Engineers studying the decomposition of liquid peroxide E at 350 K report the following observations: when initial concentrations ranging from 0.20 mol L⁻¹ to 1.00 mol L⁻¹ are used, the measured half-life remains constant at 4.6 hours within experimental error. Assume the temperature remains fixed and no side reactions occur.
The engineers wish to develop a predictive model for large-scale reactors.
(1) Based on the experimental observation, identify the overall order of the decomposition reaction with respect to E. Explain how the constancy of the half-life over the stated concentration range leads to your conclusion.
(2) Derive an expression for the concentration of E as a function of time that is consistent with the order determined in part (a). Clearly state any assumptions used in the derivation.
(3) Using your expression from part (b) and the measured half-life, calculate the rate constant k at 350 K, including proper units.
(4) Estimate the time required for the concentration of E to drop from 0.80 mol L⁻¹ to 0.050 mol L⁻¹ at 350 K. Show all steps in your calculation and state any approximations made.
(5) Suppose an impurity acts as a homogeneous catalyst and lowers the half-life to 3.2 hours without altering the reaction order. Qualitatively discuss how the rate constant and integrated rate expression would be affected, and explain the implications for reactor design.