The half-life of a zero-order reaction R → P is 30 min when the initi…

The correct answer is Option (3) → 0.15 mol L⁻¹

In a zero-order reaction the concentration falls by the same amount in every unit of time. The rate constant k is found from the half-life and then used in the integrated rate equation.

    \( \displaystyle t_{1/2} = \frac{[\mathrm{R}]_0}{2k} \)

    \( \displaystyle k = \frac{[\mathrm{R}]_0}{2\,t_{1/2}} = \frac{0.60\ \mathrm{mol\,L^{-1}}}{2 \times 30\ \mathrm{min}} = 0.010\ \mathrm{mol\,L^{-1}\,min^{-1}} \)

    \( \displaystyle [\mathrm{R}] = [\mathrm{R}]_0 - kt = 0.60 - (0.010 \times 45) = 0.60 - 0.45 = 0.15\ \mathrm{mol\,L^{-1}} \)

For a zero-order reaction the half-life is not constant: after the first 30 min, the remaining 0.30 mol L⁻¹ needs only 15 min more for the next halving.

NCERT (2026-27 edition):
3.3.1 Zero Order Reactions – “Further simplifying equation (3.6), we get the rate constant, k as”

    \( \displaystyle k = \frac{[\mathrm{R}]_0 - [\mathrm{R}]}{t} \qquad (3.7) \)

3.3.3 Half-Life of a Reaction – “\( t_{1/2} = \frac{[\mathrm{R}]_0}{2k} \) It is clear that t_1/2 for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant.”