1 mole of H_2 gas is contained in a box of volume V = 1.00m^3 at … - Vidyadip

MCQ

$1$ mole of $H_2$ gas is contained in a box of volume $V = 1.00m^3$ at $T = 300K.$ The gas is heated to a temperature of $T = 3000K$ and the gas gets converted to a gas of hydrogen atoms. The final pressure would be $($considering all gases to be ideal$).$

✓
Same as the pressure initially.
B
$2$ times the pressure initially.
C
$10$ times the pressure initially.
D
$20$ times the pressure initially.

✓

Answer

Correct option: A.

Same as the pressure initially.

The situation is shown in the diagram, $H_2$ gas is contained in a box is heated and gets converted to a gas of hydrogen atoms. Then the number of moles would become twice.
According to gas equation,
$\text{PV = nRT}$

$P =$ Pressure of gas, $n =$ Number of moles
$R =$ Gas constant, $T =$ Temperature $\text{PV = nRT}$
As volume $(V) $of the container is constant.
Hence, when temperature $(T)$ becomes $10$ times, $($from $300K$ to $3000K)$ pressure $(P)$ also becomes $10$ times, as $P\ \alpha\ T.$
Pressure is due to the bombardment of particles and as gases break, the number of moles becomes twice of initial, so $n_2 = 2n_1$
So $P\ \alpha\ nT$
$\Rightarrow\frac{\text{P}_2}{\text{P}_1}=\frac{\text{n}_2\text{T}_2}{\text{n}_1\text{T}_1}=\frac{(2\text{n}_1)(3000)}{\text{n}_1(300)}=20$
$\Rightarrow\text{P}_2=20\text{P}_1$
Hence, final pressure of the gas would be $20$ times the pressure initially.

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