A reaction `SO_(2)Cl_(2) to SO_(2)+ Cl_(2)` is first order reaction with half life period `3.15 xx 10^(4)`s at `320^(@)`C. What percentage of `SO_(2)Cl_(2)` would be decomposed on heating at `320^(@)`C for 90 minutes?

Explanation

`k=0.693/t_(1//2) = 0.693/(3.15 xx 10^(4)s) = 2.2 xx 10^(-5)sec^(-1)`
For the first order reaction, `t=2.303/k log a/(a-x)`
`k=2.2 xx 10^(-5)s^(-1),t=90` min
`=90 xx 60 = 5400s`
`(5400 s) = (2.303)/(2.2 xx 10^(-5)s^(-1)) log a/(a-x)`
`a/(x-x) = (5400 s xx 2.2 xx 10^(-5)s^(-1))/(2.303) = 0.0516`
or `a = 1.12 a - 1.126 x`
`=0.112 xx 100 = 11.2%`