Question

The root mean square velocity of hydrogen molecules at 300 K is 1930 meters/second. The velocity of oxygen molecules at 1200 K will be:

• A. 582 m/s
• B. 656 m/s
• C. 586 m/s
• D. 366 m/s

Hint:

The velocity of molecules is proportional to the square root of the temperature.

Answer 1

The Correct Option is C

Step 1: Use the equation for root mean square velocity.
The root mean square velocity \( v_{\text{rms}} \) is related to temperature by the equation: \[ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \] where \( k \) is Boltzmann's constant, \( T \) is temperature, and \( m \) is the mass of the molecule.

Step 2: Use the temperature ratio.
The velocity ratio for two gases is given by: \[ \frac{v_{\text{rms2}}}{v_{\text{rms1}}} = \sqrt{\frac{T_2}{T_1}} \] Substituting the values for hydrogen and oxygen, we get: \[ v_{\text{rms2}} = \sqrt{\frac{1200}{300}} \times 1930 = 586 \, \text{m/s} \]