JEE Advanced · Chemistry · 8. Ionic Equilibrium

The initial rate of hydrolysis of methyl acetate $(1 M)$ by a weak acid $(HA, 1 M)$ is $1 / 100^{th}$ of that by a strong acid $(HX, 1 M)$ , at $25 ° C$ . The $K_{a}$ of $HA$ is

A $1 \times 10^{- 4}$
B $1 \times 10^{- 5}$
C $1 \times 10^{- 6}$
D $1 \times 10^{- 3}$

Verified Solution

Answer & Solution

Correct Answer

(A) $1 \times 10^{- 4}$

Step-by-step Solution

Detailed explanation

$\text{CH} _3\text{COOCH} _3+ \text{H} _2 \text{O} \xrightarrow{\left[ \text{H} ^{+}\right]} \text{CH} _3 \text{COOH}$ $+\text{ CH} _3 \text{OH}$

Rate Law \Rightarrow k [MA] [H^{+}]

(as water is present in large excess)

[MA] = 1 M

in both cases

{[H^{+}]}_{Strong} = 1 M

in presence of strong acid

HX

{[H^{+}]}_{weak} = \sqrt{K_{a} . c} = \sqrt{K_{a}}

in the presence of weak acid

HA

.
Initial rate (weak acid)

= k [1] [\sqrt{K_{a}}] ...... (I)

Initial rate (strong acid)

= k [1] [1] ...... (II)

\frac{I}{II} = \sqrt{K_{a}} = \frac{1}{100} = 1 0^{- 2}

K_{a} = 1 \times 1 0^{- 4}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Atomic number	Ionization Enthalpy (kJ/mol)
	$I_{1}$	$I_{2}$	$I_{3}$
$n$	$1681$	$3374$	$6050$
$n + 1$	$2081$	$3952$	$6122$
$n + 2$	$496$	$4562$	$6910$
$n + 3$	$738$	$1451$	$7733$

The initial rate of hydrolysis of methyl acetate1M by a weak acid (HA, 1M) is 1/100th of that by a strong acid HX, 1M, at 25°C. The Ka of HA is

Step-by-step Solution

The initial rate of hydrolysis of methyl acetate $(1 M)$ by a weak acid $(HA, 1 M)$ is $1 / 100^{th}$ of that by a strong acid $(HX, 1 M)$ , at $25 ° C$ . The $K_{a}$ of $HA$ is