Question

For the reaction, $\frac{2}{3}A+\frac{2}{5}B\to \frac{3}{7}C$, the differential rate equation can be written as:

• A. $r=\frac{-3}{2}\frac{d\left[A\right]}{dt}=\frac{5}{2}\frac{d\left[B\right]}{dt}=k\left[A{]}^m\right[B{]}^n$
• B. $\frac{-3}{2}\frac{d\left[A\right]}{dt}=\frac{+7}{3}\frac{\left[dC\right]}{dt}=k\left[A{]}^m\right[B{]}^n$
• C. $\frac{+7}{3}\frac{\left[dC\right]}{dt}=\frac{-5}{2}\frac{d\left[B\right]}{dt}=k\left[A{]}^m\right[B{]}^n[C{]}^p$
• D. $\frac{-2}{3}\frac{d\left[A\right]}{dt}=\frac{-5}{2}\frac{d\left[B\right]}{dt}=\frac{+3}{7}\frac{\left[dC\right]}{dt}=k\left[A{]}^m\right[B{]}^n$

Answer 1

The correct option is B $\frac{-3}{2}\frac{d\left[A\right]}{dt}=\frac{+7}{3}\frac{\left[dC\right]}{dt}=k\left[A{]}^m\right[B{]}^n$

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

Overall rate $r$ can be expressed as:

$r=\frac{-1}{a}\times \frac{d\left[A\right]}{dt}=\frac{-1}{b}\times \frac{d\left[B\right]}{dt}=\frac{+1}{c}\times \frac{d\left[C\right]}{dt}=\frac{+1}{d}\frac{d\left[D\right]}{dt}$
Negative sign for reactants indicates disappearance of reactants and postitive sign indicates formation of products
Since the stoichiometric coeffiecients are inveresed while writing rate of reaction, so the corresponding differential rate equation is
$K\left[A{]}^m\right[B{]}^n=\frac{-3}{2}\frac{d\left[A\right]}{dt}=\frac{-5}{2}\frac{d\left[B\right]}{dt}=\frac{+7}{3}\frac{\left[dC\right]}{dt}$
Hence, option (b) is correct.