Question

Write the equilibrium expression for each of the following heterogeneous equilibria. a. \(\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{4}(l)\) b. \(2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{CH}_{4} \mathrm{O}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{Zrl}_{4}(s) \rightleftharpoons \mathrm{Zr}(s)+2 \mathrm{I}_{2}(g)\)

Short answer

The equilibrium expressions for the given heterogeneous equilibria are: a. \(Q_c = [\mathrm{SO}_{3}]\) b. \(Q_c = \frac{[\mathrm{H}_{2} \mathrm{O}]}{[\mathrm{NH}_{3}]^{2} [\mathrm{CO}_{2}]}\) c. \(Q_c = [\mathrm{I}_{2}]^{2}\)

Step-by-step solution

In this reaction, we have: - \(\mathrm{SO}_{3}(g)\): a gas - \(\mathrm{H}_{2} \mathrm{O}(l)\): a liquid - \(\mathrm{H}_{2} \mathrm{SO}_{4}(l)\): a liquid #Step 2: Write the equilibrium expression without incorporating solids and liquids#

Since we have only one gas in the reaction, the equilibrium expression will just be: \[Q_c = [\mathrm{SO}_{3}]\] b. \(2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{N}_{2}\mathrm{CH}_{4}\mathrm{O}(s)+\mathrm{H}_{2}\mathrm{O}(g)\) #Step 1: Identify solids, liquids, and gases in the reaction#

In this reaction, we have: - \(2 \mathrm{NH}_{3}(g)\): a gas - \(\mathrm{CO}_{2}(g)\): a gas - \(\mathrm{N}_{2} \mathrm{CH}_{4} \mathrm{O}(s)\): a solid - \(\mathrm{H}_{2} \mathrm{O}(g)\): a gas #Step 2: Write the equilibrium expression without incorporating solids and liquids#

Excluding the solid, write the equilibrium expression for the reaction: \[Q_c = \frac{[\mathrm{H}_{2} \mathrm{O}]}{[\mathrm{NH}_{3}]^{2} [\mathrm{CO}_{2}]}\] c. \(\mathrm{ZrI}_{4}(s) \rightleftharpoons \mathrm{Zr}(s)+2 \mathrm{I}_{2}(g)\) #Step 1: Identify solids, liquids, and gases in the reaction#

In this reaction, we have: - \(\mathrm{ZrI}_{4}(s)\): a solid - \(\mathrm{Zr}(s)\): a solid - \(2 \mathrm{I}_{2}(g)\): a gas #Step 2: Write the equilibrium expression without incorporating solids and liquids#

Since there is only one gas in the reaction, the equilibrium expression will be: \[Q_c = [\mathrm{I}_{2}]^{2}\]

Key concepts

heterogeneous equilibria

Heterogeneous equilibria involve reactions where reactants and products are in different phases. This is in contrast to homogeneous equilibria where all substances are in the same phase. Understanding this concept is crucial in predicting and calculating equilibrium expressions.
In the reactions provided:

• Example (a) involves gases interacting with liquids, such as \[\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{4}(l)\]
• Example (b) features gases and solids: \(2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{N}_{2}\mathrm{CH}_{4}\mathrm{O}(s)+\mathrm{H}_{2}\mathrm{O}(g)\)
• Example (c) includes solids and gases: \(\mathrm{ZrI}_{4}(s) \rightleftharpoons \mathrm{Zr}(s)+2 \mathrm{I}_{2}(g)\)

In heterogeneous equilibria, it's essential to consider which phases' contributions need to be evaluated in the equilibrium expression. Phases such as liquids and solids typically do not appear in the equilibrium expression because their concentrations are considered constant throughout the reaction.

equilibrium expression

The equilibrium expression is a mathematical equation that represents the balance of reactants and products at equilibrium. It involves the concentrations of gases and aqueous solutions, whereas solids and liquids are omitted as their activities are essentially constant.
To write the equilibrium expression, use the following as general guidance:

• Include concentrations of gases (denoted as \([X]\) where \(X\) is a gaseous species).
• Omit pure solids and liquids.
• Use coefficients from the balanced equation as exponents in the expression.
• For example: In \(2 \mathrm{NH}_{3}(g) + \mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{CH}_{4} \mathrm{O}(s) + \mathrm{H}_{2} \mathrm{O}(g)\), the expression omits the solid and is written as \[Q_c = \frac{[\mathrm{H}_{2} \mathrm{O}]}{[\mathrm{NH}_{3}]^2 [\mathrm{CO}_{2}]}\]

These expressions allow chemists to calculate the ratio of product concentrations to reactant concentrations when the reaction is economically balanced.

reaction phases

Reaction phases refer to the distinct states of matter in which reactants and products exist during a chemical reaction, namely solids, liquids, gases, and sometimes aqueous solutions. Identifying these phases is important for constructing the correct equilibrium expressions and understanding the behavior of the system.
Each example from the exercise involves various reaction phases:

• In the reaction \(\mathrm{SO}_{3}(g) + \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{4}(l)\), gases and liquids are present, with water acting as a liquid which isn't considered in the equilibrium expression.
• In \(2 \mathrm{NH}_{3}(g) + \mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{CH}_{4} \mathrm{O}(s) + \mathrm{H}_{2} \mathrm{O}(g)\), gases and a solid are observed. Only gaseous species enter into the expression because the solid's activity is constant.
• The final reaction \(\mathrm{ZrI}_{4}(s) \rightleftharpoons \mathrm{Zr}(s) + 2 \mathrm{I}_{2}(g)\) involves solid and gaseous phases. The gases are used to write: \[Q_c = [\mathrm{I}_{2}]^2\].

Understanding reaction phases allows us to ignore phases that do not change concentration in equilibrium expressions, primarily focusing on those that are dynamic and measurable.