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 constant (k) in a rate law (rate = k[A]^m[B]^n) is determined by:
Rearranging the rate law to isolate k.
Dividing the reaction rate by the concentration terms.
Expressing the rate constant as k = [ A ] m [ B ] n r a t e .
Identifying that the rate constant is the reaction rate divided by the concentration terms: C .
Explanation
Understanding the Rate Law The rate law expresses the rate of a chemical reaction as a function of the concentrations of reactants and a rate constant. The general form of a rate law is: 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 A and B, respectively.
Isolating the Rate Constant To determine how the rate constant (k) can be found from the rate law, we need to rearrange the equation to isolate k. Starting with: rate = k[A]^m[B]^n Divide both sides of the equation by [A]^m[B]^n to solve for k: k = rate / ([A]^m[B]^n)
Interpreting the Result The equation k = rate / ([A]^m[B]^n) shows that the rate constant k is equal to the reaction rate divided by the concentration terms ([A]^m[B]^n).
Selecting the Correct Option Now, let's compare this with the given options: A. The rate constant can be calculated from the exponents of the concentrations. - This is incorrect because the exponents determine the order of the reaction, not the rate constant itself. B. The rate constant is the reaction rate multiplied by the concentration terms. - This is incorrect because the rate constant is the reaction rate divided by the concentration terms. C. The rate constant is the reaction rate divided by the concentration terms. - This is correct based on our derived equation. D. 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, unless the concentrations are equal to 1.
Final Answer Therefore, the correct answer is: C. The rate constant is the reaction rate divided by the concentration terms.
Examples
In environmental science, understanding rate constants is crucial for predicting how quickly pollutants degrade in the environment. For example, if a pollutant's degradation rate law is known, scientists can determine the rate constant to estimate how long it will take for the pollutant's concentration to decrease to a safe level. This helps in designing effective remediation strategies and assessing environmental risks.
The rate constant can be determined from the rate law by rearranging the equation to isolate k, expressed as k = [ A ] m [ B ] n rate . This indicates that the rate constant is the reaction rate divided by the concentration terms raised to their respective powers. Therefore, the correct option is C.
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