Auto-Ionization: Videos & Practice Problems

Water undergoes self-ionization, producing hydronium (H₃O⁺) and hydroxide (OH^-) ions. This process follows the Brønsted–Lowry theory, where one water molecule acts as an acid, donating H⁺, while the other acts as a base. The ion product constant for water, K_w, is defined as K_w = [H⁺][OH^-], with a standard value of 1.0 × 10^-14 at 25°C. This relationship allows for calculations involving acid-base reactions and equilibrium expressions, emphasizing the temperature dependence of K_w.

Auto-Ionization

Water can undergo a process known as self-ionization or auto-ionization, where two water molecules interact to produce hydronium ions (H₃O⁺) and hydroxide ions (OH^-). In this reaction, one water molecule acts as an acid by donating a proton (H⁺), while the other acts as a base by accepting that proton. According to the Brønsted-Lowry theory, acids are defined as proton donors, and in this case, the water molecule that loses H⁺ becomes OH^-, while the water molecule that gains the proton becomes H₃O⁺.

The simplified representation of this reaction can be expressed as:

2 H₂O (l) ⇌ H⁺ (aq) + OH^- (aq)

It is important to note that H⁺ and H₃O⁺ are often used interchangeably, as they represent the same species in aqueous solutions.

From this self-ionization, we can derive the equilibrium expression known as the ion product constant of water, denoted as K_w. The equilibrium constant is calculated as the ratio of the concentrations of the products to the concentrations of the reactants, excluding solids and liquids. For the auto-ionization of water, the expression simplifies to:

K_w = [H⁺][OH^-]

At a standard temperature of 25 degrees Celsius, the value of K_w is 1.0 x 10^-14. This constant is crucial for calculations involving the concentrations of hydronium and hydroxide ions, as knowing one allows for the determination of the other due to the relationship established by K_w.

It is essential to remember that K_w is temperature-dependent; any changes in temperature will result in a different value for K_w. Therefore, the only K_w value that should be memorized is at 25 degrees Celsius. Understanding this relationship is fundamental for solving problems related to acid-base chemistry and the behavior of water in various conditions.

Auto-Ionization

At 0 degrees Celsius, the ion product of water, denoted as \( K_w \), is recorded as \( 1.2 \times 10^{-15} \). This value indicates the concentration of hydronium ions (\( H_3O^+ \)) and hydroxide ions (\( OH^- \)) in a neutral solution at this temperature. As temperature increases to 25 degrees Celsius, \( K_w \) rises to \( 1.0 \times 10^{-14} \). This temperature dependence of \( K_w \) is crucial in understanding the behavior of water and its autoionization process, represented by the equation:

\[ H_2O_{(l)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + OH^-_{(aq)} \]

According to Le Chatelier's principle, an increase in temperature shifts the equilibrium position away from heat. In this case, since \( K_w \) increases with temperature, it suggests that the formation of products (\( H_3O^+ \) and \( OH^- \)) is favored. This shift indicates that the reaction is endothermic, meaning heat is absorbed as a reactant in the process. Therefore, the reaction can be viewed as:

\[ \text{Heat} + H_2O_{(l)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + OH^-_{(aq)} \]

In contrast, if the temperature were to decrease, the equilibrium would shift to the left, favoring the reactants and resulting in a decrease in \( K_w \). Under thermal neutral conditions, where the change in enthalpy (\( \Delta H \)) is zero, \( K_w \) remains constant, indicating no shift in equilibrium. Thus, understanding the relationship between temperature and \( K_w \) not only helps in determining the direction of the reaction but also in classifying the reaction as endothermic or exothermic.

In summary, the increase in \( K_w \) with temperature signifies that the reaction is endothermic, aligning with the principles of chemical equilibrium and thermodynamics.

Auto-Ionization

To determine the concentration of hydronium ions (\( \text{H}_3\text{O}^+ \)) in pure water at 50 degrees Celsius, it is essential to recognize that the ion product constant of water (\( K_w \)) varies with temperature. At 50 degrees Celsius, \( K_w \) is \( 5.3 \times 10^{-14} \), which differs from the commonly referenced value of \( 1.0 \times 10^{-14} \) at 25 degrees Celsius.

