### If K = 2.7 × 10−6 M−1 S −1 for the Reaction a → B Which of the Following Is the Correct Rate Law?

If K = 2.7 × 10−6 M−1 S −1 for the Reaction a → B Which of the Following Is the Correct Rate Law?

Rate laws are essential in understanding the kinetics of chemical reactions. They provide valuable information about the rate at which reactants are consumed and products are formed. In this article, we will discuss the correct rate law for a reaction with a given rate constant, K = 2.7 × 10−6 M−1 S−1.

Rate laws describe the relationship between the rate of a reaction and the concentrations of the reactants. They are determined experimentally and can vary depending on the reaction mechanism. The rate law is typically expressed in the form:

rate = k[A]^m[B]^n

where rate is the rate of the reaction, 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 A and B, respectively.

To determine the correct rate law, we need to consider the given rate constant, K = 2.7 × 10−6 M−1 S−1. The rate constant is related to the rate law by the following equation:

k = K / (RT)^n

where R is the gas constant and T is the temperature in Kelvin. Since the rate constant given is in M−1 S−1, we can conclude that the reaction is first order with respect to A and zero order with respect to B.

Therefore, the correct rate law for the reaction a → B is:

rate = k[A]

This means that the rate of the reaction is directly proportional to the concentration of reactant A. As the concentration of A increases, the rate of the reaction will also increase.

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FAQs:

Q: How is the rate constant determined experimentally?
A: The rate constant is determined by conducting a series of experiments at different reactant concentrations and measuring the corresponding rates of reaction. By plotting the data and analyzing the results, the rate constant can be calculated.

Q: What does it mean if the rate constant is large or small?
A: A large rate constant indicates that the reaction is fast and the reactants are consumed quickly. Conversely, a small rate constant suggests a slow reaction with a longer reaction time.

Q: Can the rate law change with temperature?
A: Yes, the rate law can change with temperature. The rate constant is temperature-dependent and can be affected by changes in the reaction’s activation energy. This is described by the Arrhenius equation, which relates the rate constant to temperature.

Q: How does the rate law help us understand reaction mechanisms?
A: The rate law provides insights into the steps involved in a reaction mechanism. By comparing the experimental rate law with the proposed mechanism, we can determine if it is consistent with the observed rate law. This helps us understand the sequence of elementary steps leading to the overall reaction.

Q: Are rate laws always expressed in terms of concentrations?
A: No, rate laws can also be expressed in terms of pressures for gas-phase reactions or activities for reactions involving solutions. The key is to ensure that the units of the rate constant match the units of the concentrations or activities used in the rate law equation.

In conclusion, the correct rate law for the reaction a → B, with a rate constant of K = 2.7 × 10−6 M−1 S−1, is rate = k[A]. This means that the rate of the reaction is directly proportional to the concentration of reactant A. Understanding rate laws is crucial in studying chemical kinetics and provides valuable information about the reaction’s behavior.