# Calculus of a Single Variable: Reaction Kinetics

Description| How it works| Reaction Kinetics| Random WalkIn chemical reaction kinetics, we come across rate equations that are difficult to integrate analytically. Numerical integration can be used to handle such situations. Lets take an example.

Consider the homogeneous gas reaction A -> 3B, which has the following rate at a specified temperature and pressure:

-r

_{A}(mol/l.s) = CA

^{0.5}

If this reaction is carried out in a plug flow reactor, what is the space time needed for 90% conversion of a feed containing 50 % A and the rest inert gas ? Assume initial concentration = 1 mol/l

The answer for this is obtained by integrating the equation

[(1+X)/(1-X)]

^{0.5}from X = 0 to X = 0.9, where X is the conversion of A. Lets find the answer using the Function Analysis app.

The inputs to be keyed in are as follows:

Function : =SQRT((1+x)/(1-x))

Range: 0 to 0.9

Initial value: 0

The value of the integral is then read off from the graph. The answer is 1.684 sec.

Note that this integral can also be evaluated analytically, the integral = sin

^{-1}x - (1-x

^{2})

^{0.5}