Question: In the Wilhelmy Equation of first order reaction \({{\text{c}}_{\text{t}}}\text{ = }{{\text{c}}_{\te...

Question

In the Wilhelmy Equation of first order reaction ${{\text{c}}_{\text{t}}}\text{ = }{{\text{c}}_{\text{0}}}\text{ }{{\text{e}}^{\text{-kt}}}$ . If the initial concentration is increased ‘m’ times, then:
A.The value of k will increase m times.
B.The value of k will decrease m times.
C.The value of k will remain unchanged.
D.None of these

Answer 1

Solution

The order of a reaction is termed to be of first order when the rate of the reaction is dependent only upon the concentration of one reactant. The rate equation of this order equation is exponential in nature.

Complete answer:
Ludwig Wilhelmey was a German chemist who first studied the rate of inversion of table sugar (sucrose) into glucose and fructose in the acidic medium. Wilhelmey found that the rate of this chemical reaction was directly proportional to the existing amount of sugar at each instant in the course of the chemical reaction. This statement when expressed mathematically can be written as,
${{\text{c}}_{\text{t}}}\text{ = }{{\text{c}}_{\text{0}}}\text{ }{{\text{e}}^{\text{-kt}}}$ ,
where ${{\text{c}}_{\text{t}}}$ is the concentration of sucrose at each instant of time t and ${{\text{c}}_{0}}$ is the initial concentration of sucrose.
If the initial concentration is increased ‘m’ times, then the initial concentration becomes $\text{m}{{\text{c}}_{0}}$ .
As the reaction follows the first order rate equation, it can be clearly seen that the rate of the equation will not depend upon the value of the initial concentration of the reaction.

Hence, the correct answer is option C, the value of k will remain unchanged.
Note:
As the rate equation of a first order reaction is an exponential one, so initially the reactant decays fast initially and then the rate decreases with time. But a first order reaction never stops and it is said to continue till infinite time. The amount of time for half of the reactant to decay in a first order reaction is called the half-life of the reaction and it is inversely proportional to the decay constant or the rate constant of the reaction.