Chapter 17, Problem 65A

In a gaseous mixture of hydrogen and oxygen molecules, both with the same average kinetic energy, which molecules move faster on average?

To determine

To identify: The molecule that will moves faster on average having same kinetic energy

Answer to Problem 65A

The hydrogen molecule moves faster on average than the oxygen molecule.

Explanation of Solution

Given:

Oxygen molecular mass is 16 amu

Hydrogen molecular mass is 1 amu

Formula used:

The RMS speed of the molecule is given as follows:

  $v_{\text{RMS}}=\sqrt{\frac{3kT}{m}}$

Here, $k$ is the Boltzmann’s constant, $T$ is the temperature and $m$ is the mass.

Calculation:

The above expression indicates that the end speed of molecule is inversely proportional to the molecular mass. Therefore, molecule having lower mass has greater speed and molecule with greater mass has lower speed.

Oxygen molecular mass is 16 amu and hydrogen molecular mass is 1 amu. This implies that oxygen has 16 times the mass of the hydrogen molecule.

Conclusion:

Thus, hydrogen molecule moves faster on average than the oxygen molecule.