Dry HCl act as homogeneous catalyst for the
esterification of RCOOH.
R COOH + R ′ OH 
RCOOR ′ + H 2 O
For esterification, rate, r 1 = k.[RCOOH] [R ′ OH]
The hydrolysis of ester, RCOOR ′ is either acid
catalysed or base catalysed. The rate of ester hydrolysis r 2 ) is quite complex in nature and it is given as-
r 2 = k 1 [H + ] [ester] + k 2 [OH – ] [ester] + k 3 [ester]
(i) If the initial concentration of both RCOOH and R ′ OH are same and equal to a 0 (M), which of the following represent the integrated rate equation ?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)
Sol. RCOOH + R ′ OH 
RCOOR ′ + H 2 O
At time t = 0 a 0 a 0
At time t = t a 0 – x a 0 – x x x
∴ 
= k (a 0 – x) 2 or 
= kt
or 
= kt + C
when t = 0, C = 
or kt = 
– 
(ii)
Sol.
r 2 = K 1 [H
+ ][ester] + 
[ester] + K 3 [ester]
∴ 
= K 1 [ester] – 
[ester] + 0
At the minimum rate, 
= 0
∴ K 1 [ester] = K 2 K w 
or [H + ] = 
or log [H + ] = 
[ logK w + logK 2 – logK 1 ]
or –log [H + ] = 
[ – logK w – logK 2 + logK 1 ]
or pH = 
[ pK w + logK 1 – logK 2 ]
(iii)
Sol.
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