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Question: The rate constant for the reaction, \(2{{N}_{2}}{{O}_{5}}\to 4N{{O}_{2}}+{{O}_{2}}\)is \(2.0\times {...

The rate constant for the reaction, 2N2O5→4NO2+O22{{N}_{2}}{{O}_{5}}\to 4N{{O}_{2}}+{{O}_{2}}is 2.0×10−5s−12.0\times {{10}^{-5}}{{s}^{-1}}. If rate of reaction is 1.4×10−5molL−1s−11.4\times {{10}^{-5}}mol{{L}^{-1}}{{s}^{-1}}, what will be the concentration of N2O5{{N}_{2}}{{O}_{5}}in molL−1mol{{L}^{-1}}?
A. 0.8
B. 0.7
C. 1.2
D. 1

Explanation

Solution

Rate constant also known by the name proportionality constant which gives the relationship between molar concentration of the reactants and chemical reaction. This is generally denoted by the symbol K.

Complete step by step answer : R
ate constant can be easily calculated with the help of Arrhenius equation. This equation gives us the formula for the temperature dependence of reaction rates. The Arrhenius equation has many applications but the main and very important application of the Arrhenius equation is it is useful in determination of rate of chemical reaction and for the calculation of energy of activation.
In chemical kinetics reaction rate coefficient or reaction rate constant defines the rate and direction of any chemical reaction. Equation given in the question is
2N2O5→4NO2+O22{{N}_{2}}{{O}_{5}}\to 4N{{O}_{2}}+{{O}_{2}}
The unit of rate constant indicates that the reaction given is of first order reaction. In first order reaction the rate will be given as:
Rate=K[N2O5]Rate=K[{{N}_{2}}{{O}_{5}}]Where K = Rate constant
The value of rate constant is given in the question i.e. 2.0×10−5s−12.0\times {{10}^{-5}}{{s}^{-1}}and rate is also given i.e. 1.4×10−5molL−1s−11.4\times {{10}^{-5}}mol{{L}^{-1}}{{s}^{-1}}, Now put the both values in the equation and we find that
1.4×10−5=2.0×10−5[N2O5]1.4\times {{10}^{-5}}=2.0\times {{10}^{-5}}[{{N}_{2}}{{O}_{5}}]
1.4×10−52.0×10−5=[N2O5]\dfrac{1.4\times {{10}^{-5}}}{2.0\times {{10}^{-5}}}=[{{N}_{2}}{{O}_{5}}]
By solving the above equation we find that the value of [N2O5][{{N}_{2}}{{O}_{5}}]will be 0.7.

Thus we can say that option B is the correct answer.

Note:
First order reactions can be defined as those chemical reactions in which the reaction rate is linearly dependent on the concentration of only one reactant, concentration depends on only one therefore it is termed as first order reaction.