Question

Given below are two statements: 

• A. Statement I is false but Statement II is true
• B. Statement I is true but Statement II is false
• C. Both Statement I and Statement II are true
• D. Both Statement I and Statement II are false

Hint:

For first order reactions, the half-life is constant and independent of the initial concentration. Additionally, plotting \( \log [R] \) vs time gives a straight line with a slope related to the rate constant \( k \).

Answer 1

The Correct Option is B

- Statement (I) is false: For a first-order reaction, the half-life (\( t_{1/2} \)) is constant and independent of the initial concentration. The stated relationship between \( t_{1/2} \) and \( [R_0] \) is incorrect because the half-life of a first-order reaction is not concentration-dependent.
- Statement (II) is true: The integrated rate law for a first-order reaction is given by:\[\log [R] = \log [R_0] - \frac{k}{2.303} \cdot t.\]Consequently, a plot of \( \log [R] \) versus time yields a straight line with a slope of \( -\frac{k}{2.303} \).

Final Answer: Statement I is false, while Statement II is true.