# Third Order Reaction

A reaction is said to be of third order if the rate is determined by the variation of three concentration terms. In other words, the minimum number of molecules necessary for the reaction to take place is three.

There may be three different cases in third order reaction.

(i)   All the three species have equal concentrations.

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

(ii)   Two species have equal concentrations and one different.

$A + A+ B \to \text{Products} \\[3mm] -\dfrac{dx}{dt} = k[A]^2[B]$

(iii)    All three species have unequal concentrations.

$A + B + C \to \text{Products} \\[3mm] -\dfrac{dx}{dt} = k[A][B][C]$

Characteristics of Third Order Reactions:

(i)                  $\text{Rate} = k[\text{Reactant}]^3$

(ii)                $k = \dfrac{x(2a- x)}{2ta^2(a-x)^2}$ [when concentration are same]

(iii)               $t_{1/2} = \dfrac{3}{2ka^2} \text{or} t_{1/2} \propto (a)^{-2}$

(iv)              Unit of $k = L^2 mol^{-1} time^{-1}$

(v)                Examples:

$Fe^{3+} + 3I^- \to FeI_3 \\[3mm] 2Fe^{3+} + Sn^{++} \to 2Fe^{++} + Sn^{4+} \\[3mm] 2NO + Cl_2 \to NOCl \\[3mm] 2NO + Br_2 \to 2NOBr \\[3mm] 2NO + H_2 \to N_2O + H_2O \\[3mm] 2NO + O_2 \to 2NO_2$

Some Facts About Order of Reaction

• Order of reaction is determined from slowest step of reaction.
• It is an experimental value
• Some examples of fractional order are as follows:

(i)      $COCl_2 \to CO + Cl_2$

$\text{rate} = k[COCl]^{3/2}$

Order = 3/2 = 1.5

(ii)         $H_2 + Br_2 \to 2HBr$

$\text{Rate} = k[H_2]^1[Br_2]^{1/2}$

Order = 1.5

(iii)          $CH_3CHO \to CH_4 + CO$

$\text{Rate} = k[CH_3CHO]^{3/2}$

Order = 3/2 = 1.5

• Reactions of higher order [>3] are very rare due to very less chances of many molecules to undergo effective collisions.
• $2O_3 \to 3O_2$

Here, Rate = $k[O_3]^2 . [O_2]^{-1}$

So order with- respect to $O_2$ is -1 (i.e., negative)

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