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

The equilibrium expressions for the given reactions are: a. \( K = \frac{[\mathrm{NO}]^2}{[\mathrm{N}_{2}] \times [\mathrm{O}_{2}]} \) b. \( K = \frac{[\mathrm{NO}_{2}]^2}{[\mathrm{N}_{2}\mathrm{O}_{4}]} \) c. \( K = \frac{[\mathrm{SiCl}_{4}] \times [\mathrm{H}_{2}]^2}{[\mathrm{SiH}_{4}] \times [\mathrm{Cl}_{2}]^2} \) d. \( K = \frac{[\mathrm{PCl}_{3}]^2 \times [\mathrm{Br}_{2}]^3}{[\mathrm{PBr}_{3}]^2 \times [\mathrm{Cl}_{2}]^3} \)

Step-by-step solution

Equilibrium expression for reaction a

For the reaction: \[ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \] The equilibrium expression can be written as: \[ K = \frac{[\mathrm{NO}]^2}{[\mathrm{N}_{2}] \times [\mathrm{O}_{2}]} \]

Equilibrium expression for reaction b

For the reaction: \[ \mathrm{N}_{2}\mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \] The equilibrium expression can be written as: \[ K = \frac{[\mathrm{NO}_{2}]^2}{[\mathrm{N}_{2}\mathrm{O}_{4}]} \]

Equilibrium expression for reaction c

For the reaction: \[ \mathrm{SiH}_{4}(g)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)+2 \mathrm{H}_{2}(g) \] The equilibrium expression can be written as: \[ K = \frac{[\mathrm{SiCl}_{4}] \times [\mathrm{H}_{2}]^2}{[\mathrm{SiH}_{4}] \times [\mathrm{Cl}_{2}]^2} \]

Equilibrium expression for reaction d

For the reaction: \[ 2 \mathrm{PBr}_{3}(g)+3 \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{PCl}_{3}(g)+3 \mathrm{Br}_{2}(g) \] The equilibrium expression can be written as: \[ K = \frac{[\mathrm{PCl}_{3}]^2 \times [\mathrm{Br}_{2}]^3}{[\mathrm{PBr}_{3}]^2 \times [\mathrm{Cl}_{2}]^3} \]

Key concepts

Chemical Equilibrium

Understanding the concept of chemical equilibrium is essential in grasping how reactions work in a closed system. In a chemical reaction, reactants convert to products, but under certain conditions, the products can also revert back to the original reactants. Equilibrium is the state in which the rates of the forward reaction (reactants to products) and the reverse reaction (products to reactants) are equal. This balance results in the concentrations of both reactants and products remaining constant over time, even though the reactions continue to occur.

In an equilibrium state, it's important to note that the system is dynamic, meaning reactants and products are constantly interchanging, but their overall concentrations do not change. This concept is often demonstrated in reversible gas-phase reactions, where gaseous reactants and products are enclosed in a sealed container. Students sometimes assume equilibrium means that the quantities of reactants and products are equal, but this is not necessarily the case; what is equal are the rates at which the products form and reactants are replenished.

Equilibrium Constants

The equilibrium constant, represented as \(K\), is a value that gives us insight into the proportions of reactants and products at equilibrium. It is a snapshot of the system's position at equilibrium and indicates whether reactants or products are favored. For a given balanced chemical equation at a specific temperature, \(K\) remains constant and is calculated using the concentrations (for solutions) or partial pressures (for gases) of the reactants and products.

The expression for the equilibrium constant for a reaction is specific to the form of the reaction equation. You determine \(K\) by dividing the product of the concentrations of products, each raised to the power of its coefficient in the balanced equation, by the product of the concentrations of reactants, also each raised to the power of its coefficient. When writing equilibrium expressions, it's critical to remember that only the concentrations of gases and species dissolved in solution are included in the expression; solids and pure liquids are omitted because their concentrations do not change.

Gas-Phase Reactions

Gas-phase reactions are characterized by the involvement of substances in their gaseous state. These types of reactions are particularly interesting from an equilibrium perspective because the behavior of gases can be explained and predicted using the ideal gas law. Moreover, the concentration of a gas is directly proportional to its partial pressure, a concept that's key when dealing with equilibrium constants for gas-phase reactions.

In the space of gas-phase reactions, the term 'partial pressure' is used and is represented as \( P \) with the formula for partial pressure being \( P = nRT/V \), where \( n \) is the number of moles, \( R \) is the ideal gas constant, \( T \) is the temperature, and \( V \) is the volume. In equilibrium expressions for gas-phase reactions, we often use partial pressures instead of concentrations, especially when dealing with dilute gases. Understanding gas-phase reactions demands not only an awareness of the relevant equations but also the practical conditions under which these reactions occur, such as temperature and pressure, which can affect reaction rates and equilibrium positions.