Second order Reaction

A reaction is said to be the second order if its rate is determined by the variation of two concentration terms or rate of the reaction is proportional to the second power of the concentration of a single substance.

In general, the second order reaction may be of two types:

1. When the concentration of the reactants is same,


A + A \to \text{Products}


2. When the concentration of the reactants is different,


A + B \to \text{Products}


 Case I: When both reactants have equal concentration.

k = \dfrac{1}{t}.\dfrac{x}{a(a- x)}


Case II: When both reactants have different concentrations


\underset{a- x}{A} + \underset{b- x}{B} \to \underset{x \hspace{10mm}\text{after time t}}{\text{Products}} \\[3mm] \text{than} \hspace{3mm} k = \dfrac{2.303}{t(a- b)} \log_{10} \dfrac{b(a- x)}{a(b- x)}


Characteristics of Second Order Reactions

(i)                  \text{Rate} = k [\text{Reactant}]^2

(ii)                k = \dfrac{1}{ta} \times \dfrac{x}{a- x}

(iii)               t_{1/2} = \dfrac{1}{ak} \text{or} t_{1/2} \propto (a)^{-1}

(iv)              Unit of k = L mol^{-1} time^{-1}

(v)                Examples:

2NO \to 2NO + O_2 \\[3mm] 2N_2O \to 2N_2 + O_2 \\[3mm] C_2H_4 + H_2 \to C_2H_6 \\[3mm] S_2O^=_8 + 2I^- \to 2SO^=_4 + I_2 \\[3mm] CH_3COOC_2H_5 + NaOH \to CH_3COONa + C_2H_5OH \\[3mm] NO + O_3 \to NO_2 + O_2

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