Question

For the reaction, $N_2{O}_5\left(g\right)\to N{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)$ The value of rate of disappearance of $N_2{O}_5$ is given as $6.25\times {10}^{-3}mol{L}^{-1}{s}^{-1}.$ The rate of formation of $N{O}_2$ and $O_2$ is given respectively as:

• A. $6.25\times {10}^{-3}mol{L}^{-1}{s}^{-1}and6.25\times {10}^{-3}mol{L}^{-1}{s}^{-1}$
• B. $1.25\times {10}^{-2}mol{L}^{-1}{s}^{-1}and3.125\times {10}^{-3}mol{L}^{-1}{s}^{-1}$
• C. $6.25\times {10}^{-3}mol{L}^{-1}{s}^{-1}and3.125\times {10}^{-3}mol{L}^{-1}{s}^{-1}$
• D. $1.25\times {10}^{-}2mol{L}^{-1}{s}^{-1}and6.25\times {10}^{-3}mol{L}^{-1}{s}^{-1}$

Answer 1

The correct option is B

$1.25\times {10}^{-2}mol{L}^{-1}{s}^{-1}and3.125\times {10}^{-3}mol{L}^{-1}{s}^{-1}$

Rate of disappearance of reactant = rate of appearance of product
Or -$\frac{1}{Stoichiometriccoefficientofreactant}\frac{d\left[reactant\right]}{dt}$
$+\frac{1}{Stoichiometriccoefficientofproduct}\frac{d\left[product\right]}{dt}$
For the reaction,
$N_2{O}_5\left(g\right)\to 2N{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)-\frac{d\left[N_2{O}_5\right]}{dt}=+\frac{1}{2}\frac{d\left[N{O}_2\right]}{dt}=+\frac{2d\left[O_2\right]}{dt}$
$\therefore \frac{d\left[N{O}_2\right]}{dt}=-2\frac{d\left[N_2{O}_5\right]}{dt}=2\times 6.25\times {10}^{-3}mol{L}^{-1}{s}^{-1}=12.5\times {10}^{(}-3)mol{L}^{-1}{s}^{-1}$
$=1.25\times {10}^{-2}mol{L}^{-1}{s}^{-1}\frac{d\left[O_2\right]}{dt}=-\frac{d\left[N_2{O}_5\right]}{dt}\times \frac{1}{2}=\frac{6.25\times {10}^{-3}mol{L}^{-1}{s}^{-1}}{2}=3.125\times {10}^{-3}mol{L}^{-1}{s}^{-1}$