Question

Write the equilibrium expression (K) for each of the following gas-phase reactions. a. \(N_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)\) b. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) c. \(\operatorname{SiH}_{4}(g)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \operatorname{SiCl}_{4}(g)+2 \mathrm{H}_{2}(g)\) 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. \(K = \frac{[NO_2]^2}{[N_2O_4]}\) 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

Identify reactants and products

In this reaction, N₂(g) and O₂(g) are the reactants and 2NO(g) is the product.

Write the equilibrium expression

The equilibrium constant expression (K) for the reaction is given by: \(K = \frac{[NO]^2}{[N_2][O_2]}\) b. N₂O₄(g) ⇌ 2NO₂(g)

Identify reactants and products

In this reaction, N₂O₄(g) is the reactant, and 2NO₂(g) is the product.

Write the equilibrium expression

The equilibrium constant expression (K) for the reaction is given by: \(K = \frac{[NO_2]^2}{[N_2O_4]}\) c. SiH₄(g) + 2Cl₂(g) ⇌ SiCl₄(g) + 2H₂(g)

Identify reactants and products

In this reaction, SiH₄(g) and 2Cl₂(g) are the reactants, and SiCl₄(g) and 2H₂(g) are the products.

Write the equilibrium expression

The equilibrium constant expression (K) for the reaction is given by: \(K = \frac{[SiCl_4][H_2]^2}{[SiH_4][Cl_2]^2}\) d. 2PBr₃(g) + 3Cl₂(g) ⇌ 2PCl₃(g) + 3Br₂(g)

Identify reactants and products

In this reaction, 2PBr₃(g) and 3Cl₂(g) are the reactants, and 2PCl₃(g) and 3Br₂(g) are the products.

Write the equilibrium expression

The equilibrium constant expression (K) for the reaction is given by: \(K = \frac{[PCl_3]^2[Br_2]^3}{[PBr_3]^2[Cl_2]^3}\)

Key concepts

Equilibrium Constant

The equilibrium constant, often denoted as \( K \), plays a key role in understanding chemical reactions at equilibrium. It represents the ratio of the concentration of products to the concentration of reactants at equilibrium, each raised to the power of their coefficients in the balanced equation. - The value of \( K \) helps determine the extent of the reaction. - A large \( K \) value suggests that products are favored at equilibrium, while a small \( K \) value indicates that reactants are favored. For example, in the reaction \( N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \), the equilibrium constant expression is \( K = \frac{[NO]^2}{[N_2][O_2]} \). This expression helps us understand how concentrations relate to each other at equilibrium.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. They are represented by chemical equations that detail what substances interact and what they transform into.
The general form of a chemical reaction can be depicted as:- \( ext{Reactants} \rightarrow ext{Products} \)In gas-phase reactions, like those given in exercises, the reactants and products are in the gaseous state. A balanced chemical equation is crucial as it ensures both mass and charge conservation, which is fundamental for accurately calculating equilibrium constants.

Gas-Phase Reactions

Gas-phase reactions occur when the reactants and products of a reaction are gases. These reactions have some unique characteristics in comparison to other states of matter.- Concentrations in these reactions align with the partial pressures of the gases involved.- The ideal gas law \( PV = nRT \) can connect how gases behave in these reactions.In the exercise examples, each reaction happens in the gas phase, e.g., \( SiH_4(g) + 2Cl_2(g) \rightleftharpoons SiCl_4(g) + 2H_2(g) \). Understanding these properties is essential when writing equilibrium expressions for gas-phase reactions.

Reactants and Products

Reactants are substances consumed during a chemical reaction, whereas products are substances formed as a result of the reaction.
Identifying reactants and products is key to developing equilibrium expressions and understanding reaction dynamics.- Reactants present at the start of a reaction. - Products appear as the reaction progresses towards equilibrium.In the example \( N_2O_4(g) \rightleftharpoons 2NO_2(g) \), \( N_2O_4 \) serves as the reactant and \( 2NO_2 \) as the product. Accurately identifying these elements allows us to construct the equilibrium expression \( K = \frac{[NO_2]^2}{[N_2O_4]} \).

Chemical Equilibrium

Chemical equilibrium is achieved when the forward and reverse reactions occur at the same rate. At this point, the concentrations of reactants and products remain constant over time, though both reactions continue to occur.- It represents a dynamic but stable state for the system.- The reaction quotient \( Q \) and equilibrium constant \( K \) indicate whether a system is at equilibrium.For each of the given reactions, like \( 2PBr_3(g) + 3Cl_2(g) \rightleftharpoons 2PCl_3(g) + 3Br_2(g) \), reaching equilibrium means both sets of substances persist but without any net change, ensuring that \( K \) accurately describes the system.

Writing Expressions

Writing equilibrium constant expressions involves expressing the balanced reaction equation in terms of concentration quotients. For a general reaction \( aA + bB \rightleftharpoons cC + dD \), the expression for \( K \) is:\[ K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]- Each species in the reaction is raised to the power of its coefficient.- Only gaseous and aqueous species appear in the expression.For example, the exercise asks to write the expression for \( 2PBr_3(g) + 3Cl_2(g) \rightleftharpoons 2PCl_3(g) + 3Br_2(g) \) as:\[ K = \frac{[PCl_3]^2[Br_2]^3}{[PBr_3]^2[Cl_2]^3} \]Knowing how to write these expressions is vital for determining the equilibrium constant and analyzing reaction conditions.