Hydrogen peroxide breaks down slowly in water, but iodide ions speed it up: 2 H₂O₂(aq) → 2 H₂O(l) +…

Hydrogen peroxide breaks down slowly in water, but iodide ions speed it up: $2\,\text{H}_2\text{O}_2(aq) \rightarrow 2\,\text{H}_2\text{O}(l) + \text{O}_2(g)$. The accepted mechanism has a slow first step and a fast second step:

As NCERT does, write the rate law as $-\dfrac{d[\text{H}_2\text{O}_2]}{dt} = k[\text{H}_2\text{O}_2][\text{I}^-]$. A $50.0\ \text{mL}$ solution of hydrogen peroxide with $[\text{I}^-] = 0.0200\ \text{mol L}^{-1}$ is kept at $298\ \text{K}$. The oxygen is collected in a gas syringe at $298\ \text{K}$ and $1.00\ \text{bar}$. The graph shows the volume of oxygen against time: $18.6\ \text{mL}$ after $10.0\ \text{min}$, and $52.0\ \text{mL}$ in all once the reaction is over. The solution is stirred well, so the oxygen escapes as soon as it forms, and the volumes are those of dry oxygen. Assume that all the oxygen reaches the syringe. Take $R = 0.08314\ \text{L bar K}^{-1}\ \text{mol}^{-1}$ and $\ln 10 = 2.303$.

1. What was the starting concentration of hydrogen peroxide?
2. What is the pseudo first order rate constant $k' = k[\text{I}^-]$ in this run?
3. What is $k$?
4. In a second run, $[\text{I}^-] = 0.0500\ \text{mol L}^{-1}$ and everything else is the same. How long does it take for 90 per cent of the peroxide to break down?
5. In the first run, what was the initial rate of formation of oxygen, in moles of $\text{O}_2$ per litre of solution per minute?