Question

How will you represent first order reactions graphically?

Answer 1

(i) The differential rate law for the first-order reaction A→P is:
The equation is of the form y = mx + c. A plot of rate versus [A]_t is a straight line passing through the origin. The slope of a straight line = k.

Variation of rate with [A]:

(ii) The integrated rate law is

`k = 2.303/t log_10  [A]_0/[A]_t`

On rearrangement. the equation becomes

`(kt)/2.303 = log_10[A]_0 - log_10[A]_t`

Hence, 

The equation is of the straight line. A graph of log₁₀

`A_0/([A_t]) "versus t gives a straight line with slope"  k/2.303`  and y-axis intercepts as log₁₀[A]₀ 

A plot showing log `[At]_t/[A]_0` vs time

(iii) Rearranging the integrated rate law equation. we get

The equation has a straight-line form y = mx. Hence, the graph of `log_10  [A]_0/[A]_t`  versus t is a straight line passing through the origin.