An acid-catalysed hydrolysis of ester is carried out in the presence of HCl. Small but same volume of reaction mixture were taken out at various instant and were titrated with standard NaOH solution.

Question

An acid-catalysed hydrolysis of ester is carried out in the presence of HCl. Small but same volume of reaction mixture were taken out at various instant and were titrated with standard NaOH solution. The following data was obtained:
Time (in min): 0, 120, ∞
Volume of NaOH (ml): 20, 55, 60
If the initial concentration of ester was 6.0 M, then calculate the value of abcd, where ab = half-life for the hydrolysis of ester (in min) and cd = molar concentration of HCl used in the experiment.

Prashant Kotian · Accepted Answer

Correct answer: 4003. Rate constant k = (1/t) ln((V_inf - V0)/(V_inf - Vt)) = (1/120) ln((60-20)/(60-55)) = (1/120) ln(40/5) = (1/120) ln 8 = 3 ln 2 / 120 = ln 2 / 40. Half-life ab = ln 2 / k = 40 min. V0 (20 ml) represents HCl alone. V_inf - V0 (40 ml) represents the completely hydrolysed ester. Since 40 ml corresponds to the initial 6.0 M ester, the 20 ml for HCl corresponds to 6.0 / 2 = 3.0 M. Thus cd = 03. abcd = 4003. Therefore, correct answer is 4003.

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