Question

The following rates of reaction were obtained in three experiments with the reaction \(2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NOCl}(\mathrm{g}).\) $$\begin{array}{llll} \hline & \text { Initial } & \text { Initial } & \text { Initial Rate of } \\ \text { Expt } & \text { [NO], M } & \text { [Cl }_{2} \text { ], M } & \text { Reaction, } \mathrm{M} \mathrm{s}^{-1} \\ \hline 1 & 0.0125 & 0.0255 & 2.27 \times 10^{-5} \\ 2 & 0.0125 & 0.0510 & 4.55 \times 10^{-5} \\ 3 & 0.0250 & 0.0255 & 9.08 \times 10^{-5} \\ \hline \end{array}$$ What is the rate law for this reaction?

Short answer

The rate law for this reaction is \[ \text{rate} = k[\text{NO}]^2[\text{Cl}_2] \].

Step-by-step solution

Determine The Order Of Reaction With Respect to NO

Comparing experiments 1 and 3 will help to determine the order of reaction with respect to NO. The concentration of Cl₂ is the same in both experiments, but the concentration of NO is doubled in experiment 3 compared to experiment 1. As a result, we can see how the rate of reaction is affected when the concentration of NO changes. The rate is quadrupled when the concentration of NO is doubled which implies that the reaction is second order with respect to NO.

Determine The Order Of Reaction With Respect to Cl₂

Comparing experiments 1 and 2 will help to determine the order of reaction with respect to Cl₂. The concentration of NO is the same in both experiments, but the concentration of Cl₂ is doubled in experiment 2 compared to experiment 1. As a result, we can see how the rate of reaction is affected when the concentration of Cl₂ changes. The rate is doubled when the concentration of Cl₂ is doubled which implies that the reaction is first order with respect to Cl₂.

Formulate The Rate Law

The order of reaction with respect to each reactant has been found. The reaction is second order with respect to NO and first order with respect to Cl₂. Therefore, the rate law for this reaction is \[ \text{rate} = k[\text{NO}]^2[\text{Cl}_2] \]. Note that the brackets denote concentration and 'k' represents the rate constant.

Key concepts

Understanding Reaction Order

Reaction order is a key concept in chemical kinetics. It defines how the concentration of a reactant impacts the overall reaction rate. In simple terms, it tells you how much a change in concentration of a substance will affect the speed of the reaction. Reaction orders can be given in terms of each reactant involved and may be whole numbers, fractions, or even zero.

• Zero-order: The rate is unaffected by changes in concentration of the reactant.
• First-order: The rate changes directly with the concentration change (if the concentration doubles, so does the rate).
• Second-order: The rate changes by the square of the concentration change (if the concentration doubles, the rate increases by four times).

In the exercise, comparing different experiments helps us determine that the reaction is second-order with respect to NO. This means the rate of reaction quadruples when the concentration of NO doubles. Observations make it first-order for Cl₂, meaning the rate doubled when concentration of Cl₂ was doubled. Reaction order is crucial because it identifies how sensitive the reaction rate is to changes in concentration, providing insight into the mechanism of the reaction.

Delving into Chemical Kinetics

Chemical kinetics is the branch of chemistry that deals with understanding the speed, or kinetics, of chemical reactions. It examines how various factors influence the rate of reactions and uncovers the mechanisms involved. The rate of reaction provides valuable information because it can help in predicting how a reaction might proceed under different conditions.
Some factors that affect chemical reaction rates include:

• Concentration of reactants: Higher concentrations typically lead to increased reaction rates due to more frequent collisions.
• Temperature: Increased temperatures usually lead to faster reactions due to higher kinetic energy.
• Catalysts: These substances can significantly increase reaction rates without being consumed.
• Surface area: Greater surface areas allow more frequent interactions, speeding up the process.

In this particular problem, we focused on changes in concentration and how they impact the reaction. Chemical kinetics is essential in optimizing reactions in industrial processes where speed and efficiency are paramount.

Comprehending Reaction Rate

The reaction rate is a measure of how quickly reactants in a chemical reaction are converted into products. It is usually expressed in terms of concentration change over time. In practice, the reaction rate can be influenced by several factors, as outlined in chemical kinetics.
The rate of a reaction equation is typically written as: \[ ext{Rate} = -\frac{1}{u} \frac{d[ ext{Reactant}]}{dt} = \frac{1}{u} \frac{d[ ext{Product}]}{dt} \]where \(u\) represents stoichiometric coefficients of the reactants or products. Negative signs indicate a decrease in concentration.
In the given exercise, rates were experimentally determined by recording the initial concentration changes. This helps in formulating the rate law, which incorporates reaction order elements. Understanding reaction rates allows chemists to control conditions effectively for desired outcomes in both laboratory and real-world applications.