The root-mean-square velocity of a gas molecule is

Question

The root-mean-square velocity of a gas molecule is

a) directly proportional to the square root of its temperature in K

b) inversely proportional to its kinetic energy

c) directly proportional to the square root of its mass

d) inversely proportional to the square of its mass

e) directly proportional to the gas constant, R

Please provide an explanation for the answer and/or why the other answers are wrong. Thank you in advance.

Answer 1

rms = √3RT/M

where rms = root mean square velocity; R=gas constant; T=temperature in K; M=molar mass

a) true because T is in the numerator

b) false because kinetic energy is directly proportional to T

c) false because mass of a mole is in the denominator for it's inversely proportional

d) true; see explanation for (c)

e) true because R is in the numerator although saying it is directly proportional to a constant doesn't really make a lot of sense.