# 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,

I.e.,

$A + A \to \text{Products}$

2. When the concentration of the reactants is different,

I.e.,

$A + B \to \text{Products}$

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:

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

Related posts:

1. Zero Order Reaction Zero Order Reaction If the rate of reaction is independent...
2. Order of Reaction The order of reaction may be defined as the sum...
3. Rate constant or Specific Reaction rate According to collision theory, the rate of the reaction is...
4. Rate of reactions The rate (speed or velocity) of the reaction may be...
5. Factors Influencing Rate of Reaction Some important factors which influence the rate of reaction are...