Question

Write the condition under which a kinetic reaction is of first order. Give an example of such a reaction
\[
  {log\,2 = 0.3010} \\
  {log\,3{\text{ }} = {\text{ }}0.4771} \\
  {log\,5{\text{ }} = {\text{ }}0.6990}
\]

Answer 1

Hint:
Order of reaction: At a given temperature, the rate of a reaction at a particular instant is proportional to the product of the active masses of the reactants at that instant raised to powers which are numerically equal to the numbers of their respective molecules in the stoichiometric equation describing the reaction.
The sum of powers of concentration terms involved in rate law expression is called order of reaction.
If, for a reaction $aA + bB + cC \to dD$
If rate, $R = k{[A]^\alpha }{[B]^\beta }{[C]^\gamma }$
$\alpha + \beta + \gamma = order$

Complete step by step solution
If a bimolecular reaction the concentration of one of the reactants is taken in large excess, then in the rate equation, the concentration of that reactant is not taken into account. Then the reaction is termed first order reaction, since the concentration of one of the reactants is in large excess, it hardly changes, it does not affect the speed or rate of the reaction. It can be kinetically first order.
Eg. Hydrolysis of ester
$C{H_3}COO{C_2}{H_5} + {H_2}O\xrightarrow{{{H^ + }}}C{H_3}COOH + {C_2}{H_5}OH$
$Rate = K [C{H_3}COO{C_2}{H_5}][{H_2}O] (H_2O\,in\,excess)$
$\Rightarrow Rate = k[C{H_3}COO{C_2}{H_5}]$
The reaction is first order

Note:
Reactions whose actual order is different from that expected using rate law expression are called pseudo-order reactions,
\[\left( i \right){\text{ }}RCl + {H_2}O \to ROH + HCl{\text{ }}\]
Expected rate law,
 \[
  {\text{R = k }}\left[ {{\text{RCl}}} \right]\left[ {{{\text{H}}_{\text{2}}}{\text{O}}} \right]{\text{ }} \\
  {\text{ = 1 + 1 = 2 }}
\]
Actual rate law \[R = {\text{ }}k'{\text{ }}\left[ {RCl} \right]\]
Actual Order \[ = 1{\text{ }}\]
Water is taken in excess; therefore, its concentration may be taken constant. The reaction is, therefore, pseudo first order.