The rate constant for a zero order reaction was found to be $1.0 × 10^{-3}\ mol\, L^{-1}\,s^{-1}$. How long will 1.0 mol of the reactant take to reduce to 0.5 mol in one liter flask?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 500 s
For a zero-order reaction, the integrated rate law is:
$[A] = [A]_0 – kt$
Given:
- Initial concentration, $[A]_0 = \frac{1.0\ \text{mol}}{1\ \text{L}} = 1.0\ \text{M}$
- Final concentration, $[A] = \frac{0.5\ \text{mol}}{1\ \text{L}} = 0.5\ \text{M}$
- Rate constant, $k = 1.0 \times 10^{-3}\ \text{mol L}^{-1}\text{s}^{-1}$
Substitute:
$0.5 = 1.0 - (1.0 \times 10^{-3})t$
$t = \frac{1.0 - 0.5}{1.0 \times 10^{-3}} = \frac{0.5}{10^{-3}} = 500\ \text{s}$