Final answer:
The rate constants for bromination reactions depend on experimental conditions and the structure of the disubstituted compounds. The rate constant can be experimentally determined and varies, as seen with t-butyl bromide's hydrolysis, which is of first order. Activation energies of reactions can be estimated through temperature effects on the reaction rate using the Arrhenius equation.
Step-by-step explanation:
The student's question relates to the kinetics of bromination reactions of disubstituted compounds. Rate constants for such reactions can be obtained experimentally and will vary depending on the structure of the molecules involved and the reaction conditions. In the provided information, there is a mention of experiments involving the bromination and other related reactions (like diazotization and hydrolysis). For instance, the rate constants for the hydrolysis of t-butyl bromide and methyl bromide can be significantly different, with the former reacting faster due to steric effects which make the reaction proceed via a different mechanism. The differential rate law for t-butyl bromide's hydrolysis is directly proportional to the concentration of (CH3)3CBr and is of first order.
In regard to the reaction of 5Br¯(aq) + BrO3¯(aq) + 6H+ (aq) → 3Br2 (aq) + 3H2O(l), the rate of appearance of Br2(aq) can be calculated from the rate of disappearance of Br¯(aq). The stoichiometry of the reaction indicates that for every 5 moles of Br¯ that disappear, 3 moles of Br2 are formed. Thus, if the rate of disappearance of Br¯ is 3.5 × 10-4 mol L¹ s¹, the rate of appearance of Br2 will be a fraction of that rate based on the stoichiometry.
Activation Energy and Rate Determination
To determine the activation energy for various reactions, the Arrhenius equation is typically used, which involves the rate constant (k), the frequency factor (A), the activation energy (Ea), and the temperature (T). Furthermore, for certain reactions like the ALP-catalyzed conversion, a change in temperature from 30 °C to 37 °C causes a 1.47-fold increase in the rate of reaction, from which the activation energy can be estimated.