State whether the following sentences are true $(T)$ or false $(F)$.
$(a)$ The reaction of an ester with water produces an alcohol and an acid.
$(b)$ The concentration of water remains constant during the hydrolysis of an ester.
$(c)$ In the hydrolysis of an ester,$[H_2O]$ remains constant.
$(a)$ The reaction of an ester with water produces an alcohol and an acid.
$(b)$ The concentration of water remains constant during the hydrolysis of an ester.
$(c)$ In the hydrolysis of an ester,$[H_2O]$ remains constant.
(T, T, T) True $(T)$: The hydrolysis of an ester follows the reaction: $RCOOR' + H_2O \rightarrow RCOOH + R'OH$. This produces a carboxylic acid and an alcohol.
$(b)$ True $(T)$: In the hydrolysis of an ester,water is taken in large excess. Therefore,its concentration remains effectively constant throughout the reaction.
$(c)$ True $(T)$: Since water is in large excess,its concentration $[H_2O]$ does not change significantly during the reaction,which is why the reaction follows pseudo-first-order kinetics.
$(b)$ True $(T)$: In the hydrolysis of an ester,water is taken in large excess. Therefore,its concentration remains effectively constant throughout the reaction.
$(c)$ True $(T)$: Since water is in large excess,its concentration $[H_2O]$ does not change significantly during the reaction,which is why the reaction follows pseudo-first-order kinetics.
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When methyl acetate is hydrolyzed in $0.05 \, M$ $HCl$,the reaction occurs as follows: $CH_3COOCH_3 + H_2O \rightarrow CH_3COOH + CH_3OH$. $A$ $25 \, mL$ sample of the reaction mixture is taken at different time intervals,added to ice to stop the reaction,and then titrated with $0.05 \, M$ $NaOH$ solution. Prove that the reaction is first order using the data provided below:
Time (minute) $0$ $20$ $75$ $120$ $\infty$ Volume of $0.05 \, M$ $NaOH$ ($V_t$ in $mL$) $24.40$ $25.82$ $29.35$ $31.75$ $47.50$
| Time (minute) | $0$ | $20$ | $75$ | $120$ | $\infty$ |
| Volume of $0.05 \, M$ $NaOH$ ($V_t$ in $mL$) | $24.40$ | $25.82$ | $29.35$ | $31.75$ | $47.50$ |
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