The partial pressures of `CH_(3) OH, CO` and `H_(3)` in the equilibrium mixture for the reaction
`CO _((g)) + 2 H _(2 (g)) hArr CH _(3) OH _((g))`
`at 427 ^(@)` are 2.0, 1.0 and.0.1 atm, respectively. The value of `K_(P)` for the decomposition of `CH _(3) OH ` to CO and `H _(2)` is

Options

A. `1 xx 10^(2)` atm
B. `4 xx 10^(2)` atm
C. `5 xx 10^(-3)` atm
D. `5 xx 10^(3)` atm

Answer

C

Explanation

`CO + 2H_(2) hArr CH_(3)OH, K_(p) = ((p_(CH_(3)OH)))/((p_(CO))(p_(H_(2)))^(2)) = (2)/((1)(0.1)^(2)) = 200`
Since the decomposition reaction is reverse of the given reaction, that is,
`CH_(3)OH hArr CO + 2H_(2), " "K._(p) = (1)/(K_(p)) = (1)/(200) = 5 xx 10^(-3)` atm