Concept: Acid-Catalyzed Hydrolysis of an Ester

This reaction involves the breakdown of an ester into a carboxylic acid and an alcohol in the presence of an acid catalyst (H⁺). The general reaction is:

$\mathrm{RCOOR}\text{'}+H_{2}O\stackrel{H+}{\to }\mathrm{RCOOH}+R\text{'}\mathrm{OH}$

The rate law for this reaction is derived from experimental observations and is given by:

$\mathrm{Rate}=k\left[\mathrm{ester}\right]\left[H^{+}\right]$

This indicates the reaction is second order overall: first order with respect to both ester and H⁺ concentration.

Step-by-Step Analysis of the Options:

Step 1: Analyze the third order kinetics option.

The rate law is Rate = k[ester][H⁺]. The overall order is 1 + 1 = 2. Therefore, the reaction follows second-order kinetics, not third-order. This option is incorrect.

Step 2: Compare the rate using 1M HCl vs. 1M CH₃COOH.

HCl is a strong acid and dissociates completely, so [H⁺] = 1 M. CH₃COOH is a weak acid and dissociates only partially, so [H⁺] << 1 M. Since the rate depends directly on [H⁺], the rate will be significantly faster with 1M HCl. This option is correct.

Step 3: Compare the rate using 0.05 M HCl vs. 0.05 M H₂SO₄.

HCl is monoprotic, so [H⁺] = 0.05 M. H₂SO₄ is diprotic; for dilute solutions, the first proton dissociates completely, so [H⁺] ≈ 0.05 M. The rate law depends on the concentration of H⁺ ions, not the concentration of the acid solution. Since the [H⁺] is approximately the same in both cases, the initial rate will be the same. This option is correct.

$\mathrm{Rate}\propto \left[H^{+}\right]$

Step 4: Analyze the effect of [H⁺] concentration.

The rate law is Rate = k[ester][H⁺]. This shows the rate is directly proportional to the concentration of H⁺ ions. Changing [H⁺] will directly change the rate. This option is incorrect.

Final Answer:

The correct options are:

• Rate of reaction will be faster when 1M HCl is taken as compared to when 1M CH₃COOH is taken.
• Rate of reaction will be same if 0.05 M HCl is taken or 0.05 M H₂SO₄ is taken.

Related Topics:

• Chemical Kinetics
• Order of Reaction
• Acid-Base Chemistry (Strong vs. Weak Acids)
• Reaction Mechanisms

Key Formulae and Theory:

Rate Law: For the acid-catalyzed hydrolysis of an ester: $\mathrm{Rate}=k\left[\mathrm{ester}\right]\left[H^{+}\right]$

Overall Reaction Order: Sum of the exponents in the rate law. In this case, 1 + 1 = 2 (Second Order).

Strong Acid: An acid that completely dissociates in water (e.g., HCl, H₂SO₄, HNO₃). $\mathrm{HA}\to H^{+}+A^{-}$

Weak Acid: An acid that partially dissociates in water, establishing an equilibrium (e.g., CH₃COOH). $\mathrm{HA}\rightleftharpoons H^{+}+A^{-}$

Catalyst: A substance that increases the rate of a reaction without being consumed. The H⁺ ion is a catalyst in this hydrolysis reaction.