The reaction `SO_(2)Cl_(2) overset(k_(1))rarr SO_(2)+Cl_(2)` is a first order reaction with `k_(1) = 2.2 xx 10^(-5) s^(-1)` at `575 K`. What percentage of `SO_(2)Cl_(2)` will get decomposed in `90 min` when the reaction is carried out at `575 K`.

Explanation

Since the reaction is of the first order (given), `k=(2.303)/(t)log""(a)/(a-x)`
Here, we are given that `k=2.2xx10^(-5)"sec"^(-1)" "," "t=90" minutes "=90xx60=5400" sec".`
`:.2.2xx10^(-5)s^(-1)=(2.303)/(5400s)log""(a)/(a-x)" or "log""(a)/(a-x)=0.0516" or "(a)/(a-x)="antilog "(0.0516)=1.127.`
or `" "a=1.127a-1.127x" or "0.127a=1.127x`
`:." "(x)/(a)=(0.127)/(1.127)=0.113" or "%" decomposed "=0.113xx100=11.3%.`