The following reaction is first order in A (red spheres) and first order in B (blue spheres): A + B → Products Rate = k[A][B]
(b) What are the relative values of the rate constant k for vessels (1)–(4)?

Verified step by step guidance

1. Identify the reaction order: The reaction is first order in A and first order in B, which means the overall reaction order is 2.
2. Understand the rate law: The rate law for this reaction is given by Rate = k[A][B], where k is the rate constant, and [A] and [B] are the concentrations of reactants A and B, respectively.
3. Compare the concentrations: To determine the relative values of the rate constant k for different vessels, compare the concentrations of A and B in each vessel.
4. Analyze the rate: Since the rate is directly proportional to the product of the concentrations of A and B, the vessel with higher concentrations of A and B will have a higher rate, assuming k is constant.
5. Conclude the relative values: If the concentrations of A and B are the same across vessels, then the rate constant k is the same. If they differ, the vessel with higher concentrations will have a higher rate, but k remains constant as it is a characteristic of the reaction at a given temperature.

Key Concepts

Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. In this case, the reaction is first order in both A and B, meaning that the rate of reaction is directly proportional to the concentration of each reactant. This implies that if the concentration of either A or B is doubled, the reaction rate will also double.

Rate Constant (k)

The rate constant, denoted as k, is a proportionality factor in the rate law that relates the rate of a reaction to the concentrations of the reactants. It is specific to a given reaction at a particular temperature and is influenced by factors such as temperature and the presence of catalysts. The value of k can vary between different vessels depending on conditions like temperature and pressure.

Concentration and Reaction Rate

The concentration of reactants plays a crucial role in determining the rate of a chemical reaction. For a reaction that is first order in both A and B, the rate is affected by the product of their concentrations. This means that the relative values of k in different vessels can be compared by analyzing how the concentrations of A and B differ in those vessels, impacting the overall reaction rate.