The half‑life of the first‑order decomposition of $H_{2} O_{2}$ at $320 K$ is $7.5 min$ . Calculate the rate constant $k$ in $s^{- 1}$ .

easy 2 marks Class 12 · Chemistry · Chemical Kinetics

Answer

k = 1.54 \times 1 0^{- 3} s^{- 1}

The correct answer is $k = 1.54 \times 1 0^{- 3} s^{- 1}$ — Calculate: $k = 0.00154 s^{- 1} = 1.54 \times 1 0^{- 3} s^{- 1}$ .

Step-by-step solution

Convert the half‑life from minutes to seconds: $7.5 min \times 60 s mi n^{- 1} = 450 s$ .
For a first‑order reaction, $t_{1/2} = \frac{l n 2}{k}$ , therefore $k = \frac{l n 2}{t _{1/2}}$ .
Substitute the values: $k = \frac{0.693}{450 s}$ .
Calculate: $k = 0.00154 s^{- 1} = 1.54 \times 1 0^{- 3} s^{- 1}$ .

Common mistake: Forgetting to convert minutes to seconds before using

t_{1/2} = ln 2/ k

Concept tested: First‑order half‑life