Which of the following reaction has fractional order with respect to one of the reactant?

$CHCl_3 + Cl_2 → CCl_4 + HCl$

The correct answer is Option 2. $CHCl_3 + Cl_2 → CCl_4 + HCl$.

Let us go into detail for each reaction to understand how the reaction order is determined and why only one of the reactions may have fractional order with respect to one of the reactants.

1. \( 2NO(g) + O_2(g) \rightarrow 2NO_2(g) \) (Reaction between NO and \( O_2 \)):

This reaction is a well-known example of a third-order reaction. Experimental studies of this reaction show that it is second-order with respect to \( NO \) and first-order with respect to \( O_2 \). Therefore, the rate law is:

\(\text{Rate} = k [NO]^2 [O_2]^1\)

The overall order is \( 2 + 1 = 3 \), meaning that it follows an integer order (third order) with respect to all reactants.

No fractional orders are involved here, as both orders with respect to \( NO \) and \( O_2 \) are integers (2 and 1, respectively).

2. \( CHCl_3 + Cl_2 \rightarrow CCl_4 + HCl \) (Reaction between chloroform and chlorine):

This reaction is a photochemical process in which light initiates the reaction. The presence of light often leads to complex chain reactions that involve free radicals. A typical mechanism involves the formation of intermediate free radicals, such as:

\(Cl_2 \overset{hv}{\longrightarrow} 2Cl^\cdot \quad \text{(Chlorine radicals are formed by light energy)}\)

The chlorine radicals then react with chloroform (\( CHCl_3 \)) to produce more radicals and initiate a chain reaction. The mechanism can be represented as:

\(Cl^\cdot + CHCl_3 \rightarrow CCl_3^\cdot + HCl\)

\(CCl_3^\cdot + Cl_2 \rightarrow CCl_4 + Cl^\cdot\)

Due to the complex chain mechanism and radical involvement, the reaction can exhibit fractional order with respect to chloroform (\( CHCl_3 \)). Experimental studies often observe an order of 0.5 (half-order) with respect to chloroform, particularly under certain conditions where the concentration of radicals plays a significant role in the reaction rate. This fractional order arises because the rate-determining step may depend on the concentration of intermediates (like \( CCl_3^\cdot \)), whose concentration is proportional to \( [CHCl_3]^{0.5} \). Thus, fractional order with respect to \( CHCl_3 \) can be observed in this reaction due to the chain mechanism.

3. \( CH_3COOC_2H_5 + H_2O \rightarrow CH_3COOH + C_2H_5OH \) (Hydrolysis of ethyl acetate):

This is a classic example of the acid-catalyzed ester hydrolysis or neutral ester hydrolysis. The reaction follows a well-known mechanism where ethyl acetate is hydrolyzed by water to form acetic acid and ethanol. The reaction typically follows pseudo-first-order kinetics when water is in excess. In such cases, the concentration of water remains constant, and the rate depends primarily on the concentration of the ester (\( CH_3COOC_2H_5 \)). The rate law in this case is:

\(\text{Rate} = k [CH_3COOC_2H_5]^1\)

The reaction order with respect to ethyl acetate is 1, and since water is in large excess, its concentration is not considered for the rate law. There is no fractional order involved in this reaction.

4. \( CH_3COOC_2H_5 + NaOH \rightarrow CH_3COONa + C_2H_5OH \) (Saponification of ethyl acetate):

This is an example of a second-order reaction, where ethyl acetate undergoes base-catalyzed hydrolysis (saponification) in the presence of sodium hydroxide. The reaction rate depends on both the concentration of ethyl acetate and sodium hydroxide. The rate law is:

\(\text{Rate} = k [CH_3COOC_2H_5]^1 [NaOH]^1\)

The overall reaction order is \( 1 + 1 = 2 \).

As both orders with respect to the reactants are integers (first order with respect to each reactant), this is a second-order reaction. There is no fractional order in this reaction.

Conclusion:

The reaction \( CHCl_3 + Cl_2 \rightarrow CCl_4 + HCl \) (chloroform and chlorine) exhibits fractional order with respect to chloroform because of the involvement of free radicals and a chain mechanism, which often leads to non-integer orders of reaction.

Thus, the correct answer is the second reaction, which can have fractional order with respect to one of the reactants