Final answer:
The rate constant (k) is a proportionality factor in the rate expression of a reaction and is determined experimentally under specific reaction conditions.
Step-by-step explanation:
The question is asking for the rate constant (k) for the reaction involving peroxydisulfate ion (S₂O₈²⁻) and iodide ion (I⁻) where the rate of reaction is given by the expression rate = k[S₂O₈²⁻][I⁻]. In a kinetic study of a reaction, the rate constant is a proportionality factor that links the rate of reaction to the concentrations of the reactants. Based on the data provided in a similar scenario, where the rate constant can be determined from experimental data or provided as a known value, one would calculate or look up the rate constant based on the conditions of the reaction such as temperature and concentration of reactants.