Question

Derive an expression for the first order rate constant

Answer 1

Explanation:

Let us consider a first order reaction,

A → product

Suppose at the beginning of the reaction, that is, when t=0, the concentration of A is amolL and when t=t, the concentration of A is (a-x)molL.

For a first order reaction, the rate of reaction,



where k is the rate constant.



integrating,





Here, c is the constant of integration.

At, t=0, x=0 ; then from equation (i) we have,

putting the value of c in equation (i), we get,

ln a – ln(a-x) = kt.

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