Assertion (A): In a first order reaction, if the concentration of the reactant is doubled, its half-life is also doubled.
Reason (R): The half-life of a reaction does not depend upon the initial concentration of the reactant in a first order reaction.
To solve the problem, we need to evaluate the Assertion (A) and Reason (R) regarding the effect of doubling the reactant concentration on the half-life of a first order reaction and determine their validity and relationship.
1. Analyzing the Assertion (A):
Assertion (A) states that in a first order reaction, if the concentration of the reactant is doubled, its half-life is also doubled. For a first order reaction, the rate law is Rate = k[A], where k is the rate constant and [A] is the reactant concentration. The half-life (t\(_{1/2}\)) of a first order reaction is given by the formula:
$ t_{1/2} = \frac{\ln(2)}{k} \approx \frac{0.693}{k} $
This formula shows that the half-life depends only on the rate constant k and is independent of the initial concentration [A]\(_0\). If the initial concentration is doubled, the half-life remains the same because k does not change. Therefore, the assertion that doubling the concentration doubles the half-life is false, as the half-life stays constant.
2. Analyzing the Reason (R):
Reason (R) states that the half-life of a first order reaction does not depend upon the initial concentration of the reactant. As derived above, the half-life formula $ t_{1/2} = \frac{\ln(2)}{k} $ confirms that t\(_{1/2}\) is a function of k only and does not involve [A]\(_0\). This is a characteristic feature of first order reactions, unlike zero or second order reactions where half-life depends on concentration. Thus, the reason is true.
3. Evaluating the Relationship:
The assertion is false because doubling the reactant concentration does not affect the half-life in a first order reaction. The reason is true and directly contradicts the assertion, as it correctly states that the half-life is independent of initial concentration. In assertion-reason questions, if the assertion is false, the reason’s truth does not make the assertion true. However, the reason explains why the assertion is incorrect, as the independence of half-life from concentration means doubling the concentration cannot double the half-life.
4. Conclusion:
- Assertion (A) is false because the half-life of a first order reaction does not change when the reactant concentration is doubled.
- Reason (R) is true because the half-life of a first order reaction is independent of the initial concentration.
- The reason explains why the assertion is false, as the concentration independence of the half-life contradicts the claim that doubling concentration doubles the half-life.
Final Answer:
Assertion (A) is false, Reason (R) is true.
"___ how little changes in the environment can have big repercussions" Tishani Doshi in Journey to the End of the Earth gives an awakening call for man. Analyse the theme of the lesson in the light of the above statement.