Question

Use the rate law in Example Problem 16.2 and the concentrations given in Practice Problems 31 and 32 to calculate the instantaneous rate for the reaction between \(\mathrm{NO}\) and \(\mathrm{H}_{2} .\) $$[\mathrm{NO}]=0.00500 \mathrm{M} \text { and } \left[\mathrm{H}_{2}\right]=0.00200 \mathrm{M}$$

Short answer

Using the rate law from Example Problem 16.2 and substituting the given concentrations of the reactants \(\mathrm{[NO] = 0.00500M}\) and \(\mathrm{[H_2] = 0.00200M}\), we can calculate the instantaneous rate of the reaction between NO and H₂.

Step-by-step solution

(Step 1: Identify the Rate Law)

(First, we need to find the rate law from Example Problem 16.2. This is the equation that will be used to calculate the instantaneous rate for the reaction.)

(Step 2: Identify the Concentrations of Reactants)

(Next, we need to identify the given concentrations of the reactants: \(\mathrm{[NO] = 0.00500M}\) and \(\mathrm{[H_2] = 0.00200M} \))

(Step 3: Substitute the Concentrations into the Rate Law)

(Now, we can substitute the given concentrations of the reactants into the rate law equation to find the instantaneous rate of the reaction.)

(Step 4: Calculate the Instantaneous Rate)

(By solving the equation, we will obtain the instantaneous rate of the reaction between NO and H₂.)

Key concepts

Rate Law

Understanding the rate law is crucial when studying chemical reactions. The rate law is an equation that relates the rate of a chemical reaction to the concentration of the reactants. It usually has the form \(Rate = k[Reactant_1]^{m}[Reactant_2]^{n}\), where \(k\) is the rate constant, and \(m\) and \(n\) are the reaction orders with respect to each reactant.

This mathematical expression allows scientists to predict how changes in concentration affect the reaction rate. In our example involving the reaction between NO and \(H_2\), the rate law provided from Example Problem 16.2 will contain specific exponents for these reactants that must be used to correctly calculate the instantaneous rate. The ability to calculate this rate is a powerful tool in chemical kinetics, aiding in the prediction and control of reaction speeds.

Chemical Kinetics

Chemical kinetics is the study of the speeds at which chemical reactions occur and the factors that affect these speeds. These factors include reactant concentrations, temperature, the presence of a catalyst, and the physical state of the reactants. By understanding kinetics, we gain insights into reaction mechanisms and the sequence of steps that lead to the overall reaction.

For instance, the reaction between NO and \(H_2\) can be studied to see how rapidly it occurs under different conditions. This knowledge can then be applied in industrial processes, environmental analysis, and even in understanding biological systems. The rate law is a fundamental concept in chemical kinetics, encapsulating much of this information in a form that allows for practical use in calculations and predictions.

Reaction Concentration

Reaction concentration refers to the amount of a substance in a given volume, typically expressed in molarity (M), which is moles per liter. It's a fundamental concept because, in most cases, the rate of a chemical reaction depends on the concentration of the reactants.

In the context of our rate law, concentrations are plugged into the formula to determine the rate of reaction. If we consider the example problem with the given concentrations \(\[NO\] = 0.00500M\) and \(\[H_2\] = 0.00200M\), these values will directly affect the speed at which NO reacts with \(H_2\). The calculation of instantaneous rate will tell us how fast the reaction occurs at this specific moment, given those precise concentrations.

NO and H2 Reaction

The chemical reaction between nitric oxide (NO) and hydrogen (\(H_2\)) is an important example commonly used to illustrate concepts in chemical kinetics. It's also of practical interest in understanding environmental and combustion processes.

To calculate the instantaneous rate for this reaction, we apply the reactant concentrations to the rate law derived from experimental data. This reaction showcases how reaction rates can be influenced by changing reactant concentrations. It's a clear example of the principles of kinetics and rate laws in action, providing a tangible context for these abstract concepts.
By understanding not only how to perform this calculation but also the rationale behind it, students get a deeper grasp of chemical kinetics and the dynamic nature of chemical reactions.