What is the rate constant of a reaction if rate $=1 \times 10^{-2}(mol / L ) / s ,[ A ]$ is 2 M , [B] is $3 M, m=2$, and $n=1$ ?
$k=\frac{\text { rate }}{|A|^r|B|^r}$
A. $8.3 \times 10^{-4}$
B. $1.7 \times 10^5$
C. $2.5 \times 10^{-3}$
D. $60 \times 10^4$
Answer (1)
We are given the rate, concentrations of reactants A and B, and the orders of the reaction with respect to each reactant.
We use the formula k = [ A ] m [ B ] n rate to calculate the rate constant.
Substituting the given values, we get k = 2 2 × 3 1 1 × 1 0 − 2 = 12 0.01 .
The rate constant is k = 8.3 × 1 0 − 4 .
Explanation
Problem Analysis We are given the rate of a reaction, the concentrations of reactants A and B, and the orders of the reaction with respect to each reactant. We need to find the rate constant, k.
Formula and Given Values The rate constant is given by the formula: k = [ A ] m [ B ] n rate where:
rate = 1 × 1 0 − 2 (mol/L)/s
[A] = 2 M
[B] = 3 M
m = 2 (order with respect to A)
n = 1 (order with respect to B)
Calculation Now, we substitute the given values into the formula: k = 2 2 × 3 1 1 × 1 0 − 2 k = 4 × 3 1 × 1 0 − 2 k = 12 1 × 1 0 − 2 k = 12 0.01 k = 0.0008333... k = 8.333... × 1 0 − 4
Final Answer The rate constant, k, is approximately 8.3 × 1 0 − 4 . Therefore, the correct answer is A.
Examples
Understanding rate constants is crucial in many real-world applications. For instance, in drug development, knowing the rate at which a drug degrades in the body helps determine the appropriate dosage and frequency of administration. Similarly, in environmental science, rate constants are used to model the breakdown of pollutants in ecosystems, aiding in the design of effective remediation strategies. In the food industry, rate constants help predict the shelf life of products by modeling the rates of spoilage reactions. These examples highlight how understanding chemical kinetics and rate constants is essential for solving practical problems across various scientific and industrial fields.
