Question

What is the overall order of the reaction corresponding to the following rate constants? a. \(k=1.63 \times 10^{-4} \mathrm{M}^{-1} \mathrm{s}^{-1}\) b. \(k=1.63 \times 10^{-4} \mathrm{M}^{-2} \mathrm{s}^{-1}\) c. \(k=1.63 \times 10^{-4} \mathrm{M}^{-1 / 2} \mathrm{s}^{-1}\)

Short answer

The overall reaction orders for the given rate constants are: a. 1, b. 2, and c. 0.5 or 1/2.

Step-by-step solution

Determine the overall reaction order for a

Given the rate constant \(k = 1.63 \times 10^{-4} M^{-1}s^{-1}\). Since the units have an exponent of -1, it indicates that the reaction is first order overall. Thus, the overall reaction order for a. is 1.

Determine the overall reaction order for b

Given the rate constant \(k = 1.63 \times 10^{-4} M^{-2}s^{-1}\). Since the units have an exponent of -2, it indicates that the reaction is second order overall. Thus, the overall reaction order for b. is 2.

Determine the overall reaction order for c

Given the rate constant \(k = 1.63 \times 10^{-4} M^{-\frac{1}{2}}s^{-1}\). Since the units have an exponent of -1/2, it indicates that the reaction is of half-order overall. Thus, the overall reaction order for c. is 0.5 or 1/2.

Key concepts

rate constants

In chemical reactions, the rate constant, often represented by the letter \(k\), is a crucial factor in understanding the speed of a reaction. It is a proportionality factor in the rate equation that relates the reaction rate to the concentrations of reactants. The value of \(k\) can indicate the rate at which a reaction proceeds, and it has specific units depending on the order of the reaction.

The units of the rate constant are critical for determining the overall order of a reaction. For instance, in a first-order reaction, the rate constant \(k\) typically has units of \(s^{-1}\). In a second-order reaction, the units are usually \(M^{-1}s^{-1}\), and for a third-order reaction, \(k\) might have units of \(M^{-2}s^{-1}\). The pattern emerges that for a reaction of order \(n\), the units of \(k\) are \(M^{1-n}s^{-1}\).

Analyzing the units of \(k\) helps in determining the overall order of a given reaction. This is because the units reflect how the concentration of reactants impacts the reaction rate, which is directly tied to its order.

chemical kinetics

Chemical kinetics is a branch of chemistry that studies the speed or rate of chemical reactions. It explains how different experimental conditions and factors such as temperature, pressure, and concentration affect these rates. This field provides a detailed understanding of the transformation from reactants to products and the steps involved in the mechanism of a reaction.

One central focus of chemical kinetics is determining the order of a reaction, which is derived from the reaction's rate law. The order gives insight into how concentrations of reactants influence the speed of the reaction. For instance, if a reaction is of zero-order, changes in the reactant concentration do not affect the rate. In contrast, in a first-order reaction, the rate is directly proportional to one reactant's concentration, while a second-order reaction rate depends on either the square of one reactant's concentration or the product of the concentrations of two reactants.

Understanding these concepts helps chemists control and manipulate reaction conditions to optimize reaction rates, which is particularly important in industrial and laboratory settings.

reaction rate

The reaction rate is a measure of how quickly reactants are converted into products in a chemical process. It is typically expressed as the change in concentration of a reactant or product over time. Reaction rates are influenced by several factors including:

• Concentration of reactants
• Temperature
• Presence of catalysts
• Surface area

Each factor alters how molecules collide and react with one another,thereby affecting the speed of the reaction.

The reaction rate is fundamental to the study of chemical kinetics,and it is described mathematically by the rate law. The rate law shows the relationship between the concentration of reactants and the reaction rate, typically written as \(r = k[A]^m[B]^n\), where \(r\) is the reaction rate, \(k\) is the rate constant, \([A]\) and \([B]\) are concentrations of reactants, and \(m\) and \(n\) are the orders of the reaction with respect to those reactants.

Understanding reaction rates allows chemists to control reactions more effectively, making processes more efficient and cost-effective, which is crucial in the development of new products and technologies.