Question

For the reaction $$ \mathrm{O}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) $$ the observed rate law is $$ \text { Rate }=k[\mathrm{NO}]^{2}\left[\mathrm{O}_{2}\right] $$ Which of the changes listed below would affect the value of the rate constant \(k ?\) a. increasing the partial pressure of oxygen gas b. changing the temperature c. using an appropriate catalyst

Short answer

The changes that will affect the value of the rate constant \(k\) are: \(b.\) Changing the temperature, as it directly impacts the energy of particles in the reaction, and \(c.\) Using an appropriate catalyst, as it provides an alternative reaction pathway with a lower activation energy, thus affecting the value of \(k\).

Step-by-step solution

Consider Option a: Increasing the partial pressure of oxygen gas

Increasing the partial pressure of oxygen gas will increase the concentration of O₂ in the reaction. However, this will not affect the value of the rate constant, k. Since k is a constant, it does not change with changes in concentration.

Consider Option b: Changing the temperature

Temperature has a direct impact on the value of the rate constant, k. When the temperature changes, the energy of the particles in the reaction also changes, which affects the rate constant. Therefore, changing the temperature will indeed affect the value of k.

Consider Option c: Using an appropriate catalyst

A catalyst speeds up the reaction by providing an alternative reaction pathway with a lower activation energy, therefore affecting the value of the rate constant, k. When a catalyst is introduced, the value of k will change.

Conclusion

Based on the analysis, the changes that will affect the value of the rate constant k are: b. Changing the temperature c. Using an appropriate catalyst

Key concepts

Chemical Kinetics

Understanding chemical kinetics is essential for grasping how reactions occur and at what rate. This area of chemistry deals with the speed or rate at which a chemical process proceeds, as well as the factors affecting these rates. The rate constant, often represented by the symbol 'k,' is central to the study of chemical kinetics. It is a proportionality constant that connects the rates of a reaction to the concentration of the reactants in the rate law equation.

For a reaction such as \(\mathrm{O}_{2}(g) + 2 \mathrm{NO}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\), the rate law might look like \(\text{Rate} = k[\mathrm{NO}]^{2}[\mathrm{O}_{2}]\). In this equation, \(k\) is independent of the concentration of the reactants; it is a unique value at a particular temperature for a given reaction. Thus, chemical kinetics provides insights not only into the speed of chemical reactions but also into how temperature and the presence of a catalyst can fundamentally alter the rate constant and reaction rate.

Reaction Rates

Reaction rates tell us how quickly reactants are converted into products in a chemical reaction, which can be observed through changes in the concentration of reactants or products over time. These rates can be influenced by several factors, including reactant concentration, temperature, the presence of a catalyst, and the physical state of the reactants.

In the provided exercise, changing the concentration by increasing the partial pressure of O₂ would lead to an increase in the reaction rate but would not alter the rate constant 'k' itself. This is because 'k' is specific to the given reaction at a certain temperature and is not affected by changes in reactant concentrations. It's crucial to distinguish the reaction rate from the rate constant as students sometimes conflate these concepts. The reaction rate of \(2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) is dependent on the concentration of the reactants, but the rate constant 'k' remains unaltered unless the reaction conditions such as temperature are changed.

Catalysis

Catalysis is a process where the rate of a chemical reaction is accelerated by a substance called a catalyst. Catalysts are remarkable because they can increase the reaction rate without being consumed in the reaction itself. They achieve this by providing an alternative pathway for the reaction with a lower activation energy – the minimum energy required for reactants to transform into products.

In the context of the exercise, the introduction of a catalyst would not modify the concentrations of reactants or products, but it would increase the reaction rate by altering the reaction mechanism. The new pathway afforded by the catalyst typically enables reactants to combine more readily, reflected by a change in the rate constant 'k'. However, it's important to note that a catalyst does not have an effect on the equilibrium position of a reaction; it simply helps reach equilibrium faster. This distinction is important for students to understand when considering the impact of catalysis on reaction kinetics.