Question

Write a chemical equation for an equilibrium system that would lead to the following expressions (a-d) for \(K\). (a) \(K=\frac{\left(P_{\mathrm{H}_{2}}\right)^{2}\left(P_{\mathrm{O}_{2}}\right)^{3}}{\left(P_{\mathrm{SO}_{2}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{2}}\) (b) \(K=\frac{\left(P_{\mathrm{F}_{1}}\right)^{1 / 2}\left(P_{\mathrm{I}_{2}}\right)^{1 / 2}}{P_{\mathrm{IF}}}\) (c) \(K=\frac{\left[\mathrm{Cl}^{-}\right]^{2}}{\left(P_{\mathrm{C}_{2}}\right)\left[\mathrm{Br}^{-}\right]^{2}}\) (d) \(K=\frac{\left(P_{\mathrm{NO}}\right)^{2}\left(P_{\mathrm{H}_{3} \mathrm{O}}\right)^{4}\left[\mathrm{Cu}^{2+}\right]^{3}}{\left[\mathrm{NO}_{3}^{-}\right]^{2}\left[\mathrm{H}^{+}\right]^{8}}\)

Short answer

The balanced chemical equation for this equilibrium expression is: 2 H2 (g) + 3 O2 (g) ⇌ 2 SO2 (g) + 2 H2O (g). b) What is the balanced chemical equation for K=[F]^(1/2)[I2]^(1/2)[IF]? The balanced chemical equation for this equilibrium expression is: 1/2 F2 (g) + 1/2 I2 (g) ⇌ IF (g). c) What is the balanced chemical equation for K=[Cl-]^2[C2][Br-]^2? The balanced chemical equation for this equilibrium expression is: 2 Br- (aq) + C2 (g) ⇌ 2 Cl- (aq). d) What is the balanced chemical equation for K=[NO]^2[H3O]^4[Cu2+]^3[NO3-]^2[H+]^8? The balanced chemical equation for this equilibrium expression is: 2 NO (g) + 8 H+ (aq) + 3 Cu2+ (aq) ⇌ 2 NO3- (aq) + 4 H3O+ (aq).

Step-by-step solution

(a) Write the chemical equation for the equilibrium expression

For the equilibrium constant expression (a), we have the following powers for each species: H2 (2), O2 (3), SO2 (2), and H2O (2). Considering the stoichiometry of the expression, we can write the balanced chemical equation as: 2 H2 (g) + 3 O2 (g) ⇌ 2 SO2 (g) + 2 H2O (g)

(b) Write the chemical equation for the equilibrium expression

For equilibrium expression (b), we have the following powers for each species: F (1/2), I2 (1/2), and IF (1). Considering the stoichiometry of the expression, we can write the balanced chemical equation as: 1/2 F2 (g) + 1/2 I2 (g) ⇌ IF (g)

(c) Write the chemical equation for the equilibrium expression

For the equilibrium constant expression (c), we have the following powers for each species: Cl- (2), C2 (1), and Br- (2). Considering the stoichiometry of the expression, we can infer that two Br- will swap with two Cl- and together with C2, the balanced chemical equation will look like: 2 Br- (aq) + C2 (g) ⇌ 2 Cl- (aq)

(d) Write the chemical equation for the equilibrium expression

For the equilibrium constant expression (d), we have the following powers for each species: NO (2), H3O (4), Cu2+ (3), NO3- (2), and H+ (8). Considering the stoichiometry of the expression, we can write the balanced chemical equation as: 2 NO (g) + 8 H+ (aq) + 3 Cu2+ (aq) ⇌ 2 NO3- (aq) + 4 H3O+ (aq)

Key concepts

Equilibrium Constant

The equilibrium constant, represented as \( K \), is a crucial part of understanding chemical equilibrium systems. It provides insight into the ratio of product concentrations to reactant concentrations at a state where the reaction has reached equilibrium. The value of \( K \) gives us a snapshot of the reaction dynamics:

• A large \( K \) (greater than 1) signifies that products are favored at equilibrium.
• A small \( K \) (less than 1) indicates that reactants are more prevalent at equilibrium.

In the given exercise, each part represents a different equilibrium expression where \( K \) is derived from partial pressures or concentrations. This expression is unique to each chemical reaction and based on the stoichiometry highlighted in the chemical equations.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions in terms of chemical species. These equations succinctly describe the conversion of reactants into products. In writing chemical equations, it's essential to depict:

• The physical states of compounds (gaseous, liquid, solid, aqueous).
• The reactants and products involved, separated by a reaction arrow (⇌).

For example, in the exercise, the chemical reactions are given in steps and reflect the respective equilibrium conditions. Therefore, knowing how to read and interpret chemical equations is indispensable for solving equilibrium problems.

Stoichiometry

Stoichiometry concerns the quantitative relationships between reactants and products in a chemical reaction. It involves using ratios derived from the balanced chemical equation to predict the amounts of substances consumed or produced. Each part of the exercise involves analyzing the stoichiometric coefficients:

• These coefficients indicate the relative number of molecules or moles involved in the reaction.
• The coefficients are used to develop the exponents in the equilibrium constant expression.

For instance, part (a) involves the stoichiometric coefficients of 2 for H₂, 3 for O₂, and so forth, directly influencing the equilibrium expression for \( K \).

Balanced Reactions

Balanced reactions are critical in writing correct chemical equations for equilibrium. A balanced chemical equation means that the number of atoms for each element, as well as the total charge, is the same on both sides of the equation. Balance is achieved by adjusting the stoichiometric coefficients in the equation:

• Ensure the principle of mass conservation is followed.
• Allow for accurate calculation of the equilibrium constant \( K \).

The original exercise requires writing balanced equations to appropriately reflect the equilibrium expressions given. This ensures that the calculated \( K \) accurately reflects the dynamics of the system at equilibrium.