Molecular speeds: A 5.0-liter gas tank holds 1.7 moles of monatomic helium (He) and 1.10 mole of diatomic oxygen (O₂), at a temperature of 260 K. The ATOMIC masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. What is the ratio of the root-mean-square (thermal) speed of helium to that of oxygen?

Question

Quizplus · Accepted Answer

The root-mean-square (rms) speed of a gas molecule is given by the following equation:

Urms = √(3RT/M)

where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

For each gas, we can calculate the rms speed using the equation above. Then, we can find the ratio of the rms speeds of helium to oxygen:

(urms)he / (urms)O2 = [√(3RT/Mhe)] / [√(3RT/MO2)]

= √(MO2/Mhe)

where MO2 and Mhe are the molar masses of oxygen and helium, respectively.

MO2 = 2 x 16.0 g/mol = 32.0 g/mol
Mhe = 4.0 g/mol

(urms)he / (urms)O2 = √(32.0/4.0) = 2.83

Therefore, the ratio of the rms speed of helium to oxygen is 2.83, which is closest to answer choice C (2.8).

Molecular Speeds: a 5