A reaction between A and 2 B produces products by the stoichiometric equation
A+2B→products
Kinetic experiments at 310 K yield the rate law
rate=k[A][B] (overall order = 2)
Assume the reaction takes place in a closed, constant-volume vessel that initially contains [A]0=[B]0=0.50M and no products.
(1) Part 1: Derive an expression for the concentration of A as a function of time, starting from the differential rate law. Clearly state any mathematical steps used in your derivation.
(2) Part 2: From your integrated expression, obtain a formula for the half-life t1/2 in terms of the initial concentration [A]0 and the rate constant k.
(3) Part 3: Compare the dependence of half-life on initial concentration for this second-order reaction with that of a first-order reaction. Explain how experimental measurement of half-life versus initial concentration could be used to confirm the overall reaction order.
(4) Part 4: If k=2.0×102M−1s−1, calculate the time required for [A] to decrease to 0.10M under the stated initial conditions.