Consider the gas-phase reaction between nitric oxide and bromine at 273 C: 2 NO1g2 + Br21g2¡2 NOBr1g2. The following data for the initial rate of appearance of NOBr were obtained: Experiment 3no4 1M 2 3br2 4 1M 2 Initial Rate 1M,s2 1 0.10 0.20 24 2 0.25 0.20 150 3 0.10 0.50 60 4 0.35 0.50 735 (b) Calculate the average value of the rate constant for the appearance of NOBr from the four data sets.

Verified step by step guidance

1. Write the rate law expression for the reaction based on the stoichiometry given in the balanced chemical equation. For the reaction 2 NO(g) + Br2(g) → 2 NOBr(g), the rate law can be expressed as Rate = k[NO]^m[Br2]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to NO and Br2, respectively.
2. Use the given data from each experiment to set up an equation based on the rate law. For example, from Experiment 1, substitute the concentrations of NO and Br2 and the initial rate into the rate law equation: Rate = k[0.10]^m[0.20]^n = 24 M/s.
3. Solve the system of equations obtained from the data for each experiment to find the values of m and n. This typically involves taking logarithms of both sides of each equation and using linear algebra techniques to solve for the reaction orders m and n.
4. Once m and n are known, substitute these values back into the rate equations for each experiment to solve for k. For instance, using the values of m and n, calculate k from the equation for Experiment 1: k = 24 / (0.10^m * 0.20^n).
5. Calculate the average value of the rate constant k by averaging the k values obtained from each experiment. This gives a representative value of k for the reaction under the given conditions.

Key Concepts

Rate of Reaction

The rate of reaction refers to the speed at which reactants are converted into products in a chemical reaction. It is typically expressed as the change in concentration of a reactant or product per unit time. Understanding how to interpret and calculate reaction rates is essential for analyzing experimental data and determining the kinetics of a reaction.

Rate Law

The rate law is an equation that relates the rate of a reaction to the concentration of its reactants, typically in the form Rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to each reactant. Determining the rate law from experimental data allows chemists to understand the relationship between concentration and reaction rate, which is crucial for calculating the rate constant.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that is specific to a given reaction at a specific temperature. It reflects the intrinsic speed of the reaction and is influenced by factors such as temperature and the presence of catalysts. Calculating the average value of the rate constant from multiple experiments provides insight into the overall kinetics of the reaction being studied.