The Kinetic Theory of Gases

Question 1

Avogadro’s Number

Answer 1

N = 6.02 × 10^(23) mol ^(-1)

Question 2

relationship of molar mass M to mass m

Answer 2

M = mN

N is the Avogadro’s number

Question 3

number of moles n contained in a sample of Msam consisting of N molecules

Answer 3

n = N/NA = Msam/M = Msam/mNA

Question 4

Ideal Gas

Answer 4

pV = nRT
note: R = 8.31 J/mol × K

pV = NkT
note: k is the boltzman constant
k = R/NA = 1.38 × 10^(-23) J/K

Question 5

Work in an Isothermal Volume Change

Answer 5

W = nRT ln (Vf/Vi)

Question 6

Pressure exerted by n moles

Answer 6

p = (nMv^2(rms)/3V

vrms = sqrt(v^2 avg)
vrms is the root-mean-squared speed

Question 7

Root-mean-squared-speed

Answer 7

vrms = sqrt (3RT/M)

Question 8

Average Translational KE

Answer 8

Kavg = 3/2 kT

Question 9

Mean Free Path

Answer 9

λ = 1/[sqrt(2) πd^2 N/V]

Question 10

Maxwell Speed Distribution P(v)

Answer 10

P(v) = 4π (M/(2πRT)) ^(3/2) v^2 e^(-Mv^2/2RT)

Question 11

Distribution (average speed)

Answer 11

v avg = sqrt[ (8RT)/(πM)]

Question 12

Distribution ( most probable speed)

Answer 12

v p = sqrt[ (2RT)/(M)]

Question 13

Molar specific heat at constant volume

Answer 13

Cv = Q/(nΔT) = ΔEint/nΔT

Question 14

Molar specific heat for an ideal monatomic gas

Answer 14

Cv = 3/2 R = 12.5 J/mol K

Question 15

Molar specific heat at constant pressure

Answer 15

Cp = Q/(nΔT)
Cp = Cv + R

Question 16

molar specific heat ideal gas

Answer 16

Eint = nCvT

Question 17

Degrees of freedom and Cv

Answer 17

Cv = (f/2) R = 4.15f J/mol K

for monatomic gases f = 3 three translational degrees;
for diatomic gases f = 5 three translational and two rotational defrees