Auto-Ionization: Videos & Practice Problems

Autoionization of water involves water molecules acting as both acids and bases, resulting in the formation of hydronium ions (H₃O⁺) and hydroxide ions (OH^-). The ionization constant of water (K_w) at 25°C is 1.0 × 10^-14, which is crucial for understanding pH and pOH relationships, expressed as pH + pOH = 14. K_w is temperature-dependent, generally increasing with temperature. This equilibrium is essential for maintaining the acidity or basicity of aqueous solutions, highlighting the amphoteric nature of water.

Auto-Ionization and Kw

Autoionization of water is a fundamental process where water molecules interact with each other in an aqueous solution. Water is classified as amphoteric, meaning it can function as both an acid and a base. In this reaction, one water molecule acts as a base by accepting a proton (H⁺), while another acts as an acid by donating a proton. The result of this interaction is the formation of the hydronium ion (H₃O⁺) and the hydroxide ion (OH^-).

This reaction is associated with the ionization constant of water, denoted as K_w. K_w is an equilibrium constant that represents the ratio of the concentrations of the products (H₃O⁺ and OH^-) to the reactants. It is important to note that K_w does not include pure liquids or solids in its expression, focusing solely on aqueous and gaseous species. The expression for K_w can be written as:

K_w = [H₃O⁺][OH^-]

At 25 degrees Celsius, the value of K_w is 1.0 × 10^-14. This relationship is crucial as it connects to the formula pH + pOH = 14. The concentrations of H₃O⁺ and OH^- are inversely related; when one increases, the other decreases, which helps maintain the balance of acidity and basicity in any aqueous solution.

In pure water, the concentrations of H₃O⁺ and OH^- are equal, leading to a neutral solution. Understanding autoionization is essential for grasping the relationship between hydronium and hydroxide ion concentrations, which ultimately informs the ionization constant expression for water and the pH scale.

Kw and Temperature

At 25 degrees Celsius, the ion product of water, denoted as \( K_w \), is equal to \( 1.0 \times 10^{-14} \). This value is crucial to remember, as it serves as a reference point for understanding the behavior of water's ionization. \( K_w \) is classified as an equilibrium constant, which means it is influenced by temperature changes. As the temperature rises above 25 degrees Celsius, the value of \( K_w \) tends to increase. This trend can be observed across a temperature range from 0 degrees Celsius to 100 degrees Celsius, where \( K_w \) consistently rises with increasing temperature.

It is important to note that while you are expected to remember the value of \( K_w \) at 25 degrees Celsius, you will not be required to memorize the values at other temperatures. Instead, if the temperature deviates from 25 degrees Celsius, you will be provided with the corresponding \( K_w \) value, as it can vary significantly. Understanding this relationship between temperature and \( K_w \) is essential for grasping the dynamics of acid-base chemistry and the behavior of aqueous solutions.

Auto-Ionization Example

To determine the hydroxide ion concentration in an aqueous solution at 50 degrees Celsius, we start with the known concentration of hydronium ions, which is given as \( [H_3O^+] = 3.7 \times 10^{-4} \, \text{mol/L} \). The relationship between hydronium ions and hydroxide ions is defined by the ion product of water, \( K_w \), which at 50 degrees Celsius is \( K_w = 5.476 \times 10^{-14} \).

The equation connecting these concentrations is:

\[ K_w = [H_3O^+] \times [OH^-] \]

Substituting the known values into the equation, we have:

\[ 5.476 \times 10^{-14} = (3.7 \times 10^{-4}) \times [OH^-] \]

To find the hydroxide ion concentration, we rearrange the equation:

\[ [OH^-] = \frac{K_w}{[H_3O^+]} \]

Plugging in the values:

\[ [OH^-] = \frac{5.476 \times 10^{-14}}{3.7 \times 10^{-4}} \approx 1.48 \times 10^{-10} \, \text{mol/L} \]

Now, to classify the solution as acidic, basic, or neutral, we compare the concentrations of hydronium and hydroxide ions. Since \( [H_3O^+] = 3.7 \times 10^{-4} \) is greater than \( [OH^-] = 1.48 \times 10^{-10} \), the solution is identified as acidic. Thus, we conclude that the hydroxide ion concentration is \( 1.48 \times 10^{-10} \, \text{mol/L} \) and the solution is acidic.

Chemistry student prepared an aqueous solution at 30ºC. If the solutions contains 7.42 × 10⁻⁹ M of hydroxide ions, calculate the pH.

• A. 5.703
• B. 8.130
• C. 8.300
• D. 5.980

Answer: (A)

Calculate the K_w of pure water given the pH = 6.34.

• A. 4.57 × 10⁻⁷
• B. 6.76 × 10⁻⁴
• C. 2.09 × 10⁻¹³
• D. 4.57 × 10⁻¹⁴

Answer: (C)

Here’s what students ask on this topic:

What is the autoionization of water and how does it occur?

Autoionization of water occurs when water molecules react with each other in an aqueous solution. Water is amphoteric, meaning it can act as both an acid and a base. In this process, one water molecule donates a proton (H⁺) to another water molecule. The water molecule that accepts the proton becomes a hydronium ion (H₃O⁺), and the one that donates the proton becomes a hydroxide ion (OH^-). This reaction is represented by the equilibrium constant of water (K_w), which at 25°C is 1.0 × 10^-14. This equilibrium is crucial for understanding the pH and pOH relationships in aqueous solutions.

What is the value of the ionization constant of water (K_w) at 25°C?

The ionization constant of water (K_w) at 25°C is 1.0 × 10^-14. This value is essential for calculating the pH and pOH of aqueous solutions. The relationship between pH and pOH is given by the equation pH + pOH = 14. K_w is temperature-dependent and generally increases with increasing temperature.

How does temperature affect the ionization constant of water (K_w)?

The ionization constant of water (K_w) is temperature-dependent. As the temperature increases, the value of K_w generally increases. For example, at 25°C, K_w is 1.0 × 10^-14, but this value will change if the temperature deviates from 25°C. This trend is important to consider when studying the pH and pOH of solutions at different temperatures.

Why is the autoionization of water important for understanding pH and pOH?

The autoionization of water is crucial for understanding pH and pOH because it establishes the relationship between the concentrations of hydronium ions (H₃O⁺) and hydroxide ions (OH^-). The ionization constant of water (K_w) at 25°C is 1.0 × 10^-14, leading to the equation pH + pOH = 14. This relationship helps in determining the acidity or basicity of aqueous solutions and is fundamental in various chemical calculations.

What does it mean for water to be amphoteric in the context of autoionization?

In the context of autoionization, water being amphoteric means that it can act as both an acid and a base. During autoionization, one water molecule donates a proton (H⁺) to another water molecule. The molecule that donates the proton acts as an acid, forming a hydroxide ion (OH^-), while the molecule that accepts the proton acts as a base, forming a hydronium ion (H₃O⁺). This dual behavior is essential for the equilibrium that defines the ionization constant of water (K_w).