Calculate the Arrhenius factor for the hydrolysis of methyl acetate in acidic medium at \(298\, \ K\). This reaction was studied by titrating the liberated acetic acid against sodium hydroxide at different time interval. The concentration of ester at different time interval is:
| t/min | 0 | 30 | 60 | 90 |
| c/mol/L | 0.55 | 0.35 | 0.22 | 0.14 |
\(E_a\) for the reaction \(= 18.2 kJ/mol\)
[log 1.57 = 0.196; log 2.5 = 0.3979; log 3.93 = 0.5942; \(e^{-7.3459} = 6.45 \times 10^{-4}\); \(e^{-0.00734} = 0.9926\)]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 23.25
The acid hydrolysis of an ester is pseudo first order, so first find k from k = (2.303/t) log([R]0/[R]):
t = 30 min: k = (2.303/30) log(0.55/0.35) = (2.303/30) × 0.196 = 0.0150 min−1
t = 60 min: k = (2.303/60) log(0.55/0.22) = (2.303/60) × 0.3979 = 0.0153 min−1
t = 90 min: k = (2.303/90) log(0.55/0.14) = (2.303/90) × 0.5942 = 0.0152 min−1
The values agree, so k ≈ 0.015 min−1. Now use the Arrhenius equation, k = A e−Ea/RT:
Ea/RT = 18200 J mol−1 / (8.314 J K−1 mol−1 × 298 K) = 7.3459
e−7.3459 = 6.45 × 10−4
A = k / e−Ea/RT = 0.0150 / (6.45 × 10−4) ≈ 23.25 min−1
NCERT (2026-27 edition):
Temperature Dependence of the Rate of a Reaction – “The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation (3.18). It was first proposed by Dutch chemist, J.H. van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation.
k = A e–Ea/RT (3.18)
where A is the Arrhenius factor or the frequency factor.”