Question

Explain first order reaction with example.

Hint:

Rate depends on the first power of one reactant, rate = k[A]; recall the integrated form and an example like N2O5 decomposition.

Answer 1

Step 1: Definition. A first order reaction is a reaction whose rate depends on the concentration of only one reactant raised to the power one. If a reactant is \(A\), then
\[ \text{Rate} = k[A]^{1} = k[A] \]
where \(k\) is the rate constant.
Step 2: Integrated rate law. On integrating the above expression, the rate constant of a first order reaction is given by
\[ k = \frac{2.303}{t}\log\frac{[A]_0}{[A]} \]
where \([A]_0\) is the initial concentration and \([A]\) is the concentration after time \(t\).
Step 3: Characteristics. The unit of \(k\) is \( s^{-1} \) (time\(^{-1}\)), and the half-life \( t_{1/2} = \dfrac{0.693}{k} \) is independent of the initial concentration.
Step 4: Example. Decomposition of dinitrogen pentoxide:
\[ N_2O_5 \rightarrow 2NO_2 + \tfrac{1}{2}O_2, \quad \text{Rate} = k[N_2O_5] \]
Other examples are the decomposition of \(H_2O_2\) and all radioactive disintegrations.