Question

The rate law for the reaction below is given by the expression \[k[A][B]\] \[A + B \to products\] If the concentration of B is increased from 0.1 to 0.3 mole, keeping the value of A at 0.1 mole, the rate constant will be:
A. \[3k\]
B. \[9k\]
C. \[k/3\]
D. \[k\]

Answer 1

Hint: The rate equation is an important measure to find the rate in which the reactants are reacting with each other to find the products. The rate equation is the proportionality constant that connects the rate to the concentrations.

Step by step answer: Rate equation or rate law for a chemical reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters. There are four types of order of reaction and they are zero order, first order, second order and Pseudo first order. The common form of the rate equation is a power law given as follows:
\[{V_o} = k{[A]^x}{[B]^y}\]
Here \[k\] is the rate constant. It is also called a specific rate constant. It is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentration of the reacting substance. Now, we know about the rate of reaction and the rate constant. According to the question, the equation is given as follows:
\[A + B \to products\]
Now, writing the rate equation for the above reaction,
\[Rate = k[A][B]\]
Substituting the values of A and B in the equation we get,
\[A = 0.1\]
\[B = 0.3\]
\[Rate = k \times 0.1 \times 0.3\]
Now, from the rate equation above, we can see that rate value will change due to change in the concentration of reactants as it is directly proportional to the concentration value. But the rate constant \[k\] is not dependent on the concentrations of the reactants and therefore its value will not change. Therefore, its value will remain as it is which is \[k\].

So, the correct answer is option D.

Also, according to the Arrhenius equation, the rate constant changes only with a change in temperature or by the effect of the catalyst.
\[k = {e^{\dfrac{{ - E}}{{RT}}}}\]

Note: In the rate equation, the rate value is dependent on the concentration of the reactants and the rate constant is independent of the concentration but it is dependent on temperature or effect of catalyst.