Question

For the reaction:
$2A\to \frac{1}{4}B$
Rate of disappearance of ‘A’ related to the rate of appearance of ‘B’ by the expression:

• A. $-\frac{d\left[A\right]}{dt}=\frac{+1}{2}\times \frac{d\left[B\right]}{dt}$
• B. $-\frac{d\left[A\right]}{dt}=-8\times \frac{d\left[B\right]}{dt}$
• C. $-\frac{d\left[A\right]}{dt}=+8\times \frac{d\left[B\right]}{dt}$
• D. $-\frac{d\left[A\right]}{dt}=+2\times \frac{d\left[B\right]}{dt}$

Answer 1

The correct option is C $-\frac{d\left[A\right]}{dt}=+8\times \frac{d\left[B\right]}{dt}$

For a reaction, if:
$aP+bQ\to cR+dS$

Overall rate $r$ can be expressed as:

$r=\frac{-1}{a}\times \frac{d\left[P\right]}{dt}=\frac{-1}{b}\times \frac{d\left[Q\right]}{dt}=\frac{+1}{c}\times \frac{d\left[R\right]}{dt}=\frac{+1}{d}\frac{d\left[S\right]}{dt}$

The given reaction is :

$2A\to \frac{1}{4}B$

$r=\frac{-1}{2}\times \frac{d\left[A\right]}{dt}=\frac{+4}{1}\times \frac{d\left[B\right]}{dt}$

$-\frac{d\left[A\right]}{dt}=+8\times \frac{d\left[B\right]}{dt}$