Question

The inversion of cane sugar proceeds with half life of 50 minute at pH=5 for any concentration of sugar. However if pH=6, the half life changes to 500 minute of any concentration of sugar. The rate law expression for the invention of cane sugar is written as: $r=K\left[sugar{]}^1\right[H^{+}{]}^y$. Determine the value of y.

• A. $r=K\left[sugar{]}^1\right[H^{+}{]}^{-1}$
• B. $r=K\left[sugar{]}^1\right[H^{+}{]}^2$
• C. $r=K\left[sugar{]}^1\right[H^{+}{]}^1$
• D. $r=K\left[sugar{]}^1\right[H^{+}{]}^0$

Answer 1

The correct option is B $r=K\left[sugar{]}^1\right[H^{+}{]}^2$

given : $t_{1/2}$ does not depends upon the sugar concentration means its an first order w.r.t [sugar]

solution :

$\therefore$

$t_{1/2}\alpha$ $[sugar{]}^1$

using $t_{1/2}$ x $a^y-1=K$

$\frac{t{[}_{1/2}{]}^a}{t{[}_{1/2}{]}^b}$ = $[\frac{[H^{+}{]}^a}{[H^{+}{]}^b}{]}^{1-y}$

$\frac{50}{500}$= ${\left[\frac{{10}^6}{{10}^5}\right]}^{1-y}$

by solving we get y =2

Hence correct opt : B