How can the rate constant be determined from the rate law?
A. The rate constant can be calculated from the exponents of the concentrations.
B. The rate constant is the reaction rate multiplied by the concentration terms.
C. The rate constant is the reaction rate divided by the concentration terms.
D. The rate constant is the same thing as the reaction rate for the reaction.
Answer (2)
The rate law is expressed as rate = k[A]^m[B]^n.
Rearrange the rate law to isolate the rate constant: k = rate / ([A]^m[B]^n).
The rate constant is the reaction rate divided by the concentration terms.
Therefore, the correct answer is OC.
Explanation
Understanding the Problem The question asks how to determine the rate constant from the rate law. The rate law expresses the rate of a reaction as a function of the rate constant and the concentrations of the reactants. The rate law generally has the form: rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are reactant concentrations, and m and n are reaction orders.
The Rate Law The rate law expresses the rate of a reaction as a function of the rate constant and the concentrations of the reactants. The rate law generally has the form: rate = k [ A ] m [ B ] n where:
rate is the reaction rate,
k is the rate constant,
[A] and [B] are the concentrations of reactants,
m and n are the orders of the reaction with respect to reactants A and B, respectively.
Isolating the Rate Constant To find the rate constant (k), we need to rearrange the rate law equation to isolate k: k = [ A ] m [ B ] n rate This shows that the rate constant is the reaction rate divided by the concentration terms.
Analyzing the Options Now, let's analyze the given options: OA. The rate constant can be calculated from the exponents of the concentrations: This is incorrect because the exponents (m and n) only determine the order of the reaction, not the value of the rate constant. OB. The rate constant is the reaction rate multiplied by the concentration terms: This is the opposite of what the rearranged rate law shows. OC. The rate constant is the reaction rate divided by the concentration terms: This matches our derived equation for k. OD. The rate constant is the same thing as the reaction rate for the reaction: This is incorrect because the rate constant is a proportionality constant and not the same as the rate.
Final Answer Based on our analysis, the correct answer is: OC. The rate constant is the reaction rate divided by the concentration terms.
Examples
In chemical kinetics, understanding how reaction rates change with varying concentrations is crucial. For instance, in drug development, knowing the rate constant helps predict how quickly a drug will degrade or react in the body. By determining the rate law and subsequently the rate constant, scientists can optimize drug formulations and dosages to ensure efficacy and stability. This ensures that medications deliver the intended therapeutic effect over their shelf life and within the patient's system.
To find the rate constant (k) from the rate law, you rearrange the law to k = rate / ([A]^m[B]^n). The correct answer to the question is C, indicating that the rate constant is the reaction rate divided by the concentration terms. The importance of understanding the rate constant lies in its ability to describe how reaction rates change with varying reactant concentrations.
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