Heat and Thermodynamics 4 Question 30
32. At room temperature, the rms speed of the molecules of a certain diatomic gas is found to be $1930 m / s$. The gas is
(a) $H _2$
(b) $F _2$
(c) $O _2$
(d) $Cl _2$
Assertion and Reason
Mark your answer as
(a) If Statement I is true, Statement II is true; Statement II is the correct explanation for Statement I
(b) If Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
(c) If Statement I is true; Statement II is false
(d) If Statement I is false; Statement II is true
Show Answer
Solution:
- $v _{rms}=\sqrt{\frac{3 R T}{M}}$
Room temperature $T \approx 300 K$
$$ \begin{aligned} & \therefore \quad 1930=\sqrt{\frac{3 \times 8.31 \times 10^{3} \times 300}{M}} \\ & \therefore \quad M=2.0 g / mol \text { or the gas is } H _2 \text {. } \end{aligned} $$
