Auto-Ionization: Videos & Practice Problems

Autoionization of water occurs when water molecules react with each other, producing hydronium ions (H₃O⁺) and hydroxide ions (OH^-). This process involves one water molecule acting as an acid (donating H⁺) and another as a base (accepting H⁺). The ion product constant for water (K_w) is defined as K_w = [H₃O⁺][OH^-], with a value of 1.0 x 10^-14 at 25°C, which increases with temperature. Understanding this equilibrium is crucial for acid-base reactions and calculations in aqueous solutions.

Auto-Ionization Concept 1

The autoionization of water is a fundamental process in aqueous solutions where water molecules interact with each other, resulting in the formation of hydronium ions (H₃O⁺) and hydroxide ions (OH^-). This phenomenon, also known as self-ionization, occurs when one water molecule acts as an acid, donating a proton (H⁺), while another acts as a base, accepting that proton. According to the Brønsted-Lowry definitions, the acid is the proton donor and the base is the proton acceptor. Consequently, the water molecule that donates the proton transforms into OH^-, while the one that accepts it becomes H₃O⁺.

In this context, it is important to note that while water exists in its liquid form, the ions produced during autoionization are considered aqueous, meaning they are dissolved in water. This process can be simplified to the equation: H₂O ⇌ H₃O⁺ + OH^-. It is also crucial to recognize that H⁺ is often represented as H₃O⁺, indicating that they are effectively the same entity in solution.

The equilibrium constant for the autoionization of water is referred to as the ion product, denoted as K_w. The expression for K_w is given by:

K_w = [H₃O⁺][OH^-]

At a standard temperature of 25 degrees Celsius, the value of K_w is 1.0 x 10^-14. It is essential to understand that K_w is temperature-dependent; as the temperature increases, the value of K_w also increases. For exam purposes, if no temperature is specified, it is safe to assume the temperature is 25 degrees Celsius, thus using K_w = 1.0 x 10^-14.

Understanding the autoionization of water and the significance of K_w is crucial for grasping concepts related to acid-base chemistry and the behavior of aqueous solutions.

Auto-Ionization Example 1

To determine the concentration of hydronium ions (H₃O⁺), which is equivalent to the concentration of hydrogen ions (H⁺), we first need to understand the concept of neutrality in a solution. A neutral solution is one where the concentrations of H₃O⁺ and hydroxide ions (OH^-) are equal, meaning that H₃O⁺ = OH^- = x.

At 25 degrees Celsius, the ion product of water (K_w) is 1.0 x 10^-14. Since we have established that H₃O⁺ and OH^- are equal in a neutral solution, we can set up the equation:

K_w = [H₃O⁺][OH^-] = x * x = x².

To find x, we take the square root of K_w:

x = √(1.0 x 10^-14) = 1.0 x 10^-7 M.

This value represents the concentration of H₃O⁺ in a neutral solution at 25 degrees Celsius, and it is also the concentration of OH^-.

When considering a neutral solution at 50 degrees Celsius, the value of K_w changes to 5.476 x 10^-14. We apply the same principle:

K_w = [H₃O⁺][OH^-] = x * x = x².

Taking the square root gives us:

x = √(5.476 x 10^-14) = 2.34 x 10^-7 M.

This indicates the concentration of H₃O⁺ in a neutral solution at 50 degrees Celsius. It is crucial to remember that K_w is temperature-dependent, and for calculations where the temperature is not specified, K_w is typically assumed to be 1.0 x 10^-14.

Understanding the relationship between H₃O⁺ and OH^- concentrations is fundamental for calculating pH and pOH in various aqueous solutions. The equation K_w = [H₃O⁺][OH^-] serves as a key reference point in these calculations.

Here’s what students ask on this topic:

What is the autoionization of water?

The autoionization of water is a process where water molecules react with each other to form hydronium ions (H₃O⁺) and hydroxide ions (OH^-). In this reaction, one water molecule acts as an acid by donating a proton (H⁺), and another acts as a base by accepting the proton. The equilibrium constant for this reaction, known as the ion product of water (K_w), is given by the equation:

$K_w=\left[H_{3}O\right]\left[\mathrm{OH}\right]$

At 25°C, K_w is 1.0 x 10^-14, and it increases with temperature.

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

The ion product constant (K_w) of water is temperature-dependent. As the temperature increases, the value of K_w also increases. This is because higher temperatures provide more energy for water molecules to overcome the activation energy barrier for autoionization, leading to more frequent formation of hydronium (H₃O⁺) and hydroxide (OH^-) ions. At 25°C, K_w is 1.0 x 10^-14, but this value will be higher at elevated temperatures.

What is the significance of the ion product constant (K_w) in aqueous solutions?

The ion product constant (K_w) is crucial for understanding acid-base reactions in aqueous solutions. It defines the relationship between the concentrations of hydronium ions (H₃O⁺) and hydroxide ions (OH^-) in water. Knowing K_w allows us to calculate the pH and pOH of a solution, which are measures of its acidity and basicity, respectively. At 25°C, K_w is 1.0 x 10^-14, meaning that in pure water, [H₃O⁺] and [OH^-] are both 1.0 x 10^-7 M.

How do you calculate the pH of a solution using the ion product constant (K_w)?

To calculate the pH of a solution using the ion product constant (K_w), you first need to know the concentration of hydronium ions (H₃O⁺). The pH is then calculated using the formula:

$\mathrm{pH}=-\log \left(\right[H_{3}O\left]\right)$

Since K_w = [H₃O⁺][OH^-] and at 25°C, K_w is 1.0 x 10^-14, you can find [H₃O⁺] if you know [OH^-], and vice versa. For example, if [OH^-] is 1.0 x 10^-6 M, then [H₃O⁺] = 1.0 x 10^-8 M, and pH = 8.

What is the relationship between pH, pOH, and K_w?

The relationship between pH, pOH, and K_w is given by the equation:

$\mathrm{pH}+\mathrm{pOH}=-\log \left(K_w\right)$

At 25°C, K_w is 1.0 x 10^-14, so:

$\mathrm{pH}+\mathrm{pOH}=14$

This means that if you know either the pH or pOH of a solution, you can easily calculate the other. For example, if the pH of a solution is 5, then the pOH is 9.