Derive an expression for the rate constant of a first order reaction. Give its units.


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



Equation (ii) is the required expression.

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Unit of k:
From equation (ii) we found that the unit of k depends on the unit of t . The unit of k may be s-1, min-1, h-1, day-1 and so on.

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