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 time the pressure initially
C. 10 times the pressure initially
D. 20 times the pressure initially

Answer

D

Explanation

Consider the diagram, when the molecules bracks into atoms, the number of moles would become twice. Now, by ideal gas equation ltbtgt 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 ecomes twice of initial, so `n_(2)= 2n_(1)So," "p propnT`
`rArr" "(P_(2))/(p_(1))=(n_(2)T_(2))/(n_(1)T_(1))=((2n_(1))(3000))/(n_(1)(300))=20 rArr p_(2)=20p_(1)`
Hence, final pressure of the gas would be 20 times the pressure initially.