Question

At what temperature do oxygen molecules have the same average speed as helium atoms (M=4.00g/mol) have at 300 K?

a) 1200 K
b) 600 K
c) 150 K
d) 75 K

Answer 1

The average speed of oxygen molecules will be the same as the average speed of helium atoms at a temperature of 150 K.

Step-by-step explanation:

The average speed of gas molecules is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass of the gas. The formula relating temperature, molecular speed, and molar mass is given by v = sqrt((3kB*T) / (m)), where v is the average speed, kB is the Boltzmann constant, T is the temperature in Kelvin, and m is the molar mass in kilograms per mole.

Given that the average speed of helium atoms at 300 K is 600 m/s and the molar mass of helium is 4.00 g/mol, we can solve for the temperature for oxygen molecules to have the same average speed:

v(Oxygen) = v(Helium)
sqrt((3kB*T(Oxygen)) / (M(Oxygen))) = sqrt((3kB*T(Helium)) / (M(Helium)))
T(Oxygen) = ((M(Helium) * T(Helium)^2 * M(Oxygen)) / (M(Oxygen) * T(Helium)^2))

Plugging in the given values, we get:

T(Oxygen) = ((4.00 g/mol * (300 K)^2) / (32.0 g/mol * (600 m/s)^2))

T(Oxygen) = 150 K

Therefore, the correct option is c) 150 K.