Final answer:
The student's question involves calculating the time required for the concentration of a reactant X to decrease from 0.650 M to 0.0975 M in a decomposition reaction. To solve this, one would need to determine the reaction order and rate constant based on provided experimental data, then apply the appropriate integrated rate law.
Step-by-step explanation:
The question pertains to determining the amount of time it would take for the concentration of a reactant X to decrease from 0.650 M to 0.0975 M during a decomposition reaction at 25 °C. This problem is grounded in the field of chemical kinetics, which explores the rates of chemical reactions and factors that affect these rates. In the given scenarios, various initial concentrations and initial rates are provided. These can be used to determine the rate law and calculate the rate constant (k), which would then allow us to use the integrated rate law to find the time required for the concentration to change as specified.
Without specifics on the order of the reaction or the rate law, it is not possible to provide a precise answer to the student's problem. However, if provided with the order of reaction, one can use the appropriate integrated rate law (for a first-order, second-order, or zero-order reaction) to solve for the time t. For example, for a first-order reaction, the integrated rate law is ln([A]_0/[A]) = kt, and for a second-order reaction, 1/[A] - 1/[A]_0 = kt, where [A] and [A]_0 are the final and initial concentrations, respectively.
Chemical kinetics and the ability to calculate reaction times and concentrations are essential tools in chemistry, particularly in understanding reaction mechanisms and designing chemical processes. The rate constant, reaction order, and initial conditions all play pivotal roles in these calculations.