Problem 50 - Chemistry The Molecular Nature of Matter

Question

Write the equilibrium law corresponding to \(K_{c}\) for each of the following heterogeneous reactions. (a) \(\mathrm{CaCO}_{3}(s)+\mathrm{SO}_{2}(g) \rightleftharpoons \mathrm{CaSO}_{3}(s)+\mathrm{CO}_{2}(g)\) (b) \(\mathrm{AgCl}(s)+\mathrm{Br}^{-}(a q) \rightleftharpoons \mathrm{AgBr}(s)+\mathrm{Cl}^{-}(a q)\) (c) \(\mathrm{Cu}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{Cu}^{2+}(a q)+2 \mathrm{OH}^{-}(a q)\) (d) \(\mathrm{Mg}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (e) \(3 \mathrm{CuO}(s)+2 \mathrm{NH}_{3}(g) \rightleftharpoons\) \(3 \mathrm{Cu}(s)+\mathrm{N}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

a) \(K_{c} = \frac{[CO_2(g)]}{[SO_2(g)]}\), b)\(K_{c} = \frac{[Cl^- (aq)]}{[Br^- (aq)]}\), c) \(K_{c} = [Cu^{2+}(aq)][OH^- (aq)]^2\), d) \(K_{c} = \frac{[H_2O(g)]}{\text{No reactants in the denominator as they are solids}}\), e) \(K_{c} = \frac{[N_2(g)][H_2O(g)]^3}{[NH_3(g)]^2}\)

Step 1: Identify the Phase of Each Substance

Determine the physical state of each reactant and product. According to the convention in this context, (s) denotes a solid, (g) denotes a gas, and (aq) denotes an aqueous solution that’s well-dissolved in water.

Step 2: Write the Initial Equilibrium Expression

The equilibrium constant expression (\(K_c\)) for a reaction is the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their respective stoichiometric coefficients in the balanced equation.

Step 3: Exclude Solids and Liquids from the Equilibrium Expression

Remember that the concentrations of pure solids and pure liquids don't appear in the equilibrium expression because their concentrations don't change during the reaction.

Step 4: Write the Equilibrium Expression for Each Reaction

For each reaction, write the equilibrium expression including only the terms for the gases and aqueous solutions.

Key Concepts

Chemical Equilibrium

When a chemical reaction occurs, reactants are transformed into products. However, not all reactions go to completion. In some cases, the products can react to form the reactants again. This two-way process continues until the rates of the forward and reverse reactions are the same, leading to a state called chemical equilibrium. At equilibrium, the concentrations of the reactants and products remain constant over time, although they are not necessarily equal. It's important to note that this is a dynamic process－molecules are constantly reacting, but there's no net change in concentration.

For students looking to truly understand this concept, it helps to imagine a busy intersection with cars coming and going at the same pace. Just as the number of cars on each road remains constant despite the ongoing traffic, the concentration of each chemical species in a reaction at equilibrium remains unchanged even as the reactions proceed.

Heterogeneous Reactions

Heterogeneous reactions involve reactants and products that are in different phases, such as solids, liquids, gases, or aqueous solutions. A prime example is the reaction between a solid and a gas, resulting in another solid and gas. What's peculiar about these reactions is that the rules for writing equilibrium expressions change slightly. Unlike homogeneous reactions, where all reactants and products are in the same phase and all are included in the equilibrium expression, heterogeneous reactions do not include pure solids or liquids in the equilibrium expression.

This omission is due to the fact that the concentrations of pure solids and liquids remain constant throughout the reaction, their presence does not change the overall reaction rate significantly. Therefore, when you're writing an equilibrium constant expression for a heterogeneous reaction, remember to include only gases and aqueous solutions. Visualizing the reaction mixture as a pie with distinct sections can help students remember that only the 'slices' (phases) that can change in size (concentrations) are included in the calculations.

Equilibrium Constant Expression

The equilibrium constant expression is a quantitative representation of the ratio of product concentrations to reactant concentrations at equilibrium, with each raised to the power of their stoichiometric coefficients from the balanced chemical equation. In math terms, for a general reaction \(aA + bB \rightleftharpoons cC + dD\), the equilibrium constant expression for the reaction quotient, \(K_{c}\), would be \[K_{c} = \frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}}\] where the square brackets represent the molarity of each species. It’s crucial to understand that 'Kc' is only concerned with species in the gas or aqueous phase; pure solids and liquids are not included as their concentrations are constant and do not affect the value of the equilibrium constant.

For students revisiting their textbook problems, remember that 'Kc' is dependent on temperature, so the same reaction can have different equilibrium constants if carried out at different temperatures. The constant provides insight into the extent of the reaction: a large 'Kc' suggests a greater concentration of products at equilibrium, while a small 'Kc' implies a reaction that favors the reactants.