How are integrated rate laws used to determine reaction

Solution 29P

Here we have to explain how are integrated rate laws used to determine reaction order and what is the order in reactant if a plot of

(a)   The natural logarithm of [reactant] vs. time is linear

(b)   The inverse of [reactant] vs. time is linear

(c) [Reactant] vs. time is linear

Step 1

The integrated rate law is used to determine the order of reaction by plotting graphs. When the plot of [reactant] versus time is linear, the order of the reaction is zero.

Thus for zero order reaction the integrated rate law is,

Here [A]t is the concentration of A at time t and [A]0 is the concentration at time t=0, -k is the slope.

If the plot of ln [reactant] versus time is linear, the order of the reaction will be 1st order.

Thus for 1st order reaction the integrated rate law is,

The plot of  ln[A]t versus ln [A]0 will give a linear plot with slope -k.

The order of a reaction will be second order if the plot of inverse concentration versus time is linear. Thus the rate will be written as,