Question

Time	t	$\infty$
Rotation of Glucose & Fructose	$r_t$	$r_{\infty }$

$S\to$ $G+F$
What id the value of $k$ for the above reaction under given circumstances?

• A. $k=\frac{1}{t}ln\frac{r_{\infty }}{(r_{\infty }-r_t)}$
• B. $k=\frac{1}{t}ln\frac{r_t}{(r_{\infty }-r_t)}$
• C. $k=\frac{1}{t}ln\frac{r_{\infty }}{(r_t-r_{\infty })}$
• D. $k=\frac{1}{t}ln\frac{r_t}{(r_t-r_{\infty })}$

Answer 1

Answer: (A)

$k=\frac{1}{t}ln\frac{r_{\infty }}{(r_{\infty }-r_t)}$

The rate law expression for the first order reaction is $k=\frac{2.303}{t}log\frac{a}{a-x}$.

But $a\propto r_{\infty }$ and $x\propto r_t$

Substitute values in the above equation.

$k=\frac{1}{t}ln\frac{r_{\infty }}{(r_{\infty }-r_t)}$