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.

Key Concepts

Reaction Order

The order of a reaction indicates how the rate of the reaction depends on the concentration of reactants. In this case, the reaction is first order in H2O2, meaning that the rate is directly proportional to the concentration of H2O2. This relationship is crucial for calculating the concentration of H2O2 over time and ultimately determining the amount of O2 produced.

Rate Constant

The rate constant (k) is a proportionality factor in the rate law that relates the rate of a reaction to the concentrations of the reactants. For a first-order reaction, the rate constant is given as 0.00752 s⁻¹ at 20.0 °C. This constant is essential for calculating the change in concentration of H2O2 over time, which is necessary to find the volume of O2 produced.

Gas Collection Over Water

When collecting gas over water, the total pressure of the gas collected is the sum of the partial pressure of the gas and the vapor pressure of water. In this scenario, the barometric pressure is 742.5 mmHg, and the vapor pressure of water at 20.0 °C is 17.5 mmHg. Understanding this concept is vital for accurately calculating the volume of O2 produced, as it allows for the adjustment of the measured pressure to account for the water vapor.