1 mole of `H_(2)` gas is contained in box of volume `V= 1.00 m^(3) at T = 300 K`. The gas is heated to a temperature of T = 3000 K and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal)

Options

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

Answer

D

Explanation

Consider the diagram, when the molecules breaks into atoms, the number of moles would become twice. Now, by ideal gas equation
P= Pressure of gas n= Number of moles
R = Gas constant, T = Temperature
`pV = nRT`
As volume (V) of the container is constant.

As gases breaks number of moles becomes twice of initial, so `n_2 = 2n_1`
So, `p prop nT`
`rArr p_2/p_1 = (n_2 T_2)/(n_1T_1) = ((2n_1)(3000))/(n_1 (300)) = 20`
`rArr p_2 = 20 p_1`
Hence, final pressure of the gas would be 20 times the pressure initially.