Q.For a first order reaction $A \rightarrow B$, the rate constant is $x\ \text{min}^{-1}$. If the initial concentration of A is 0.01 M, the concentration of A after one hour is given by the expression.

A first order reaction has $\text{Rate}=k[A]^1$. Integrating $-d[A]/dt=k[A]$ gives $\ln\dfrac{[A]_0}{[A]}=kt$, or in base-10 form, $k=\dfrac{2.303}{t}\log\dfrac{[A]_0}{[A]}$ -- the single most-used formula in this chapter. Rearranged as $\ln[A]=-kt+\ln[A]_0$, a plot of $\ln[A]$ against time is a straight line with NEGATIVE slope $-k$, the standard test for first order behaviour. Real examples include decomposition of $N_2O_5$, $SO_2Cl_2$ and $H_2O_2$, and cyclopropane's isomerisation.

A genuinely second (or higher) order reaction involving two reactants can be made to BEHAVE as first order by taking one reactant in large excess -- a pseudo first order reaction. In acid-catalysed ester hydrolysis, $\text{Rate}=k[\text{ester}][H_2O]$ is truly second order, but with water in vast excess (often the solvent itself), $[H_2O]$ stays essentially constant, so $k[H_2O]=k'$ folds into a new constant and $\text{Rate}=k'[\text{ester}]$ is experimentally observed as first order.