Question

For the reaction, $2A+3B\to 5C$, the differential rate equation can be written as:

• A. $k\left[A{]}^n\right[B{]}^n=-\frac{d\left[A\right]}{dt}=-\frac{d\left[B\right]}{dt}=+\frac{d\left[C\right]}{dt}$
• B. $k\left[A{]}^n\right[B{]}^n=+\frac{d\left[A\right]}{dt}=+\frac{d\left[B\right]}{dt}=+\frac{d\left[C\right]}{dt}$
• C. $k\left[A{]}^n\right[B{]}^n=-2\times \frac{d\left[A\right]}{dt}=-3\times \frac{d\left[B\right]}{dt}=+5\times \frac{d\left[C\right]}{dt}$
• D. $k\left[A{]}^n\right[B{]}^n=\frac{-1}{2}\times \frac{d\left[A\right]}{dt}=\frac{-1}{3}\times \frac{d\left[B\right]}{dt}=\frac{+1}{5}\times \frac{d\left[C\right]}{dt}$

Answer 1

The correct option is D $k\left[A{]}^n\right[B{]}^n=\frac{-1}{2}\times \frac{d\left[A\right]}{dt}=\frac{-1}{3}\times \frac{d\left[B\right]}{dt}=\frac{+1}{5}\times \frac{d\left[C\right]}{dt}$

For a reaction, if:
$aA+bB\to cC+dD$

Differential rate equation can be expressed as:

$k\left[A{]}^n\right[B{]}^n=\frac{-1}{a}\times \frac{d\left[A\right]}{dt}=\frac{-1}{b}\times \frac{d\left[B\right]}{dt}=\frac{+1}{c}\times \frac{d\left[C\right]}{dt}=\frac{+1}{d}\frac{d\left[D\right]}{dt}$

So, for the given reaction :
$2A+3B\to 5C$

$k\left[A{]}^n\right[B{]}^n=\frac{-1}{2}\times \frac{d\left[A\right]}{dt}=\frac{-1}{3}\times \frac{d\left[B\right]}{dt}=\frac{+1}{5}\times \frac{d\left[C\right]}{dt}$