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Question: The rate constant of a reaction is \[0.0693mi{n^{ - 1}}\]. Starting with \[10\] mol, the rate of the...

The rate constant of a reaction is 0.0693min−10.0693mi{n^{ - 1}}. Starting with 1010 mol, the rate of the reaction after 1010 min is:
A.0.0693molmin⁡−10.0693mol{\min ^{ - 1}}
B.0.0693×2molmin⁡−10.0693 \times 2mol{\min ^{ - 1}}
C.0.0693×5molmin⁡−10.0693 \times 5mol{\min ^{ - 1}}
D.0.0693×52molmin⁡−10.0693 \times {5^2}mol{\min ^{ - 1}}

Explanation

Solution

We need to know that the rate constant is also known as proportionality constant and it can be explained on the basis of rate of a chemical reaction and the molar concentration of the reactants. The rate constant of a reaction is expressed by ‘k’ and t is also called reaction rate coefficient. And according to chemical kinetics, the rate constant will express the direction and rate of the chemical reaction.

Complete answer:
The concentration of reactant after 1010 minutes is not equal to 0.0693molmin⁡−10.0693mol{\min ^{ - 1}}. Hence, option (A) is incorrect.
The concentration of reactant after 1010 minutes is not equal to 0.0693×2molmin⁡−10.0693 \times 2mol{\min ^{ - 1}}. Hence, option (B) is incorrect.
According to the question, the rate constant of a reaction is equal to 0.0693  min−10.0693\;mi{n^{ - 1}} and the initial concentration is equal to 1010 mol.
The rate of the reaction after 1010 minutes can be find out by using the equation of half - life of first order reaction and that is,
t1/2=0.693k{t_{1/2}} = \dfrac{{0.693}}{k}
Where, k is the rate constant of the reaction which is equal to 0.0693min−10.0693mi{n^{ - 1}}. Substitute the value in the above equation will get,
t1/2=0.6930.0693=10min⁡{t_{1/2}} = \dfrac{{0.693}}{{0.0693}} = 10\min
The concentration of reactant after 1010 minutes is equal to 55 mol. Therefore, rate of the reaction after 1010 min is equal to,
rate(dxdt)=k[A]=0.0693×5molmin⁡−1rate\left( {\dfrac{{dx}}{{dt}}} \right) = k\left[ A \right] = 0.0693 \times 5mol{\min ^{ - 1}}
Hence, option (C) is correct.
The concentration of reactant after 1010minutes is not equal to 0.0693×5molmin⁡−10.0693 \times 5mol{\min ^{ - 1}}. Hence, option (D) is incorrect.

Hence, option (C) is correct.

Note:
According to the rate law, it expresses how the rate of chemical reaction will depend on the concentration of the reactant. The order of the rate law is equal to the sum of exponents in the term of concentration. And the concentration directly depends on the rate of reaction. In a chemical reaction, the rate is always expressed in terms of concentration units over the unit of time.