Chemical Reaction

Step 1: Understanding the reaction.
For a first-order reversible reaction, the rate of decay of the concentration of A can be described by the rate constant, which depends on both the forward rate constant ( ) and the reverse rate constant ( ). The time constant for the exponential decay is influenced by both and combined, as the reaction proceeds in both directions.
Step 2: Analyzing the options.
(1) : This is incorrect because it only considers the forward reaction and ignores the reverse.
(2) : This is incorrect as it only considers the reverse reaction.
(3) :} This is incorrect as the time constant is a sum, not a difference of the rate constants.
(4) :} Correct — The time constant is derived by combining the effects of both the forward and reverse rate constants, making this the correct choice.
Step 3: Conclusion.
The correct answer is , which correctly describes the time constant for the first-order reversible reaction.