1 mole of `H_(2)` gas in contained in a box of volume V 1.00 `m^(3)` at T =300 K. 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)

Options

A. same as the initial pressure
B. 2 times the initial pressure
C. 10 times the initial pressure
D. 20 times the initial pressure

Answer

D

Explanation

For an ideal gas, PV = nRT
where n = number of moles.
As the volume of the container (box) remains constant,
`PpropnT" "....(1)`
When the `H_(2)` molecules are converted into hydrogen atoms, number of moles is doubled i.e. `n_(2)=2n_(1)`.
`thereforeP_(2)/P_(1)=(n_(2)T_(2))/(n_(1)T_(1))=(2n_(1))/(n_(1))xx300/300=20`
`thereforeP_(2)=20P_(1)`