Half life of zero order reaction A ? product is 1 hour, when initial concentration of reaction is 2.0 mol . The time required to decrease concentration of A from 0.50 to 0.25 mol is: [2025]

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Solution

Q.
Half life of zero order reaction A → product is 1 hour, when initial concentration of reaction is 2.0 mol $L^{- 1}$ . The time required to decrease concentration of A from 0.50 to 0.25 mol $L^{- 1}$ is: [2025]

1 0.5 hour

2 4 hour

3 15 min

4 60 min

Ans.
(3)

Half-life $(t_{1 / 2})$ of a zero order reaction is related to initial concentration $(a_{0})$ by:

$t_{1 / 2} = \frac{a_{0}}{2 k}$

Thus, rate constant $(k)$ is:
$k = \frac{a_{0}}{2 t_{1 / 2}} = \frac{2 mol/L}{2 \times 1 hour} = \frac{2 mol/L}{2 \times 60 min} = \frac{1}{60} {mol L}^{- 1} {min}^{- 1}$

Concentration at any time $t$ $(a_{t})$ is given by:

$a_{t} = a_{0} - k t,$ $0.25 = 0.5 - (\frac{1}{60}) t, t = 15 min.$

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