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Question: The rate constant for the reaction, \(2{N_2}{O_5} \to 4N{O_2} + {O_2}\), is \(3 \times {10^{ - 5}}{\...

The rate constant for the reaction, 2N2O5→4NO2+O22{N_2}{O_5} \to 4N{O_2} + {O_2}, is 3×10−5sec⁡−13 \times {10^{ - 5}}{\sec ^{ - 1}} . If the rate is 2.4×10−5molL−1s−12.4 \times {10^{ - 5}}mol{L^{ - 1}}{s^{ - 1}}, then the concentration of N2O5{N_2}{O_5} (in mol litre-1) is:
A.1.41.4
B.1.11.1
C.0.040.04
D.0.80.8

Explanation

Solution

To determine the extent and applications of a reaction it is important to calculate the rate of the reaction and the factors affecting the rate of the reaction. The rate constant is a proportionality constant which is denoted by kk . It gives the relationship between the molar concentration of the reactants and the rate of a reaction.

Formula used: Rate=k[A]xRate = k{[A]^x}

Complete step by step answer:
It is very important to determine the rate of a reaction and the factors to measure the feasibility and applications of a reaction. Chemical kinetics explains the rate of a given reaction. Ionic reactions are fast reactions whereas rusting of iron is a slow reaction which occurs in the presence of moisture and air. The rate of reaction depends on the concentration of the reactants in the reaction and the passage of time for which the reaction has been occurring because with time the rate of reaction decreases because the concentration of the reactant decreases.
The relationship between the molar concentration of the reactants and the rate of a reaction is known as the rate constant which is proportionality constant. It is denoted by kk .
For the above question,
2N2O5→4NO2+O22{N_2}{O_5} \to 4N{O_2} + {O_2}
According to the rate law, Rate=k[N2O5]Rate = k[{N_2}{O_5}] where kk is the rate constant
The unit of the rate constant indicates that the reaction is a first order reaction.
Given that, k=3×10−5sec⁡−1k = 3 \times {10^{ - 5}}{\sec ^{ - 1}} and Rate=2.4×10−5molL−1s−1Rate = 2.4 \times {10^{ - 5}}mol{L^{ - 1}}{s^{ - 1}}
Now substitute the given values
⇒2.4×10−5=3×10−5[N2O5]\Rightarrow 2.4 \times {10^{ - 5}} = 3 \times {10^{ - 5}}[{N_2}{O_5}]
⇒810=[N2O5]\Rightarrow \dfrac{8}{{10}} = [{N_2}{O_5}]
⇒[N2O5]=0.8molL−1\Rightarrow [{N_2}{O_5}] = 0.8mol{L^{ - 1}}

Thus, the correct option is (D) 0.8molL−10.8mol{L^{ - 1}}.

Note:
The reaction which depends on the concentration of just one reactant in the reaction is known as the first order reaction. It is a unimolecular reaction. Various natural and artificial decays of unstable nuclei take place by first order reaction.