Question

Does the equilibrium for water autoionization lie to the left or to the right? What constant verifies your answer?

Short answer

The equilibrium for water autoionization lies to the left, as the ion product of water (Kw) is \(1.0 \times 10^{-14}\) at 25°C, which is less than 1. This constant verifies that the equilibrium favors the reactants, meaning there are primarily unreacted water molecules.

Step-by-step solution

Understanding Water Autoionization

Water autoionization is the process by which water molecules (H2O) split into hydrogen ions (H+) and hydroxide ions (OH-). The reaction can be represented as follows: \[2H_2O \rightleftharpoons H_3O^+ + OH^-\]

The Concept of Equilibrium and the Equilibrium Constant

For a reaction to be in equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. Consequently, the concentrations of reactants and products remain constant. The equilibrium constant (K) is the ratio of product concentrations and reactant concentrations raised to their stoichiometric coefficients at equilibrium. For this reaction above, we have a specific equilibrium constant called the ion product of water (Kw): \[K_w = [H_3O^+] [OH^-]\] If K > 1, then the equilibrium favors the formation of products; whereas if K < 1, it favors the reactants.

Determine Which Side of the Equilibrium Favors the Autoionization of Water

The ion product of water, Kw, has a value of \(1.0 \times 10^{-14}\) at 25°C. Since Kw is less than 1, the equilibrium favors the reactants, meaning that the autoionization of water lies to the left.

Provide the Constant that Verifies the Answer

The constant that verifies our answer is the ion product of water (Kw), which is \(1.0 \times 10^{-14}\) at 25°C. This value is less than 1, indicating that the equilibrium lies to the left and primarily consists of unreacted water molecules.

Key concepts

Chemical Equilibrium

When we talk about chemical reactions, they typically reach a point where the forward and reverse reactions occur at the same rate, leading to a stable ratio of reactants and products. This state is known as chemical equilibrium. At this point, no net change in the concentration of reactants and products occurs, even though both reactions continue to happen. This concept is crucial because it allows us to predict the concentrations of various components in a reaction at any given time.

For the autoionization of water, equilibrium means that water molecules are constantly changing to ions and vice versa, but the system becomes stabilized with a fixed ratio of water (H₂O) to hydronium (H₃O⁺) and hydroxide (OH^-) ions.

Ion Product of Water (Kw)

The ion product of water (Kw) is a special equilibrium constant for the autoionization of water. This constant quantifies the extent to which water dissociates into its ions. At 25°C, the value of Kw is always 1.0 x 10^-14. This tiny value indicates that, even though the autoionization of water is an equilibrium process, very few water molecules are ionized at any moment.

The ion product has important implications for understanding pH, a measure of acidity and alkalinity in a solution. The equilibrium of water shows us that the product of the molar concentrations of H₃O⁺ and OH^- is constant, providing a foundational concept for exploring the behavior of acids and bases in water.

Equilibrium Constant (K)

The equilibrium constant (K) is a number that expresses the ratio of the concentrations of products to reactants for a reversible chemical reaction at equilibrium. Each concentration is raised to the power of its coefficient in the balanced chemical equation. The magnitude of the constant gives us insight into the position of equilibrium.

If K is much greater than 1, the products are favored at equilibrium; conversely, if K is much less than 1, the reactants are favored. In the case of water’s autoionization, the equilibrium constant (Kw) is significantly less than 1, which helps to clarify why there are far more unreacted water molecules than ions present. This particular constant is a foundational concept not just for chemical equilibrium, but also for the fields of acid-base chemistry, solubility, and many other areas in chemistry.