Following data were obtained for the catalytic decomposition of ammonia :

Find the order of reaction.

Answer

second order

Explanation

`(i) (t_(1//2)) // (t_(1//2)) = (p_2 //P_1)^(n-1) or ((3.52 )/(1.92 ) )= ((100 )/(50 ) )^(n-1)`
Taking logs ` log 3.52 - log 1.92 = ( n-1) log 2`
` or 0.5465 - 0.2833 = (n-1) xx 0.3010 `
` or ( 0.2632 )/( 0.3010 ) n=1 or n=1 + 0.874 = 1.874 ~~ 2`
`(ii) (t_(1//2))_1 //(t_(1//2) )_2 = (p_2 //P_1 ) ^(n-1) or ( 1.92 )/( 1 )=((200)/(100))^(n-1)`
` or log 1.92 = (n-1) log 2 or 0.2833 = (n-1) ( 0.3010 )`
` therefore (n-1) = ( 0.2833 )/( 0.3010 ) = 0.941 )`
or `n=1 + 0.941 = 1.941 ~~ 2`
hence , the order n in both cases is 2.