Question

Write the chemical equation for (a) the autoionization of water and (b) the equilibrium law for \(K_{\mathrm{w}}\).

Short answer

The autoionization of water is represented by the equation: \(2 H_2O (l) \leftrightarrow H_3O^+ (aq) + OH^- (aq)\), and the equilibrium constant (\(K_{\mathrm{w}}\)) expression is \(K_{\text{w}} = [H_3O^+][OH^-]\).

Step-by-step solution

Write the autoionization of water

Autoionization of water refers to the reaction where two water molecules react to produce a hydronium ion (\(H_3O^+\right)\) and a hydroxide ion (\(OH^-\right)\). The chemical equation for this process is: \[2 H_2O (l) \leftrightarrow H_3O^+ (aq) + OH^- (aq)\]

Express the equilibrium constant expression for autoionization of water

The equilibrium constant for the autoionization of water (\(K_{\text{w}}\right)\) is expressed by the concentrations of the ions product over reactant, taking into account their stoichiometric coefficients. Since the water (\(H_2O\right)\) is in large excess and is a pure liquid, its concentration remains constant and is not included in the expression. Thus, the equilibrium law for water autoionization is given by: \[K_{\text{w}} = [H_3O^+][OH^-]\]

Key concepts

Chemical Equation

Understanding the autoionization of water involves examining a chemical equation that depicts a reaction where water molecules produce ions. Essentially, two water molecules (\(H_2O\right)\) interact to form a hydronium ion (\(H_3O^+\right)\) and a hydroxide ion (\(OH^-\right)\). This process is vital because it establishes water's ability to conduct electricity and its role as a neutral substance in terms of acidity and basicity.

The balanced chemical equation is represented as: \[2 H_2O (l) \leftrightarrow H_3O^+ (aq) + OH^- (aq)\] This equation showcases a reversible reaction, indicating that it reaches a state of equilibrium where the rates of the forward and reverse reactions are equal. The presence of double arrows (\(\rightleftharpoons\)) symbolizes this equilibrium state, where water can ionize to form ions and ions can recombine to form water.

Equilibrium Constant

The equilibrium constant, denoted as \(K_{\text{w}}\) when referring to water, is a numerical value that expresses the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium.

For the autoionization of water, the equilibrium constant expression is: \[K_{\text{w}} = [H_3O^+][OH^-]\] where \([H_3O^+]\) is the concentration of hydronium ions and \([OH^-]\) is the concentration of hydroxide ions at equilibrium. It's important to note that because water (\(H_2O\right)\) is a pure liquid and is present in a much larger amount than the ions, its concentration is essentially constant and does not change during the reaction. Therefore, water is not included in the equilibrium expression. The value of \(K_{\text{w}}\) is temperature-dependent and is roughly \(1 \times 10^{-14}\) at 25°C, which underscores the low degree of autoionization under typical conditions.

Hydroxide Ion

The hydroxide ion, represented by the symbol \(OH^-\), plays a central role in the autoionization of water and is one of the products formed during the reaction. It is a negatively charged ion, or anion, and is crucial for determining the basicity of a solution.

The concentration of hydroxide ions in a solution affects its pH level—higher concentrations of \(OH^-\) correspond to a more basic (or alkaline) solution, while lower concentrations indicate a more neutral or acidic solution. The presence of \(OH^-\) ions is directly related to the presence of \(H_3O^+\) ions due to the equilibrium nature of the autoionization of water. As such, these ions are constantly being formed and re-formed in water, contributing to its capacity as a solvent and its critical role in chemical reactions.

Hydronium Ion

The hydronium ion, shown as \(H_3O^+\), is the other product of the autoionization of water. It is a positive ion, or cation, formed when a water molecule gains a proton (\(H^+\)). A common misconception is that free protons exist in solution; however, in reality, they are always associated with a water molecule, thus forming the hydronium ion.

The hydronium ion concentration is a key determinant of a solution's acidity. A higher concentration of \(H_3O^+\) leads to a more acidic solution, while a lower concentration suggests a more basic or neutral solution. Understanding how \(H_3O^+\) ions interact within the autoionization of water provides valuable insights into the balance of acidic and basic properties in water and aqueous solutions, influencing pH levels and the behavior of substances dissolved in water.