxwell Boltzman distribution (of particle speeds)

Answer 9

Bell curve shape
Most probable speed < mean speed < root mean square speed
When temperature increases, there is a greater range and the distribution becomes more spread out

Question 10

The Boltzman constant(k)

Answer 10

k=R/NA (avagadro’s constant) = 1.38 x10^-23

Question 11

pV=NkT derrivation

Answer 11

R=KNa
pV= nRT
pV = nkNaT
pV=NkT

Question 12

Relationship between kinetic energy and temp

Answer 12

pV =1/3 Nmc^2
pV =NkT
1/3mc^2 = kT
1/2mc^2 =3/2KT
Ek is directly proportional to temperature in kelvin

Question 13

internal energy of gases

Answer 13

electrostatic forces are negligible so potential energy =0
internal energy = kinetic energy
internal energy is proportional to temperature