Final answer:
To calculate the rate constant, Beer's Law is applied to convert absorbance into concentration, after which the rate of reaction can be found by dividing the concentration change by the time interval. The slope of the concentration versus time represents the reaction rate for the early time points, and the rate constant is deduced from the rate law.
Step-by-step explanation:
Calculating Rate Constant from Absorbance and Time
To calculate the rate constant from absorbance and time, one must apply Beer's Law to relate the absorbance of a reaction mixture to the concentration of a product or reactant. If the molar absorptivity is known, as well as the path length of the cuvette, the concentration at different times can be calculated. The rate of reaction, which is the change in concentration over time, can be determined by subtracting the initial concentration from the final concentration and dividing by the time interval. In the provided instance, the molar absorptivity is given as 14,150 M¹cm¹.
Once the concentrations are found, the initial reaction rate (vo) can be estimated from a graph of concentration versus time by considering the slope of the line through the origin for the first few time points. This slope represents the change in concentration (Δ[Concentration]) over the change in time (ΔTime). The rate constant can then be deduced using the rate law, which links the rate of a reaction with the rate constant and the concentrations of the reactants to a certain power, according to the order of the reaction.