The rate constant for an isomerisation reaction, `ArarrB " is " 4.5xx10^(-3)"min"^(-1).` If the initial concentration of A is 1(M), calculate the rate of the reaction after 1 h.

Explanation

From the unit of rate constant `("Min"^(-1))` , it is evident that the reaction is a first order reaction. For a first order reaction `ArarrB`,
reaction -rate = k [A] and `t=(2.303)/(k)log.(a)/(a-x)`
Here, a = 1 (M) , k = `4.5xx10^(-3)"min"^(-1) and t=60"min"`

`therefore1xx60min=(2.303)/(4.5xx10^(-3))log.(1)/(1-x)`
or , `log.(1)/(1-x)=0.1172" or, " (1-x)=0.7634(M)`
`therefore` Concentration of the reactant after 1 h (=60min),
(1 - x)=0.7634(M)
`therefore` Rate of reaction after 1 h = [A] = k (1-x)
`=4.5xx10^(-3)xx0.7634(M)."min"^(-1)`
`=3.435xx10^(-3)(M)."min"^(-1)`