Problem 25 - A Complete Resource Book in Chemistry for JEE Main

Question

The rate law for the reaction \(\mathrm{RCl}+\mathrm{NaOH}(\mathrm{aq}) \longrightarrow \mathrm{ROH}+\mathrm{NaCl}\) is given by Rate \(=k[\mathrm{RCl}]\). The rate of the reaction will be (a) doubled on doubling the concentration of sodium hydroxide (b) halved on reducing the concentration of alkyl halide to one half (c) decreased on increasing the temperature of reaction (d) unaffected by increasing the temperature of the reaction.

Step-by-Step Solution

Answer

The correct answer is (b).

Step 1: Understand the Rate Law

The rate law given is Rate = k[RCl]. This indicates that the reaction rate depends only on the concentration of the alkyl halide (RCl) and is independent of the concentration of sodium hydroxide (NaOH).

Step 2: Analyze the Effect of Concentration of NaOH

Since the rate law does not include NaOH, doubling the concentration of NaOH will not affect the reaction rate. Therefore, option (a) is incorrect.

Step 3: Analyze the Effect of Changing RCl Concentration

The rate is directly proportional to the concentration of RCl. If the concentration of RCl is halved, the rate will also be halved based on the given rate law. Therefore, option (b) is correct.

Step 4: Analyze the Effect of Temperature

The rate law does not explicitly include temperature, but generally, increasing the temperature increases the reaction rate. However, the options (c) and (d) mention effects opposite to this general rule. So neither (c) nor (d) are correct in terms of directly reflecting the rate law.

Key Concepts

Understanding Rate Law

In reaction kinetics, the rate law is an equation that relates the rate of a reaction to the concentration of its reactants. For the reaction of an alkyl halide (RCl) with sodium hydroxide (NaOH) to produce an alcohol (ROH) and sodium chloride (NaCl), the rate law provided is Rate \( = k[\mathrm{RCl}] \). This means the reaction rate is solely dependent on the concentration of RCl. Here, \( k \) is the rate constant, a unique value for every reaction. It reflects how quickly a reaction proceeds. This rate law is of the first order concerning RCl, as it involves the concentration to the power of one. Importantly, it specifies no dependence on NaOH concentration, indicating that even significant changes in NaOH won't alter the rate unless the concentration of RCl changes.

The Concentration Effect

The effect of concentration on reaction rates is pivotal in understanding how modifications might influence reaction progress. Given the rate law Rate \( = k[\mathrm{RCl}] \), the rate of reaction is influenced by changes in the concentration of RCl. If you double the concentration of RCl, the rate also doubles, displaying a direct proportionality per the rate law. Conversely, halving the concentration of RCl will halve the rate. - This highlights the first-order dependence on RCl in this reaction.- However, any alteration in NaOH concentration will not impact the rate, as it is not a factor in the given rate law. Understanding the concentration effect helps predict how changes in reaction conditions affect the speed of reaction, thereby aiding in preparation and control over chemical processes.

The Temperature Effect

Although temperature is not explicitly included in the rate law provided, it is generally acknowledged that temperature significantly affects reaction speed. According to the Arrhenius equation, with increasing temperature, most reaction rates increase because molecules move faster and collide more often with the energy sufficient to surpass their activation energy. This enhanced collision frequency typically means more product formation in a shorter time. - However, specific options in this case study challenge this understanding. Neither option (c) nor (d) about temperature effects were suitable under this rate law since they incorrectly inferred the behavior of temperature. - While the rate law as given only dictates concentration impacts, in practical scenarios, temperature modification will commonly influence rates even if the original rate law remains unchanged.

Alkyl Halide Reactions

Alkyl halide reactions are types of substitution reactions where an alkyl halide replaces a halide ion with a nucleophile, such as OH\(^-\) in the given example. Typically, these reactions can follow either a single-step (SN1) or a multi-step (SN2) mechanism, influenced by factors like the nature of the solvent, temperature, and concentration. - In SN2 reactions, typical for primary alkyl halides, the rate depends on both the alkyl halide and nucleophile concentrations. For the current exercise's rate law, which included only the concentration of RCl, the reaction here does not follow the classical SN2 behavior where both reactants' concentrations generally matter. - Thus, this particular rate law suggests a unique scenario where even though the product formation entails a substitution, the reaction's rate doesn't conform broadly to SN2 theories.In summary, understanding alkyl halide reactions aids in explaining diverse reaction conditions and tailoring them for desired outcomes in synthetic chemistry.