1. Tardigrade
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  3. Physics
  4. One mole of hydrogen gas in its molecular form is heated from temperature of 200 K to 3000 K in a box of volume 2.05 m 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.

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Q. One mole of hydrogen gas in its molecular form is heated from temperature of $200\, K$ to $3000\, K$ in a box of volume $2.05\, m ^{3}$. 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.

Kinetic Theory

Solution:

When the $H _{2}$ molecule breaks into atoms, the number of moles would become twice.
$\therefore n _{2}=2 n _{1}$
From ideal gas equation,
$PV = n RT$
$\because$ Volume (V) of the container is constant,
$\therefore P \propto n T$
$\therefore \frac{P_{2}}{P_{1}}=\frac{n_{2} T_{2}}{n_{1} T_{1}}$
$=\frac{\left(2 n_{1}\right)(3000)}{n_{1}(200)}=30$
$\therefore P_{2}=30 P_{1}$