The acid catalysed hydrolysis of an organic compound A at $30 ° C$ has a time for half change of 100 min, when carried out in a buffer solution at pH = 5, and 10 min. when carried out at pH = 4. Both times of half change are Independent of the initial concentration of A. If the rate constant K is given by $\frac{- d [A]}{d t} = K [A]^{α} {[H^{+}]}^{b}$ what are the values of a and b?

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a= 0, b = 2

a= 1, b = 0

a= 2, b = 1

a= 0, b = 1

answer is A.

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Detailed Solution

As the rection is independent from the concentration of A, thus value of a will be 0.

For b,

$b = \frac{1 + \log {(t_{1 / 2})}_{1} - \log {(t_{1 / 2})}_{2}}{\log a_{2} - \log a_{1}}$

$b = 1 + \frac{\log {(t_{1 / 2})}_{1} - \log {(t_{1 / 2})}_{2}}{\log {(H^{+})}_{1} - \log {(H^{- 1})}_{2}}$

$b = 1 + \frac{\log 100 - \log 10}{- 4 + 5} =$

$1 + 1 = 2 = b$

$b = 2, a = 0$

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