In pure water, the concentrations of hydronium ions and hydroxide ions (\( \text{OH}^- \)) are equal, indicating that the solution is neutral. We can denote both concentrations as \( x \). The relationship between these concentrations and \( K_w \) is expressed by the equation:

\[ K_w = [\text{H}_3\text{O}^+][\text{OH}^-] = x^2 \]

Substituting the value of \( K_w \) at 50 degrees Celsius into the equation gives:

\[ x^2 = 5.3 \times 10^{-14} \]

To find \( x \), we take the square root of both sides:

\[ x = \sqrt{5.3 \times 10^{-14}} \approx 2.30 \times 10^{-7} \, \text{M} \]

This result indicates that the concentration of hydronium ions (\( \text{H}_3\text{O}^+ \)) in pure water at 50 degrees Celsius is \( 2.30 \times 10^{-7} \, \text{M} \). Since the solution is neutral, the concentration of hydroxide ions is also \( 2.30 \times 10^{-7} \, \text{M} \). It is crucial to remember that the value of \( K_w \) is temperature-dependent, and the standard value to memorize is that at 25 degrees Celsius.

Understanding the relationship between hydronium and hydroxide ions in relation to the ion product constant \( K_w \) is fundamental in acid-base chemistry, especially when considering changes in temperature.

Here’s what students ask on this topic:

What is the auto-ionization of water?

The auto-ionization of water is a process where two water molecules react to form hydronium (H₃O⁺) and hydroxide (OH^-) ions. This reaction can be represented as:

$H_2\left(l\right)+H_2\left(l\right)\to H_{3}O+\left(\mathrm{aq}\right)+{\mathrm{OH}}_{-}$

In this process, one water molecule acts as an acid, donating an H⁺ ion, while the other acts as a base, accepting the H⁺ ion. This equilibrium is characterized by the ion product constant for water, K_w, which is 1.0 × 10^-14 at 25°C.

What is the ion product constant for water (Kw) and how is it used?

The ion product constant for water, denoted as K_w, is the equilibrium constant for the auto-ionization of water. It is defined as:

$K_w=\left[H_{+}\right]\left[{\mathrm{OH}}_{-}\right]$

At 25°C, K_w is 1.0 × 10^-14. This constant allows us to calculate the concentrations of H⁺ and OH^- ions in water. If we know the concentration of one ion, we can determine the other using the relationship:

$K_w=\left[H_{+}\right]\left[{\mathrm{OH}}_{-}\right]$

This is crucial for understanding acid-base reactions and pH calculations.

How does temperature affect the ion product constant (Kw) of water?

The ion product constant for water, K_w, is temperature-dependent. At 25°C, K_w is 1.0 × 10^-14. However, as temperature increases, K_w also increases because the auto-ionization of water is an endothermic process. Conversely, as temperature decreases, K_w decreases. This means that the concentrations of H⁺ and OH^- ions in water will vary with temperature. For accurate calculations involving K_w at temperatures other than 25°C, the specific K_w value at that temperature must be provided.

What is the relationship between H⁺ and H₃O⁺ in the context of auto-ionization of water?

In the context of the auto-ionization of water, H⁺ and H₃O⁺ are often used interchangeably. H⁺ represents a proton, which does not exist freely in water but associates with a water molecule to form the hydronium ion, H₃O⁺. Therefore, H⁺ is a simplified notation for H₃O⁺. The reaction can be represented as:

$H_2\left(l\right)+H_2\left(l\right)\to H_{3}O+\left(\mathrm{aq}\right)+{\mathrm{OH}}_{-}$

Thus, H⁺ and H₃O⁺ are essentially the same in aqueous solutions.

Why is the value of Kw important in acid-base chemistry?

The value of K_w is crucial in acid-base chemistry because it defines the relationship between the concentrations of H⁺ and OH^- ions in water. This relationship is given by:

$K_w=\left[H_{+}\right]\left[{\mathrm{OH}}_{-}\right]$

At 25°C, K_w is 1.0 × 10^-14. This constant allows us to calculate the pH and pOH of solutions, which are measures of acidity and basicity, respectively. Understanding K_w helps in predicting the behavior of acids and bases in water, making it fundamental for solving equilibrium problems and understanding the nature of aqueous solutions.