The decompoistion of `Cl_(2)O_(7)` at `400 K` in gas phase to `Cl_(2)` and `O_(2)` is a first order reaction.
a. After `55 s` at `400 K`, the pressure of `Cl_(2)O_(7)` falls form `0.062` to `0.044 atm`. Calculate `k`.
b. Calculate the pressure of `Cl_(2)O_(7)` after `100 s` of decompoistion.

Explanation

`{:(,Cl_(2)O_(7),rarr,Cl_(2)+,(7)/(2)O_(2)),(Initial,a,,0,0),("At eq",a-x,,x,(7)/(2)x):}`
(a) `a prop 0.062 (a-x) prop 0.044`
`k = (2.303)/(55) log. (0.062)/(0.044)`
`= (2.303)/(55) xx 0.1489 = 6.23 xx 10^(-3) s^(-1)`
(b) `t = 100s, (a-x) prop P`
`:. 6.23 xx 10^(-3) = (2.303)/(100) log.(0.062)/(P)`
`:. P = 0.033 atm`