For the first order reaction:

(A) The degree of dissociation is equal to $(1-e^{kt})$
(B) A plot of reciprocal concentration of the reactant v/s time gives a straight line
(C) The time taken for the completion of 75% reaction is thrice the half of the reaction
(D) 1st order reaction never completes

Choose the correct answer from the options given below:

(A), (D)

The correct answer is Option (1) → (A), (D)

Let us go through the explanation for why Option (1) → (A), (D) is the correct answer:

(A) The degree of dissociation is equal to \(1 - e^{-kt}\):

This statement is correct for a first-order reaction. In a first-order reaction, the fraction of reactant that has dissociated (or reacted) by time \( t \) is given by:

\(\text{Degree of dissociation} = 1 - \frac{[A]}{[A]_0} = 1 - e^{-kt}\)

Where:

\( [A]_0 \) is the initial concentration of the reactant

\( [A] \) is the concentration of the reactant at time \( t \).

\( k \) is the rate constant, and \( t \) is the time elapsed.

This equation represents the fraction of the reaction that has been completed, which matches the statement in (A).

(D) A first-order reaction never completes:

This statement is correct. In a first-order reaction, the concentration of the reactant decreases exponentially with time, but it never reaches zero within a finite amount of time. This means that while the reaction approaches completion, it theoretically never fully completes. The reactant concentration approaches zero asymptotically but doesn't become exactly zero in finite time.

Why the other statements are incorrect:

(B) A plot of reciprocal concentration of the reactant versus time gives a straight line:

This statement is incorrect for a first-order reaction. For a first-order reaction, the plot of ln([A]) versus time gives a straight line, not 1/[A]. The reciprocal concentration plot (1/[A] vs. time) is characteristic of a second-order reaction.

(C) The time taken for the completion of 75% of the reaction is thrice the half-life:

This statement is incorrect. For a first-order reaction, the time taken for 75% completion is not exactly three times the half-life. The time taken for 75% completion is approximately 1.386 times the half-life:

\(t_{75\%} = \frac{\ln(4)}{k} = 1.386 \times t_{1/2}\)

Conclusion:

The correct answer is indeed Option (1) → (A), (D), as these two statements correctly describe characteristics of a first-order reaction.