254. Consider a typical first order gas phase reaction
$\mathrm{A}\left(\mathrm{g}\right) \to \mathrm{B}\left(\mathrm{g}\right) + \mathrm{C}\left(\mathrm{g}\right)$
P₁ be the initial pressure of A, P_t the total pressure at time ‘t’. Derive integrated rate equation.

Total pressure P₁ = P_A + P_B ⁺ P_c (pressure units)
p_A, p_B and p_c are the partial pressures of A, B and C respectively. When x is the amount of A converted into products, when pi is the initial pressure at time t = 0

       $$\begin{gathered} p_t=(p_i-\mathrm{x}) + \mathrm{x} + \mathrm{x} = p_i +\mathrm{x} \\ \mathrm{x} = p_t - p_i \end{gathered}$$

where  


$$\begin{gathered} {\mathrm{p}}_{\mathrm{A}} = p_i-\mathrm{x}=p_i-(p_t-p_i) = 2p_i-p_t \\ \mathrm{k} =\frac{ 2.303}{\mathrm{t}} \log \frac{ p_i}{p_A} = \frac{ 2.303}{\mathrm{t}} \log \frac{ p_i}{(2p_i-p_t)} \end{gathered}$$

Pseudo first order reaction: Although in most reactions, order and molecularity are same, there are certain reactions whose order and molecularity differ. For example, hydrolysis of
sugarcane,

$$\begin{gathered} {\mathrm{C}}_{12}{\mathrm{H}}_{12}{\mathrm{O}}_{11}+{\mathrm{H}}_2\mathrm{O} \to {\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6+{\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6 \\ \mathrm{Sucrose} \mathrm{Glucose} \mathrm{Fructose} \end{gathered}$$

Molecularity of this reaction is 2 but its order 1 because its rate depends only on the concentration of surcrose. The concentration of water remains is very high and does not change during the reaction (i.e., concentration of water remains practically constant throughout the reaction). Such reactions are known as pseudo-unimolecular or pseudo first order reactions. Other examples, of pseudo-unimolecular reaction is the acidic hydrolysis of esters where water
remains in excess.

${\mathrm{CH}}_3{\mathrm{COOC}}_2{\mathrm{H}}_5+{\mathrm{H}}_2\mathrm{O} \stackrel{\left(\mathrm{excess}\right) {\mathrm{H}}^{+}}{\to } {\mathrm{CH}}_3\mathrm{COOH}+{\mathrm{C}}_2{\mathrm{H}}_2\mathrm{OH}$

Although it is termolecular (molecularity = 3) reaction, its order is one as concentration of H⁺ and H₂O⁺ remains constant during reaction. Hydrolysis of organic chlorides is also an example of first order reaction small water (one of the reactants) is again in large excess and its concentration remains constant throughout the reactions.

Thus when one of the reactants is present in large excess, the second order reaction conforms to the first order and is known as a pseudo-unimolecular reaction.
Reaction between acetic anhydride and excess of ethanol to form ester and conversion of N-Chloroacetanilide to p-chloroacetanilide are also examples of pseudo-unimolecular reactions.