Question

In the following reaction, what is the relationship between the rate at which the nitrous oxide is used up, the rate at which the oxygen is used, and the rate at which the nitrogen dioxide is produced?2N2O(g)+ 3O2(g) → 4NO2(g)

Answer 1

Answer :

The relationship between the rate at which the nitrous oxide is used :

$\text{Rate of disappearance of }N_2O=-\frac{1}{2}\frac{d[N_2O]}{dt}$

The relationship between the rate at which the oxygen is used :

$\text{Rate of disappearance of }O_2=-\frac{1}{3}\frac{d[O_2]}{dt}$

The relationship between the rate at which the nitrogen dioxide is used :

$\text{Rate of formation of }NO_2=+\frac{1}{4}\frac{d[NO_2]}{dt}$

Explanation :

The general rate of reaction is,

$aA+bB\rightarrow cC+dD$

Rate of reaction : It is defined as the change in the concentration of any one of the reactants or products per unit time.

The expression for rate of reaction will be :

$\text{Rate of disappearance of A}=-\frac{1}{a}\frac{d[A]}{dt}$

$\text{Rate of disappearance of B}=-\frac{1}{b}\frac{d[B]}{dt}$

$\text{Rate of formation of C}=+\frac{1}{c}\frac{d[C]}{dt}$

$\text{Rate of formation of D}=+\frac{1}{d}\frac{d[D]}{dt}$

$Rate=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}$

From this we conclude that,

In the rate of reaction, A and B are the reactants and C and D are the products.

a, b, c and d are the stoichiometric coefficient of A, B, C and D respectively.

The negative sign along with the reactant terms is used simply to show that the concentration of the reactant is decreasing and positive sign along with the product terms is used simply to show that the concentration of the product is increasing.

Now we have to determine the expression for rate of reaction.

The balanced chemical equations is:

$2N_2O(g)+3O_2(g)\rightarrow 4NO_2(g)$

The relationship between the rate at which the nitrous oxide is used :

$\text{Rate of disappearance of }N_2O=-\frac{1}{2}\frac{d[N_2O]}{dt}$

The relationship between the rate at which the oxygen is used :

$\text{Rate of disappearance of }O_2=-\frac{1}{3}\frac{d[O_2]}{dt}$

The relationship between the rate at which the nitrogen dioxide is used:

$\text{Rate of formation of }NO_2=+\frac{1}{4}\frac{d[NO_2]}{dt}$