The following first order reaction takes places at `410 K`:
`2CO(g) rarr CO_(2)(g)+C(s)`
The total pressure at the end of `401 s` after starting with pure `CO(g)` is found to be `0.313 atm`. At the time the reaction is `100%` complete, the total pressure is found to be `0.1645 atm`. Find
(a) The rate constant of the reaction.
(b) The pressure of `CO` after `401 s`.
Note: Here `C` is the solid form.

Explanation

(a) `2CO(g) rarr CO_(2)(g) + C(s)`
or
`Co(g) rarr (1)/(2)CO_(2)(g) + (1)/(2)C(s)`
`{:("Initial",a,,0,0),("At time t",a-x,,(x)/(2),0),([100%]decompoistion,0,,(a)/(2),-):}`
`(a)/(2) = 0.1645 rArr a = 0.329`
Total moles at time `t`
`a - x + (x)/(2) = 0.313`
`:. x = 0.032`
`k = (2.303)/(t)log.(a)/(a-x)`
`= (2.303)/(401) log.(0.329)/(0.329 - 0.032)`
`= (2.303)/(401)log.(0.329)/(0.297)`
`= (2.303)/(401) xx 0.0443 = 2.5 xx 10^(-4) s^(-1)`
(b) Pressure of `CO` after `401 s` is `a-x`
`= 0.329 - 0.320 = 0.297`