Discussion Forum

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

Answer:

Explanation:

plan    $RCOOR'+H_{2}0$    $\underrightarrow{H^{+}}$         $RCOOH+R'OH$

 Acid hydrolysis  of ester is follows first order kinetics

 For same concentration of ester in each case rate in dependent on [H⁺]  from acid

 Rate = k[RCOOR']

 Also for weak acid HA   $\rightleftharpoons H^{+}+A^{-}$

 $K_{a}=\frac{[H^{+}][A^{-}]}{[HA]}$

     [Rate]_HA =k[H⁺]_HA

  [Rate]_HX= k[H⁺]_HX

 (Rate)_HX  =100(Rate)_HA

$\therefore$ Also in strong acid [H⁺]=[HX]=1M

$\frac{(Rate)_{HX}}{(Rate)_{HA}}=100=\frac{[H^{+}]_{HX}}{[H^{+}]_{HA}}$

                 $=\frac{1}{[H^{+}]_{HA}}$

 $\therefore$      $[H^{+}]_{HA}=\frac{1}{100}$

          $HA\rightleftarrows H^{+}+A^{-}$

           1           0     0

     (1-x)         x        x

    x= 0.01

$\therefore$            $k_{a}=\frac{[H^{+}][A^{-}]}{[HA]}$

   $=\frac{0.01\times 0.01}{0.99}

          $=1.01\times 10^{-4}$