Question

Mercury(I) oxide decomposes into elemental mercury and elemental oxygen: \(2 \mathrm{Hg}_{2} \mathrm{O}(s) \rightleftharpoons 4 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\) (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures. (b) Explain why we normally exclude pure solids and liquids from equilibrium- constant expressions.

Short answer

(a) The equilibrium constant expression for the given reaction in terms of partial pressures is: \[K_p = P_{O_2}\] (b) We normally exclude pure solids and liquids from equilibrium-constant expressions because their concentrations do not change during the course of the reaction, and their chemical potentials remain constant. Their contribution to the equilibrium is already included in the equilibrium constant itself.

Step-by-step solution

(a) Equilibrium constant expression in terms of partial pressures

To find the equilibrium constant expression for the given reaction, we have to use the formula: \(K_p = \frac{(P_{products})^{\Delta n}}{(P_{reactants})^{\Delta n}}\) Where \(K_p\) represents the equilibrium constant in terms of partial pressures, and \(\Delta n\) refers to the stoichiometric coefficient in the balanced chemical equation. So, the balanced chemical equation: \[2{Hg_2O(s)} \rightleftharpoons 4{Hg(l)} + {O2(g)}\] Now, let's plug in the values for the partial pressures: \(K_p = \frac{P_{O_2}}{1}\) Note that pure solids (Hg²O) and liquids (Hg) are excluded, and we will explain the reason for that in part (b). The final equilibrium constant expression for the given reaction in terms of partial pressures is: \[K_p = P_{O_2}\]

(b) Explanation for excluding pure solids and liquids from equilibrium-constant expressions

The equilibrium constant expressions are based on the activities or concentrations of the chemical species involved in the reaction. Since pure solids and liquids have fixed compositions and their concentrations do not change during the course of the reaction, their activities are considered constant. In other words, their contribution to the equilibrium is included in the equilibrium constant itself. Excluding pure solids and liquids from equilibrium-constant expressions can also be attributed to an important concept related to chemical potentials. Chemical potential, a thermodynamic quantity that is related to the activity of a chemical species, doesn't change for pure solids and liquids during a reaction. Since the equilibrium constant is directly proportional to the ratio of the chemical potentials of the products and reactants, any term involving a pure solid or liquid has no impact on the reaction, so it is excluded from the expression. Thus, we usually disregard pure solids and liquids from equilibrium-constant expressions due to their constant nature and unchanging chemical potentials during a reaction.

Key concepts

Understanding Chemical Equilibrium

Chemical equilibrium is a fundamental concept in the study of chemical reactions and is crucial to predicting the behavior of a system. It occurs when the rates of the forward and reverse reactions are equal, resulting in no net change in the proportions of reactants and products. At equilibrium, the system is static at a macroscopic level, but at a molecular level, the exchange of substances continues.

For instance, in the decomposition of Mercury(I) oxide, as given in the problem, the forward reaction converts the oxide into elemental mercury and oxygen, while the reverse reaction reforms the Mercury(I) oxide. Equilibrium is achieved when these two rates balance out. In writing the equilibrium constant expression, we consider the concentrations or, in the case of gases, the partial pressures of the reactants and products. Understanding how to correctly form these expressions is key for students to grasp how different variables might influence the equilibrium state of a reaction.

The Role of Partial Pressures in Equilibrium

Partial pressures play a pivotal role when dealing with gases at equilibrium. The pressure exerted by a particular gas in a mixture is known as its partial pressure, and it reflects the concentration of that gas in the mixture. When gases are involved in a chemical equilibrium, the equilibrium constant can be expressed in terms of partial pressures, often denoted as K_p.

In our example involving Mercury(I) oxide, the equilibrium expression takes into account the partial pressure of oxygen, given that it is the only gas present. The concentration or activity of solids and liquids remains constant during the reaction and does not figure in the equilibrium expression. This simplification, focusing exclusively on gases, augments students' comprehension of reactions involving phase differences and how the concentration of different states of matter respond to changes in equilibrium.

Thermodynamics and Equilibrium

Thermodynamics is the branch of physical science that deals with the relations between heat and other forms of energy. It is acutely important when studying chemical equilibria since it helps explain how energy changes affect the equilibrium position. Specifically, it can forecast which direction a reaction will proceed when it is not at equilibrium, and the extent of the reaction at equilibrium.

Regarding the decomposition of Mercury(I) oxide, thermodynamics provides insight into the energy required to break the chemical bonds in the compound and form elemental mercury and oxygen. It also explains why pure solids and liquids are not incorporated in the equilibrium constant expression, as their energy does not vary in the way it does for gases. Thermodynamics, thus, aids in developing a more nuanced understanding of chemical equilibrium by adding a layer of quantitative analysis to predict and explain reaction changes.

Chemical Reactions and Their Equilibrium States

Chemical reactions involve the transformation of reactants into products, a process that can be reversible or irreversible. The decomposition of Mercury(I) oxide is an example of a reversible reaction, where products can reform the original reactants. Understanding chemical reactions entails more than simply writing down the reactants and products; it involves a deep dive into the stoichiometry, reaction rates, and energy profiles of a reaction.

Equilibrium states provide a snapshot of where a reaction rests under specific conditions. The equilibrium constant, denoted as K, is a measure of this state and offers valuable insight into whether reactants or products are favored in a reversible reaction. For students to truly understand chemical reactions, they must also understand the conditions, such as temperature and pressure, that can shift the equilibrium and affect the extent of the reaction. The concept of equilibrium underpins this understanding, highlighting the delicate balance that governs chemical processes in nature and industry alike.