Question

One mole of hydrogen gas in its molecular form is heated from temperature of $200K$ to $3000K$ in a box of volume $2.05m^3$. It is observed that the gas gets converted to a gas of hydrogen atoms. Considering all gases to be ideal, the final pressure would be _____ times the initial pressure.

Answer 1

Answer: 30

When the $H_2$ molecule breaks into atoms, the number of moles would become twice.
$\therefore n_2=2n_1$
From ideal gas equation,
$PV=nRT$
$\because$ Volume (V) of the container is constant,
$\therefore P\propto nT$
$\therefore \frac{P_2}{P_1}=\frac{n_2{T}_2}{n_1{T}_1}$
$=\frac{\left(2n_1\right)(3000)}{n_1(200)}=30$
$\therefore P_2=30P_1$