Question

Write the equilibrium expression \((K)\) for each of the following gas-phase reactions. a. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)\) b. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) c. \(\mathrm{SiH}_{4}(g)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)+2 \mathrm{H}_{2}(g)\) d. \(2 \mathrm{PBr}_{3}(g)+3 \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{PCl}_{3}(g)+3 \mathrm{Br}_{2}(g)\)

Short answer

a. \(K = \frac{[NO]^2}{[N_{2}][O_{2}]}\) b. \(K = \frac{[NO_{2}]^2}{[N_{2}O_{4}]}\) c. \(K = \frac{[SiCl_{4}][H_{2}]^2}{[SiH_{4}][Cl_{2}]^2}\) d. \(K = \frac{[PCl_{3}]^2[Br_{2}]^3}{[PBr_{3}]^2[Cl_{2}]^3}\)

Step-by-step solution

Write the equilibrium expression for reaction a.

According to the given reaction a, we need to write the equilibrium expression for the reaction: \(N_{2}(g) + O_{2}(g) \rightleftharpoons 2NO(g)\) The equilibrium expression for this reaction can be written as: \(K = \frac{[NO]^2}{[N_{2}][O_{2}]}\) b. N2O4(g) ⇌ 2NO2(g)

Write the equilibrium expression for reaction b.

According to the given reaction b, we need to write the equilibrium expression for the reaction: \(N_{2}O_{4}(g) \rightleftharpoons 2NO_{2}(g)\) The equilibrium expression for this reaction can be written as: \(K = \frac{[NO_{2}]^2}{[N_{2}O_{4}]}\) c. SiH4(g) + 2Cl2(g) ⇌ SiCl4(g) + 2H2(g)

Write the equilibrium expression for reaction c.

According to the given reaction c, we need to write the equilibrium expression for the reaction: \(SiH_{4}(g) + 2Cl_{2}(g) \rightleftharpoons SiCl_{4}(g) + 2H_{2}(g)\) The equilibrium expression for this reaction can be written as: \(K = \frac{[SiCl_{4}][H_{2}]^2}{[SiH_{4}][Cl_{2}]^2}\) d. 2PBr3(g) + 3Cl2(g) ⇌ 2PCl3(g) + 3Br2(g)

Write the equilibrium expression for reaction d.

According to the given reaction d, we need to write the equilibrium expression for the reaction: \(2PBr_{3}(g) + 3Cl_{2}(g) \rightleftharpoons 2PCl_{3}(g) + 3Br_{2}(g)\) The equilibrium expression for this reaction can be written as: \(K = \frac{[PCl_{3}]^2[Br_{2}]^3}{[PBr_{3}]^2[Cl_{2}]^3}\)

Key concepts

Chemical Equilibrium

Understanding chemical equilibrium is crucial for anyone studying chemistry. It refers to a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentration of reactants and products over time. This does not mean that the reactants and products are equal in concentration, but that their concentrations have stabilized in a fixed ratio.

When writing equilibrium expressions like those in the given exercise, we follow a standard format. For a balanced chemical equation, the equilibrium constant (\(K\textsubscript{eq}\)) is defined by the ratio of the concentrations of the products (each raised to the power of their stoichiometric coefficients) to the concentrations of the reactants (also raised to the power of their stoichiometric coefficients).

\begin{itemize}

For reaction (a), the equilibrium expression is \(K = \frac{[NO]^2}{[N_2][O_2]}\), indicating how the concentration of nitrogen monoxide to the second power is set over the product of the concentrations of nitrogen and oxygen gases.

Similarly, reactions (b), (c), and (d) have their own unique expressions based on the stoichiometry of the balanced equations provided.

Grasping the concept of chemical equilibrium allows students to predict and understand how different changes will affect the system at equilibrium.

Reaction Quotient

The reaction quotient (\(Q\textsubscript{c}\)) is a value obtained similarly to the equilibrium constant; however, it applies to any moment in the reaction—not just at equilibrium. It represents the ratio of product concentrations to reactant concentrations at any point in time, giving us a snapshot of where the reaction is in terms of going to completion.

The formula for the reaction quotient mirrors that of the equilibrium expression, using the current concentrations as opposed to the concentrations at equilibrium. This concept is particularly useful when you want to understand which direction a reaction will proceed to reach equilibrium. These might include non-standard conditions or any scenario where the system is not already balanced.

For instance, when \(Q < K\), it suggests the forward reaction will be favored to produce more products until equilibrium is achieved. Conversely, if \(Q > K\), the system will favor the reverse reaction to reduce the product concentration. Should \(Q = K\), it indicates the reaction is already at equilibrium—no further shift in the concentrations of reactants and products will occur.

Le Chatelier's Principle

When chemical systems at equilibrium experience a change in concentration, temperature, volume, or pressure, the principle developed by Henri Louis Le Chatelier provides valuable insight into the system's response. Le Chatelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will move to counteract the change.

Here's a closer look at how different changes might affect a chemical equilibrium:

• Concentration: Adding more reactant will push the equilibrium to form more products, whereas adding more product will shift the equilibrium towards the reactants.
• Temperature: Increasing the temperature in an endothermic reaction will shift the equilibrium toward the products; for exothermic reactions, the effect is the opposite.
• Pressure and Volume: For reactions involving gases, an increase in pressure (by decreasing volume) will shift the equilibrium towards the side with fewer moles of gas, and reducing pressure (by increasing volume) shifts it towards the side with more moles of gas.

Understanding this principle helps us predict how changes will affect the concentrations of reactants and products for reactions in a closed system and is a valuable tool in industrial chemical processes where control of conditions is essential for optimising yields.