Question

For the reaction $2{{{N}}_2}{{{O}}_{5\left( {{g}} \right)}} \to 4{{N}}{{{O}}_{2\left( {{g}} \right)}} + {{{O}}_{2\left( {{g}} \right)}}$, the rate of formation of ${{N}}{{{O}}_{2\left( {{g}} \right)}}$ is $2.8 \times {10^{ - 3}}{{M}}{{{s}}^{ - 1}}$. Calculate the rate of disappearance of ${{{N}}_2}{{{O}}_{5\left( {{g}} \right)}}$.

Answer 1

Hint: The rate of reaction tells us about how fast or slow a reaction is. It can be determined by observing either the appearance of products or the disappearance of reactants. The change in the quantity of reactants or products in unit time is referred to as the reaction rate.

Complete step by step solution:
When the reaction starts, the reactants will be at maximum and it will be very fast. Then the reactants are used up and then the slowing down of reaction occurs. Also, the amount of product is dependent upon the amount of reactants.
Consider the given reaction is: $2{{{N}}_2}{{{O}}_{5\left( {{g}} \right)}} \to 4{{N}}{{{O}}_{2\left( {{g}} \right)}} + {{{O}}_{2\left( {{g}} \right)}}$
It is given that the rate of formation of ${{N}}{{{O}}_{2\left( {{g}} \right)}}$, ${{r}} = 2.8 \times {10^{ - 3}}{{M}}{{{s}}^{ - 1}}$
Here, the rate of reaction can be expressed as $ - \dfrac{1}{2}\dfrac{d}{{dt}}\left[ {{{{N}}_2}{{{O}}_5}} \right] = + \dfrac{1}{4}\dfrac{d}{{dt}}\left[ {{{N}}{{{O}}_2}} \right] = + \dfrac{d}{{dt}}\left[ {{{{O}}_2}} \right]$. This expression can be related to both the rate of disappearance of reactants and appearance of products.
i.e. $\dfrac{d}{{dt}}\left[ {{{N}}{{{O}}_2}} \right] = 2.8 \times {10^{ - 3}}{{M}}{{{s}}^{ - 1}}$
The rate of disappearance of ${{{N}}_2}{{{O}}_{5\left( {{g}} \right)}}$, $ - \dfrac{1}{2}\dfrac{d}{{dt}}\left[ {{{{N}}_2}{{{O}}_5}} \right] = \dfrac{1}{4}\dfrac{d}{{dt}}\left[ {{{N}}{{{O}}_2}} \right]$
Cross-multiplying, we get
$\Rightarrow$ $ - \dfrac{d}{{dt}}\left[ {{{{N}}_2}{{{O}}_5}} \right] = 2 \times \dfrac{1}{4}\dfrac{d}{{dt}}\left[ {{{N}}{{{O}}_2}} \right]$
$\Rightarrow$ $ - \dfrac{d}{{dt}}\left[ {{{{N}}_2}{{{O}}_5}} \right] = \dfrac{1}{2}\dfrac{d}{{dt}}\left[ {{{N}}{{{O}}_2}} \right]$
Substituting the value of $\dfrac{d}{{dt}}\left[ {{{N}}{{{O}}_2}} \right]$, we get
$\Rightarrow$ $ - \dfrac{d}{{dt}}\left[ {{{{N}}_2}{{{O}}_5}} \right] = \dfrac{1}{2} \times 2.8 \times {10^{ - 3}}{{M}}{{{s}}^{ - 1}}$
$\Rightarrow$ $ - \dfrac{d}{{dt}}\left[ {{{{N}}_2}{{{O}}_5}} \right] = 1.4 \times {10^{ - 3}}{{M}}{{{s}}^{ - 1}}$


Thus the rate of disappearance of ${{{N}}_2}{{{O}}_{5\left( {{g}} \right)}}$ is equal to $1.4 \times {10^{ - 3}}{{M}}{{{s}}^{ - 1}}$.

Additional information:
Order of reaction can be determined from the reaction rate and the concentration of reactants. It is the manner in which the reaction rate is varied with respect to the concentration of the reactants. It can be of zero order, pseudo zero order, first order, pseudo first order and second order reactions.

Note:
Reactions occur when reactants bump to make products. More collisions occur during faster reactions. Less collisions are occurred during slower reactions. Rate of the reactions is influenced by several factors like concentration of reactants, pressure, particle size, catalyst, temperature, and light.