Initial rate data at 25 °C are listed in the table for the reaction NH4 +1aq2 + NO2 -1aq2S N21g2 + 2 H2O1l2 (b) What is the value of the rate constant?

Verified step by step guidance

1. Step 1: Write the rate law expression for the reaction: rate = k[NH4+][OH-].
2. Step 2: Use the data from experiments 1 and 2 to determine the order of the reaction with respect to NH4+. Compare the rates and concentrations of NH4+ while keeping OH- constant.
3. Step 3: Use the data from experiments 2 and 3 to determine the order of the reaction with respect to OH-. Compare the rates and concentrations of OH- while keeping NH4+ constant.
4. Step 4: Once the orders of the reaction with respect to NH4+ and OH- are determined, use the rate law expression and data from any experiment to solve for the rate constant k.
5. Step 5: Substitute the known values of concentrations and initial reaction rate into the rate law expression to calculate the value of k.

Key Concepts

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are the concentrations of the reactants, and m and n are the reaction orders with respect to each reactant. Understanding the rate law is essential for determining how changes in concentration affect the reaction rate.

Order of Reaction

The order of a reaction refers to the exponent to which the concentration of a reactant is raised in the rate law. It indicates how sensitive the reaction rate is to changes in that reactant's concentration. For example, if a reaction is first order with respect to a reactant, doubling its concentration will double the reaction rate. Determining the order of reaction 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 particular reaction at a given temperature. It reflects the speed of the reaction and is influenced by factors such as temperature and the presence of catalysts. The value of k can be determined experimentally by analyzing the initial rates of reaction at varying concentrations of reactants, as shown in the provided data.