Question

Write the equilibrium expression for each of the following heterogeneous equilibria. a. \(\mathrm{P}_{4}(s)+6 \mathrm{~F}_{2}(g) \rightleftharpoons 4 \mathrm{PF}_{3}(g)\) b. \(\operatorname{Xe}(g)+2 \mathrm{~F}_{2}(g) \rightleftharpoons \mathrm{XeF}_{4}(s)\) c. \(2 \mathrm{SiO}(s)+4 \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{SiCl}_{4}(l)+\mathrm{O}_{2}(g)\)

Short answer

The equilibrium expressions for the given heterogeneous equilibria are: a. \(K = \frac{[\mathrm{PF_3}]^4}{[\mathrm{F_2}]^6}\) b. \(K = \frac{1}{[\mathrm{Xe}][\mathrm{F_2}]^2}\) c. \(K = \frac{[\mathrm{O_2}]}{[\mathrm{Cl_2}]^4}\)

Step-by-step solution

Identify the reactants and products for each equation

For this step, we need to identify the substances involved in the reaction and state their physical states (s-solid, l-liquid, g-gas). We can see that each given equation already has the substances and their states provided.

Write the equilibrium expressions for each heterogeneous equilibrium

For each given reaction, we will write an equilibrium expression which is formed by the multiplication of concentrations of products raised to their stoichiometric coefficients, divided by the multiplication of concentrations of reactants raised to their stoichiometric coefficients. For heterogeneous equilibria, we only include the concentrations of gaseous and aqueous species in the equilibrium expression. Solids and liquids are excluded. a. The heterogeneous equilibrium for the reaction: \(\mathrm{P}_{4}(s)+6 \mathrm{ ~F}_{2}(g) \rightleftharpoons 4 \mathrm{PF}_{3}(g)\) The equilibrium expression for this reaction will be: \[ K = \frac{[\mathrm{PF_3}]^4}{[\mathrm{F_2}]^6} \] b. The heterogeneous equilibrium for the reaction: \(\operatorname{Xe}(g)+2 \mathrm{ ~F}_{2}(g) \rightleftharpoons\mathrm{XeF}_{4}(s)\) The equilibrium expression for this reaction will be: \[ K = \frac{1}{[\mathrm{Xe}][\mathrm{F_2}]^2} \] c. The heterogeneous equilibrium for the reaction: \(2 \mathrm{SiO}(s)+4 \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{SiCl}_{4}(l)+\mathrm{O}_{2}(g)\) The equilibrium expression for this reaction will be: \[ K = \frac{[\mathrm{O_2}]}{[\mathrm{Cl_2}]^4} \]

Key concepts

Equilibrium Expression

Understanding the equilibrium expression is a fundamental aspect of studying chemical reactions that reach a state of balance. In essence, an equilibrium expression represents the ratio of the concentrations of products to reactants, each raised to the power of their stoichiometric coefficients. The coefficients indicate the number of moles participating in the reaction. However, a key point to remember when dealing with heterogeneous equilibria is that only the concentrations of gases and species in solution are included. Solids and liquids, due to their constant concentrations, are omitted because their amount does not change the system's equilibrium.
For instance, if you're presented with the reaction involving phosphorus and fluorine gases producing phosphorus trifluoride, you're inclined to write the equilibrium expression that includes only the gas concentrations. For gaseous reactants and products, you denote their concentration with square brackets and exponentiate them by their stoichiometric coefficients. Within this context, learning to write accurate equilibrium expressions is crucial for predicting the behavior of a chemical system under various conditions.

Stoichiometric Coefficients

Significance of Stoichiometric Coefficients

The stoichiometric coefficients in a chemical equation hold considerable importance as they dictate the proportions in which reactants combine and products form. These coefficients can be thought of as the recipe for a chemical reaction. When writing equilibrium expressions, these coefficients become exponents, which significantly influences the equilibrium position.
Inclusion of these coefficients as exponents demonstrates how sensitive the system's equilibrium is to changes in the concentration of reactants and products. A thorough understanding of how to apply stoichiometric coefficients when constructing equilibrium expressions is a vital skill for anyone learning chemistry. As such, these numbers are more than arbitrary markers; they are quantitative representatives of the precise ratios needed for a reaction to occur under equilibrium conditions.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction proceeds in both the forward and reverse directions at equal rates, leading to a constant composition of the reaction mixture over time. This state does not mean that the reactants and products are present in equal amounts; rather, their ratios are fixed and depend on the specific reaction under consideration.
Exploring equilibrium also means delving into Le Chatelier’s principle, which predicts how a system at equilibrium will respond to external changes. A temperature or pressure change, or the addition of more reactants or products, can shift the position of equilibrium. Understanding chemical equilibrium enhances your capacity to foresee such changes and manipulate conditions to favor the production of desired substances in industrial and laboratory settings. It's the balance between the push and pull in a chemical system that seasoned chemists learn to navigate with precision.

Physical States of Reactants and Products

Relevance of Physical States in Equilibrium

The physical states of reactants and products—solid (s), liquid (l), gas (g), and aqueous (aq)—provide crucial information when analyzing chemical reactions. In the context of heterogeneous equilibria, reactions that involve more than one phase, the state symbols play a critical role. As mentioned earlier, the concentrations of solids and liquids do not appear in the equilibrium expressions since their concentrations are not deemed to change under equilibrium conditions.
It’s essential to acknowledge that different states of matter respond differently to temperature and pressure, and this response, in turn, affects chemical equilibria. Students are encouraged to learn how to identify and correctly denote these states, as it lays the foundation for predicting how a given system might react under a set of specific circumstances. A nuanced comprehension of these concepts is key to mastering the dynamic and ever-evolving dance of atoms and molecules in chemical reactions.