The reaction `SO_2 Cl_2 hArr SO_2 + Cl_2` is a first order gas reaction with `t_(1//2) = 3.15 xx 10^(4) s `at `320^@ `C. What percentage of `SO_2 Cl_2` is decomposed on heating this gas for 90 minutes ?

Answer

`11.2 %`

Explanation

`t_(1//2) = 3.15 x 10^4 s`
` k=( 0.693 )/(t_(1//2)) = (0.693 )/( 3.15 xx 10^4 ) s^(-1) = 2.2 xx 10^(5) s^(-)`
` t= 90 xx 60 = 5400 s `
Now ` t=( 2.303 )/(k) log "" (a)/((a-x))`
` 5400 s = ( 2.303)/( 2.2 xx 10^(-5)) log"" (a)/((a-x))`
` log ""(a)/((a-x)) = ( 5400 xx 2.2 xx 10^(-5))/( 2.303 ) = 0.0516`
` (a)/((a-x))`=antilog `0.0516 = 1.1262 `
on solving ,` a= 1.1262 (a-x) or a= 1.262 a - 1.1262 x `
` or 1.1262 x = 0.1262 or (x)/(a) = ( 0.1262 )/(1.1262 ) = 0.1120 `
if `a=100 ,x=0 .1120 xx 100 = 11.20 % `