Question

Choose the reaction for which overall rate of reaction (r) can be represented as :
$r=\frac{-3}{2}\frac{d\left[A\right]}{dt}=\frac{-5}{2}\frac{d\left[B\right]}{dt}=\frac{+7}{3}\frac{\left[dC\right]}{dt}$

• A. $\frac{3}{2}A+\frac{5}{2}B\to \frac{7}{3}C$
• B. $\frac{2}{3}A+\frac{2}{5}B\to \frac{3}{7}C$
• C. $\frac{2}{3}A+\frac{2}{5}B\to \frac{7}{3}C$
• D. None of the above

Answer 1

The correct option is B $\frac{2}{3}A+\frac{2}{5}B\to \frac{3}{7}C$

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 coefficients are inveresed while writing rate of reaction, so the corresponding reaction for
$r=\frac{-3}{2}\frac{d\left[A\right]}{dt}=\frac{-5}{2}\frac{d\left[B\right]}{dt}=\frac{+7}{3}\frac{\left[dC\right]}{dt}$

$\frac{2}{3}A+\frac{2}{5}B\to \frac{3}{7}C$