Question

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

• A. 4 : 1
• B. 1 : 2
• C. 1 : 1
• D. 1 : 4

Answer 1

The Correct Option is A

Using the formula for the speed of sound, \(v = \sqrt{\frac{\gamma RT}{m}}\), we can write for hydrogen and oxygen: \[ \frac{v_{\text{H}_2}}{v_{\text{O}_2}} = \sqrt{\frac{m_{\text{O}_2}}{m_{\text{H}_2}}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4 : 1 \] Thus, the ratio is \(4 : 1\).

Answer 2

The root mean square (rms) speed of a gas molecule is given by:
\(V_{rms} = \sqrt{(\frac{3RT}{M})}\)
where k is the Boltzmann constant, T is the temperature, and m is the mass of the gas molecule.
Since the temperature of both oxygen and hydrogen gases is the same, we can write:\(\frac{V_{rms}O_2}{v_{rms}H_2} = \sqrt{\frac{mH_2}{mO_2}}\)
The molecular weight of hydrogen (H₂) is 2 grams per mole, while that of oxygen (O₂) is 32 grams per mole.
Substituting these values, we get:
\(\frac{V_{rms}O_2}{v_{rms}H_2} = \sqrt{\frac{32}{2}}=\sqrt{16}=4\)
Therefore, the ratio of the rms speed of oxygen gas molecules to that of hydrogen gas molecules is 4:1.
Hence, the answer is (A) \(\frac{1}{4}\).
Answer. A