Question

What is meant by the ion-product constant for water, \(K_{\mathrm{w}}\) ? What does this constant signify? Write an equation for the chemical reaction from which the constant is derived.

Short answer

The ion-product constant for water, \(K_w\), represents the equilibrium constant for the self-ionization of water, where water molecules dissociate into hydrogen ions (H^+) and hydroxide ions (OH^-). It is given by the expression \(K_w = [H^+][OH^-]\) and is significant for understanding the behavior of acids and bases in aqueous solutions and calculating pH. The chemical reaction for the self-ionization of water is \(H_2O_{(l)} \longleftrightarrow H^+_{(aq)} + OH^-_{(aq)}\). At 25 degrees Celsius, \(K_w\) is nearly \(1.0 \times 10^{-14}\), and its value changes with temperature.

Step-by-step solution

Definition of \(K_w\)

\(K_w\) is the ion-product constant for water, also known as the dissociation constant of water. It represents the equilibrium constant for the self-ionization of water, where water molecules dissociate into hydrogen ions (H^+) and hydroxide ions (OH^-). The constant is given by the expression: $$K_w = [H^+][OH^-]$$ where [H^+] and [OH^-] represent the concentrations of hydrogen and hydroxide ions in the solution, respectively.

Significance of \(K_w\)

\(K_w\) is significant because it helps to understand the behavior of acids and bases in aqueous solutions. In pure water, the ion product constant remains constant at a given temperature, and the concentrations of H^+ and OH^- ions are equal. As we add an acid or base to the solution, the concentrations of these ions change, but their product remains equal to \(K_w\). This constant also plays an essential role in calculating the pH and acidity of a solution. Experimentally, at 25 degrees Celsius, the ion-product constant for water, \(K_w\), is found to be nearly \(1.0 \times 10^{-14}\). This value changes with temperature, increasing with an increase in temperature, and vice versa.

Chemical reaction equation

The ion-product constant for water is derived from the equilibrium constant of the self-ionization reaction of water. The chemical reaction is given by: $$H_2O_{(l)} \longleftrightarrow H^+_{(aq)} + OH^-_{(aq)}$$ This reaction shows water molecules dissociating into hydrogen ions (H^+) and hydroxide ions (OH^-). At equilibrium, the ion-product constant for water, \(K_w\), can be calculated by multiplying the concentrations of hydrogen ions and hydroxide ions, as mentioned earlier.

Key concepts

Equilibrium Constant

The concept of an equilibrium constant is fundamental in understanding chemical reactions. It represents the numeric value that expresses the ratio of the concentration of the products to reactants at equilibrium. In the case of water, the equilibrium constant is known as the ion-product constant for water, denoted as \( K_w \).
This constant is a specific example that applies to the self-ionization of water. Equilibrium constants help chemists predict the position of equilibrium and the extent of reactions. For water, the constant showcases how water weakly ionizes into ions that are crucial to acid-base chemistry. At 25°C, this equilibrium constant \( K_w \) equals \( 1.0 \times 10^{-14} \). Understanding these constants can deepen your grasp of how substances interact in solutions.
In summary, knowing the equilibrium constant helps in predicting how changes in concentration, temperature, or pressure can shift equilibrium positions in various chemical reactions.

Self-Ionization of Water

Water is an extraordinary molecule, and one reason is its ability to self-ionize. This means water can dissociate into its ions even without the presence of an acid or base. The process can be represented by the reaction:
\[ H_2O_{(l)} \longleftrightarrow H^+_{(aq)} + OH^-_{(aq)} \]
This self-ionization is essential for many processes in chemistry, particularly in acid-base behavior. In pure water, this auto-ionization is in dynamic equilibrium. The ions \( H^+ \) and \( OH^- \) are produced and consumed at the same rate. The product of their concentrations at this equilibrium state is referred to as \( K_w \), the ion-product constant of water.
This intrinsic ionization is crucial for understanding water's role as a neutral medium and serves as a baseline when studying acidic or basic solutions.

Acid-Base Behavior

Acids and bases are integral to chemical reactions, especially in aqueous solutions. Understanding their behavior involves exploring how they dissociate in water to form \( H^+ \) or \( OH^- \) ions. With \( K_w \), we grasp how acids and bases affect water's balance.

• Adding an acid increases \( H^+ \) ion concentration, affecting the equilibrium.
• Adding a base increases \( OH^- \) ion concentration, impacting the same equilibrium.

Despite the changes, the product \( [H^+][OH^-] \) remains constant, equal to \( K_w \). Understanding this constant hint allows us to predict how different substances interact in water, influencing reactions and solubility.
This knowledge is foundational for chemistry as it helps forecast reactions, design solutions, and understand natural processes like buffer systems and titrations.

pH Calculation

The pH of a solution is a measure of its acidity or basicity. It is intimately linked to the concentrations of \( H^+ \) ions in a solution. The pH is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
Water's self-ionization gives equal concentrations of \( H^+ \) and \( OH^- \), making pure water neutral with a pH of 7 at 25°C. Since the product \( [H^+][OH^-] = K_w \), knowing one concentration allows calculation of the other, crucial for pH calculations.
This understanding aids in adjusting the pH of solutions for practical applications like agriculture, medicine, and industry. It underscores the importance of moles over mass; it's the ratio that matters most.
Grasping pH calculation empowers you to predict and control how substances react in various environments, ensuring safety and efficacy in chemical applications.