Question

1. arrange the following gases in order of increasing average molecular speed at 25°c. n₂, o₂, co₂, he a. co₂ < o₂ < n₂ < he b. n₂ < o₂ < co₂ < he c. he < o₂ < co₂ < n₂ d. o₂ < n₂ < he < co₂ e. all the gases have the same average molecular speed at 25°c.

Explanation:

The average molecular speed of a gas is inversely proportional to the square root of its molar mass (at a given temperature). The formula for the root - mean - square speed is \(v_{rms}=\sqrt{\frac{3RT}{M}}\), where \(R\) is the gas constant, \(T\) is the temperature, and \(M\) is the molar mass.

• Molar mass of \(CO_2\): \(M_{CO_2}=(12 + 2\times16)\space g/mol=44\space g/mol\)
• Molar mass of \(O_2\): \(M_{O_2}=2\times16\space g/mol = 32\space g/mol\)
• Molar mass of \(N_2\): \(M_{N_2}=2\times14\space g/mol=28\space g/mol\)
• Molar mass of \(He\): \(M_{He}=4\space g/mol\)

Since \(M_{CO_2}>M_{O_2}>M_{N_2}>M_{He}\), the order of average molecular speed (inversely proportional to \(\sqrt{M}\)) is \(CO_2 < O_2

Answer:

A. \(CO_2 < O_2