The decomposition of H₂O₂ in basic solution is first order in H₂O₂.
2H₂O₂(aq) → 2H₂O₂ (l) x O₂(g)
the rate constant is 1.6 x 10^–5 s^–1 at 25°C and initial concentration of H₂O₂ is 0.20 M.
(a) What is the concentration of H₂O₂ after 2 hrs.
(b) How long will it take for H₂O₂ concentration to drop to 0.08 M.
(c) How long will it take for 90% of H₂O₂ to decompose?

Solution

(a) $k = 2.303 \log \frac{(R)_{0} / R_{t}}{t}$

or $1.6 \times 10^{- 5} = 2.303 \log \frac{[0.2 / [R]}}{2 \times 60 \times 60}$

or $[R] = 0.178 M$

(b)
$1.6 \times 10^{- 5} = 2.303 \log (0.2 M / 0.08 M) / t t = 2.303 \times 0.398 / 1.6 \times 10^{- 5} t = 5.73 \times 10^{4} s$

$(c) 1.6 \times 10^{- 5} = 2.303 \log \frac{{0.2 / (0.2 0.18)}}{t} or t = 2.303 \log (0.2 / 0.02) 1.6 \times 10^{- 5} or t = 2.303 / 1.6 \times 10^{- 5} = 1.43 \times 10^{5} s$

Table 4.2. Integrated rate laws for the reactions of simpler order.