Question

onsider the reaction, NO2(g) + CO(g) → NO(g) + CO2(g), for which the rate law has been determined to be: Rate = k[NO2]2[CO]. Which of the following statements is/are true?I: The rate of change of NO2 is twice the rate of change of CO.II: Doubling the concentrations of NO2 and CO simultaneously will increase the rate of the reaction by a factor of four.A) Only IB) Only IIC) I and IID) None

Answer 1

Answer: A) Only I

Explanation:

Rate law says that rate of a reaction is directly proportional to the concentration of the reactants each raised to a stoichiometric coefficient determined experimentally called as order.

$NO_2(g)+CO(g)\rightarrow NO(g)+CO_2(g)$

Given:

$Rate=k[NO_2]^2[CO]^1$

k= rate constant

Order with respect to $NO_2$ =2

Order with respect to $CO$ = 1

I. The rate in terms of reactants is given as negative as the concentration of reactants is decreasing with time whereas the rate in terms of products is given as positive as the concentration of products is increasing with time.

$Rate=-\frac{1d[NO_2]}{2dt}=-\frac{1d[CO]}{dt}$

$-\frac{1d[NO_2]}{dt}=-2\times \frac{1d[CO]}{dt}$

Thus the rate of change of $NO_2$ is twice the rate of change of $CO$.

II.  Doubling the concentrations of  $NO_2$ and $CO$ simultaneously will increase the rate of the reaction by a factor of four

$Rate'=k[2NO_2]^2[2CO]^1$

$Rate'=k[2]^2[NO_2]^2[2]^1[CO]^1$

$Rate'=k\times 8[NO_2]^2[2]^1[CO]^1$

$Rate'= 8\times Rate$

Thus the rate increases by a factor of 8 and not 4.

Thus the correct statement is only  the rate of change of $NO_2$ is twice the rate of change of $CO$.

Answer 2

Answer:

The correct answer is option D.

Explanation:

Rate of the reaction is a change in the concentration of any one of the reactant or product per unit time.

$NO_2(g) + CO(g)\rightarrow NO(g) + CO_2(g)$

Rate of the reaction:

$R=-\frac{1}{1}\times \frac{d[NO_2]}{dt}=-\frac{1}{1}\times \frac{d[CO]}{dt}$

Rate of decrease in nitrogen dioxide concentration is equal to the rate of decrease in carbon monoxide.

Given rate expression of the reaction:

$R = k[NO2]^2[CO]$

Rate of the reaction on doubling concentration of nitrogen dioxide and carbon monoxide : R'

$R'=k(2\times [NO_2])^2(2\times [CO])=8\times k[NO2]^2[CO]=8R$

Doubling the concentrations of nitrogen dioxide and carbon monoxide simultaneously will increase the rate of the reaction by a factor of eight.

Hence, none of the given statements are true.