Chemistry - Ideal Gas Question with Solution | TestHub

Initial temperature = $300K$.

Let the new temperature corresponding to t℃ be $TK$.

Let the number of moles present at $TK$ be $n$.

Moles of air escaped at $TK$ = $n/3$.

So, the number of moles at $300K$ = $n+\frac{n}{3}=\frac{4n}{3}$.

Since volume and pressure are kept constant,

we can use the relationship:

$\frac{n_1}{n_2}=\frac{T_2}{T_1}$

$\frac{4n}{3}\times 300=nT$

$T=400K$

Now, rms velocity :

$v_{rms}=\sqrt{\frac{3RT}{M}}==\sqrt{\frac{3\times 8.314\times 400}{28.8\times 10^{-3}}}=588.6m{s}^{-1}$