Question

Indicate each of the following for the ionization of pure water: (a) the simplified ionization equation (b) the ionization constant equation, \(K_{w}\) (c) the ionization constant at \(25^{\circ} \mathrm{C}\)

Short answer

(a) \(\text{H}_2\text{O} (l) \rightleftharpoons \text{H}^+ (aq) + \text{OH}^- (aq)\) ; (b) \(K_w = [\text{H}^+][\text{OH}^-]\) ; (c) \(K_w = 1.0 \times 10^{-14}\) at 25°C.

Step-by-step solution

Identify the Ionization Equation

The ionization of water involves the dissociation of water molecules into hydrogen ions (H^+) and hydroxide ions (OH^-). The simplified ionization equation for the ionization of water can be represented as:\[ \text{H}_2\text{O} (l) \rightleftharpoons \text{H}^+ (aq) + \text{OH}^- (aq) \]

Write the Ionization Constant Equation

The ionization constant (K_w) for water is defined by the equilibrium concentrations of hydrogen and hydroxide ions produced by its ionization. The equation representing this constant is:\[ K_w = [\text{H}^+][\text{OH}^-] \]This relation is derived from the concentration of products over reactants in the ionization equation, considering that the concentration of liquid water remains effectively constant in dilute solutions.

State the Ionization Constant at 25°C

At 25°C, the ionization constant for water, K_w, has a well-known value. The value of K_w at this temperature is:\[ K_w = 1.0 \times 10^{-14} \]This means that, at 25°C, the product of the concentrations of hydrogen ions and hydroxide ions in pure water is 1.0 \times 10^{-14}.

Key concepts

Ionization Equation

In the context of water ionization, we aim to understand how water molecules break down into ions. Water, as a pure substance, can self-ionize, which means it splits into its ionic components without the need for other substances.

The simplified ionization equation for water is crucial for understanding this process. It shows the splitting of water (\( ext{H}_2 ext{O} (l) \) ) into two ions:

• Hydrogen ions (\( ext{H}^+ (aq) \))
• Hydroxide ions (\( ext{OH}^- (aq) \))

This can be summarized by the following equation:\[\text{H}_2\text{O} (l) \rightleftharpoons \text{H}^+ (aq) + \text{OH}^- (aq)\]The double arrow indicates that this reaction is in equilibrium, constantly shifting back and forth between the formation of water and its ions.

This equation is fundamental because it shows the basic action of ionization in water, which sets the stage for understanding related concepts such as the ionization constant and equilibrium.

Ionization Constant

The concept of the ionization constant is a step further in understanding how water's ionization behaves in a quantitative manner. To engage with this, we must recognize the establishment of an equilibrium that occurs when water ionizes.

The ionization constant, symbolized as \( K_w \), helps us quantify the equilibrium state of ionized water. It expresses how much hydrogen and hydroxide ions are present in the system at any given time, without considering the concentration of water itself, which remains essentially constant.

The ionization constant equation is written as:\[K_w = [\text{H}^+][\text{OH}^-]\]

• \( [\text{H}^+] \) is the concentration of hydrogen ions.
• \( [\text{OH}^-] \) is the concentration of hydroxide ions.

This equation reflects only the concentrations of ions created during ionization and assumes the reaction has reached an equilibrium state.

Understanding the value of \( K_w \) is pivotal for any calculations involving the pH of solutions, as it directly relates to how acidic or basic a system can become.

Equilibrium Constant

The equilibrium constant is a critical concept in chemistry that tells us about the balance of a reversible reaction. When applied to the ionization of water, it shows how balanced the ionization process is at a particular temperature, such as the standard lab temperature of 25°C.

At 25°C, the ionization constant \( K_w \) reaches a specific value, showing the consistency of ion formation in water under these conditions. The equilibrium constant for water at this temperature is given as:\[K_w = 1.0 \times 10^{-14}\]Now, what does this number mean? This key value indicates that the product of the concentrations of \( [\text{H}^+] \) and \( [\text{OH}^-] \) in pure water is extremely low.

• This value implies that only a very tiny fraction of water molecules dissociate into ions at any given moment.
• The low dissociation is why pure water is neutral, having a pH of around 7.

Grasping the equilibrium constant helps us predict how changes in temperature could affect this balance, impacting everything from reaction rates to acidity levels in chemical processes.