Question

Write an expression for the equilibrium constant of each chemical equation. \begin{equation} \begin{array}{l}{\text { a. } \operatorname{SbCl}_{5}(g) \Longrightarrow \operatorname{SbCl}_{3}(g)+\mathrm{Cl}_{2}(g)} \\ {\text { b. } 2 \mathrm{BrNO}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)} \end{array}\end{equation} \begin{equation} \begin{array}{l}{\text { c. } \operatorname{CH}_{4}(g) \Longrightarrow \operatorname2 \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{CS}_{2}(g)} \\ {\text { d. } 2 \mathrm{CO}(g) \rightleftharpoons \mathrm{O}_{2}(g)+\mathrm2 \mathrm{CO}_{2}(g)} \end{array}\end{equation}

Short answer

The equilibrium constants are: a) \(Ka = \frac{[\text{SbCl}_3][\text{Cl}_2]}{[\text{SbCl}_5]}\), b) \(Kb = \frac{[\text{NO}]^2[\text{Br}_2]}{[\text{BrNO}]^2}\), c) \(Kc = \frac{[\text{H}_2\text{S}]^2[\text{CS}_2]}{[\text{CH}_4]}\), d) \(Kd = \frac{[\text{O}_2][\text{CO}_2]^2}{[\text{CO}]^2}\).

Step-by-step solution

- Understanding the Equilibrium Constant Expression

Recognize that the equilibrium constant expression for any chemical equation is written as the product of the concentrations of the products raised to their stoichiometric coefficients, divided by the product of the concentrations of the reactants raised to their stoichiometric coefficients. The general form is given as: \[ K = \frac{[\text{Products}]^{\text{coefficients}}}{[\text{Reactants}]^{\text{coefficients}}} \] Where the square brackets denote the concentration of the chemical species in moles per liter (M) and gaseous species are considered in terms of partial pressure.

- Writing the Expression for Equation a

For the reaction: \[ \text{SbCl}_{5}(g) \Longrightarrow \text{SbCl}_{3}(g) + \text{Cl}_{2}(g) \] The equilibrium constant expression is: \[ K_a = \frac{[\text{SbCl}_3][\text{Cl}_2]}{[\text{SbCl}_5]} \]

- Writing the Expression for Equation b

For the reaction: \[ 2 \text{BrNO}(g) \rightleftharpoons 2 \text{NO}(g) + \text{Br}_2(g) \] The equilibrium constant expression is: \[ K_b = \frac{[\text{NO}]^2[\text{Br}_2]}{[\text{BrNO}]^2} \]

- Writing the Expression for Equation c

For the reaction: \[ \text{CH}_4(g) \Longrightarrow 2 \text{H}_2\text{S}(g) + \text{CS}_2(g) \] The equilibrium constant expression is: \[ K_c = \frac{[\text{H}_2\text{S}]^2[\text{CS}_2]}{[\text{CH}_4]}\]

- Writing the Expression for Equation d

For the reaction: \[ 2 \text{CO}(g) \rightleftharpoons \text{O}_2(g) + 2 \text{CO}_2(g) \] The equilibrium constant expression is: \[ K_d = \frac{[\text{O}_2][\text{CO}_2]^2}{[\text{CO}]^2} \]

Key concepts

Chemical Equilibrium

In chemistry, chemical equilibrium is a state where the concentrations of reactants and products in a closed system remain constant over time. This does not mean the reactants and products are equal in concentration, but rather that their rates of reaction are equal, leading to a stable ratio.

Understanding equilibrium is crucial when studying reactions, as it gives insight into whether the products or reactants are favored under specific conditions. The position of equilibrium can be predicted by the equilibrium constant, a numerical value that represents the ratio of the concentration of the products to the reactants, each raised to the power of their respective stoichiometric coefficients in the balanced chemical equation.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It is based on the conservation of mass where the amount of each element must remain the same before and after a chemical reaction.

Stoichiometric coefficients play a key role because they are used to balance the chemical equation, ensuring that atoms are conserved in the transformation. These coefficients are also used in calculating the equilibrium constant expression. They dictate how to raise the concentration terms in the equilibrium constant expression, reflecting the proportion at which molecules react or are produced.

Gas-Phase Reactions

Gas-phase reactions involve reactants and products that are in the gaseous state under the conditions at which the reaction occurs. These types of reactions are particularly important when working with the equilibrium constant expressions because the concentrations are often expressed in terms of partial pressures.

Importance of Partial Pressure

For gases, partial pressure is a measure of the concentration and is used in the equilibrium expressions in place of molar concentrations. This is because gases behave differently than solids or liquids, and their reactivity is affected by pressure. Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases.

Concentration of Reactants and Products

The concentration of reactants and products is fundamental in determining the direction and extent of a chemical reaction. In the context of chemical equilibrium, the concentrations—or partial pressures for gases—are used to express the position of equilibrium through the equilibrium constant expression.

Understanding Concentration Terms

The square brackets \[ [ ] \] traditionally represent the concentration of species in moles per liter (Molarity). However, for the gas-phase reactions, as stated before, these can also be in terms of partial pressures. The equilibrium constant expression puts these concentrations into a mathematical formula that quantifies the relationship between reactants and products at equilibrium, helping chemists predict how a reaction will proceed under given conditions.