$$\text{A} \to \text{B}$$
The above reaction is of zero order. Half life of this reaction is $$50$$ min. The time taken for the concentration of A to reduce to one-fourth of its initial value is ______ min. (Nearest integer)

For a zero-order reaction $$\text{A} \to \text{B}$$, the half-life is 50 minutes. We need to find the time for the concentration to reduce to one-fourth of its initial value.

Recall the zero-order kinetics formula.

For a zero-order reaction: $$[A] = [A]_0 - kt$$

Half-life: $$t_{1/2} = \frac{[A]_0}{2k}$$

Find the rate constant.

$$t_{1/2} = \frac{[A]_0}{2k} = 50 \implies k = \frac{[A]_0}{100}$$

Find the time for $$[A] = \frac{[A]_0}{4}$$.

$$\frac{[A]_0}{4} = [A]_0 - kt$$

$$kt = [A]_0 - \frac{[A]_0}{4} = \frac{3[A]_0}{4}$$

$$t = \frac{3[A]_0}{4k} = \frac{3[A]_0}{4} \times \frac{100}{[A]_0} = 75 \text{ min}$$

The correct answer is 75.