Question

For a reaction, the initial concentrations and corresponding rates are given. Which method is used to calculate the rate constant?

• A. Integration method
• B. Differential method
• C. Initial rate method
• D. Half-life method

Hint:

If you see a table with "Experiment 1, 2, 3" showing different starting Molarities and Rates, you are looking at the Initial Rate Method. You can find the order \(n\) by using the ratio: \(\frac{Rate_1}{Rate_2} = \left(\frac{[A]_1}{[A]_2}\right)^n\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In chemical kinetics, there are several experimental methods to determine the order of a reaction and its rate constant. The choice of method depends on the type of data provided.
Step 2: Key Formula or Approach:
The initial rate method relies on analyzing a data table that lists various initial reactant concentrations ($[A]_0, [B]_0$) and their corresponding initial reaction rates ($r_0$).
Step 3: Detailed Explanation:
Let's analyze the given methods:
Integration method: Used when concentration vs. time data is given over the entire course of the reaction. We plug the data into integrated rate equations of different orders to see which one yields a constant $k$.
Half-life method: Used when the half-life period ($t_{1/2}$) of the reaction is given at different initial concentrations.
Differential method (van 't Hoff): Evaluates the rate using logarithms of rates and concentrations, $r = k[A]^n \implies \log r = \log k + n \log [A]$.
Initial rate method: This method is specifically utilized when a table of various {initial concentrations} of reactants and their corresponding {initial rates} is provided. By comparing how the initial rate changes when the concentration of one reactant is varied, the order with respect to each reactant is found. Once the rate law is determined, the rate constant $k$ is calculated.
Since the data provided consists of initial concentrations and corresponding rates, the initial rate method is the correct choice.
Step 4: Final Answer:
The Initial rate method is used to calculate the rate constant.