The rate constant for an isomerization reaction, `A rarr B` is `4.5 xx 10^(-3) min^(-1)`. If the initial concentration of `A` is `1 M`, calculate the rate of the reaction after `1 h`.

Explanation

`A to B`
`{:("At t = 0",1M,0),("After 1h",(1-x)M,xM):}`
Rate of reaction after 1 h = k(1 – x) ...(i)
For the calculatinof 1 – x, first order kinetic equation is used as follows :
`k = 2.303/t log""([A]_0)/([A]_1)`
`or 4.5 xx 10^(-1) "min"^(-1)=2.303/(1xx60)log_10(1)/((1-x)) or log""(1)/((1-x)) = (4.5xx 10^1)/2.303 = 0.1172`
`:. 1/(1-x)=1.310`
`:. (1-x) = 0.7633 M`
Rate of reaction 1 h
`= 4.5 xx 10^(-3) xx 0.7633 = 3.435 xx 10^(-3) M "min"^(-1)`