# For the reaction ${\text{2N}}_{\text{2}}{\text{O}}_{\text{5(g)}}\to 4{\text{NO}}_{\text{2(g)}}+{\text{O}}_{\text{2(g)}}$, the rate of reaction in terms of  in terms of ${\text{N}}_{2}{\text{O}}_{5}$ it will be

1. A
$-\frac{\text{d}\left[{\text{N}}_{2}{\text{O}}_{5}\right]}{\text{dt}}$
2. B
$+\frac{\text{d}\left[{\text{N}}_{2}{\text{O}}_{5}\right]}{\text{dt}}$
3. C
$-\frac{1}{2}\frac{\text{d}\left[{\text{N}}_{2}{\text{O}}_{5}\right]}{\text{dt}}$
4. D
$-2\frac{\text{d}\left[{\text{N}}_{2}{\text{O}}_{5}\right]}{\text{dt}}$

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### Solution:

The given chemical reaction is

${\text{2N}}_{\text{2}}{\text{O}}_{\text{5}}{}_{\left(\text{g}\right)}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\to 4{\text{NO}}_{\text{2}}{}_{\left(\text{g}\right)}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{O}}_{\text{2}}{}_{\left(\text{g}\right)}$

The rate is

$-\frac{1}{2}\frac{\text{d}\left[{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}\right]}{\text{dt}}=+\frac{1}{4}\frac{\text{d}\left[{\text{NO}}_{\text{2}}\right]}{\text{dt}}=+\frac{{\text{d[O}}_{\text{2}}\right]}{\text{dt}}$

The rate in terms of ${\text{N}}_{\text{2}}{\text{O}}_{\text{5}}$ $=-\frac{1}{2}\frac{\text{d}\left[{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}\right]}{\text{dt}}$

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