For the reaction, $2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)⟶4{\mathrm{NO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$

If the concentration of ${\mathrm{NO}}_2$ increases by $5.2\times {10}^{-3} M$ in 100 seconds, then the rate of reaction is: 

Given reaction is:

$2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)\to 4{\mathrm{NO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$

Rate of reaction of the given reaction is:

$-\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{dt}}=\frac{1}{4}\frac{\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{dt}}$

Determining the rate of reaction with respect to ${\mathrm{NO}}_2$ is calculated as:

Given reaction is:

$2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)\to 4{\mathrm{NO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$

Rate of reaction of the given reaction is:

$-\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{dt}}=\frac{1}{4}\frac{\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{dt}}$

Determining the rate of reaction with respect to ${\mathrm{NO}}_2$ is calculated as:

$$\begin{gathered} \mathrm{rate}=\frac{1}{4}\times \frac{5.2\times {10}^{-3}\mathrm{M}}{100 \mathrm{s}} \\ \mathrm{rate}=0.000013 \mathrm{M}.{\mathrm{s}}^{-1} \end{gathered}$$