Question

What is the ratio of kinetic energies of \(3 \, {g}\) of hydrogen and \(4 \, {g}\) of oxygen at a certain temperature?

• A. \(3:4\)
• B. \(6:1\)
• C. \(12:1\)
• D. \(1:12\)

Hint:

Remember, the kinetic energy of gases at a specific temperature is the same for all gases, provided the number of molecules is the same. Hence, it scales with the number of moles.

Answer 1

The Correct Option is C

The kinetic energy of an ideal gas at a particular temperature is directly proportional to the number of moles, and not dependent on the mass directly. The molar masses of hydrogen and oxygen are \(2 \, \text{g/mol}\) and \(32 \, \text{g/mol}\) respectively. \[ \text{Moles of hydrogen} = \frac{3}{2} \, \text{mol}, \quad \text{Moles of oxygen} = \frac{4}{32} = 0.125 \, \text{mol} \] \[ \text{Ratio of kinetic energies} = \frac{\text{Moles of hydrogen}}{\text{Moles of oxygen}} = \frac{\frac{3}{2}}{0.125} = 12:1 \]