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.

Options

A. `5.2 xx 10^(-4) sec^(-1), 0.05 atm`
B. `6.2 xx 10^(-3) sec^(-1), 0.033 atm`
C. `5.8 xx 10^(-3) sec^(-1), 0.44 atm`
D. `4.6 xx 10^(-3) sec^(-1), 0.005 atm`

Answer

B

Explanation

The equation for first order reaction is
`K = (2.303)/(t)log((a)/(a-x))`
(i) Here `a = 0.062 a-x = 0.044`
`k = (2.303)/(55)"log"(0.062)/(0.044) = 6.2 xx 10^(-3) sec^(-1)`
(ii) Here we are to find the value of `a-x`
`6.20 xx 10^(-3) = (2.303)/(100) "log"(0.062)/(a-x)`
`"log"(0.062)/(a-x) = 2.69 xx 10^(-1)`
`(0.062)/(a-x) = 1.86`
`a-x = (0.062)/(1.80) = 0.033 atm`