The reaction 2 H2O2(aq) → 2 H2O(l) + O2(g) is first order in H2O2 and under certain conditions has a rate constant of 0.00752 s⁻¹ at 20.0 °C. A reaction vessel initially contains 150.0 mL of 30.0% H2O2 by mass solution (the density of the solution is 1.11 g/mL). The gaseous oxygen is collected over water at 20.0 °C as it forms. What volume of O2 forms in 85.0 seconds at a barometric pressure of 742.5 mmHg? (The vapor pressure of water at this temperature is 17.5 mmHg.)

Verified step by step guidance

1. Calculate the initial mass of H2O2 in the solution using the volume, density, and percentage by mass.
2. Convert the mass of H2O2 to moles using its molar mass.
3. Use the first-order rate equation \( [A] = [A]_0 e^{-kt} \) to find the concentration of H2O2 remaining after 85.0 seconds.
4. Determine the moles of H2O2 that have decomposed and use stoichiometry to find the moles of O2 produced.
5. Use the ideal gas law \( PV = nRT \) to calculate the volume of O2 at the given conditions, adjusting for the vapor pressure of water.