Question

Given below are two statements :
Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2v$.
In the light of the above statements, choose the correct answer from the options given below :

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

Answer: (D)

$\left[P_{avg}=0\right]$ (due to random motion)
$v_{rms}=\sqrt{\frac{3RT}{M}}$
$T_{\text{ new }}=2T$
$M_{\text{new }}=\frac{M}{2}$
$\frac{v_{\text{new }}}{v}=\frac{\sqrt{\frac{2T}{M/2}}}{\sqrt{\frac{T}{M}}}$