derive an expression for rate constant of ist order reaction , write the unit of K.

Question

Derive an expression for rate constant of fist order reaction , write the unit of K.

Answer 1

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 amol L^-1 and when t = t, the concentration of A is (a-x)mol L^-1.  

For a first order reaction, the rate of reaction,

Here, c is the constant of integration.

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

c = -In a  

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

ln a – ln(a-x) = kt

Equation (ii) is the required expression.

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.