Question

A saturated solution of milk of magnesia, \(\mathrm{Mg}(\mathrm{OH})_{2},\) has a pH of \(10.52 .\) What is the hydronium ion concentration of the solution? What is the hydroxide ion concentration? Is the solution acidic or basic?

Short answer

[H+] ≈ 3.02 × 10^(-11) M; [OH-] ≈ 3.31 × 10^(-4) M. The solution is basic.

Step-by-step solution

Calculate H+ Concentration from pH

To find the hydronium ion concentration, use the formula: \[ [\text{H}^+] = 10^{-\text{pH}} \]Given the pH is 10.52, substitute this value into the formula:\[ [\text{H}^+] = 10^{-10.52} \approx 3.02 \times 10^{-11} \text{ M} \]

Determine OH- Concentration using Water Ion Product

Using the formula for the ionic product of water, which is given by:\[ [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14} \]Substitute the value of \([\text{H}^+]\) found previously:\[ [\text{OH}^-] = \frac{1.0 \times 10^{-14}}{3.02 \times 10^{-11}} \approx 3.31 \times 10^{-4} \text{ M} \]

Determine if the Solution is Acidic or Basic

The solution has a pH of 10.52, which is above 7, indicating that it is basic. Additionally, the hydroxide ion concentration \([\text{OH}^-]\) is higher than the hydronium ion concentration \([\text{H}^+]\), confirming that the solution is basic.

Key concepts

Hydronium Ion Concentration

The hydronium ion concentration is a key factor in understanding the acidity of a solution. When we measure the hydronium ion concentration in water-based solutions, we use the term \( H^+ \) to denote these ions, even though in reality, they are associated with water molecules as hydronium ions (\( H_3O^+ \)).

To calculate the hydronium ion concentration from the pH of a solution, we use the formula: \[ [H^+] = 10^{-\text{pH}} \]

This formula shows the inverse relationship between pH and hydronium ion concentration. For instance, the lower the pH, the higher the hydronium ion concentration, indicating an acidic solution.

In our exercise, with a pH of 10.52, the hydronium ion concentration is calculated as \( 3.02 \times 10^{-11} \) M, suggesting that the solution has a very low concentration of hydronium ions and is therefore basic.

Hydroxide Ion Concentration

Hydroxide ion concentration is crucial in determining the basicity of a solution. The presence of hydroxide ions \( OH^- \) in water impacts whether a solution is considered basic or not.

The relationship between hydronium and hydroxide ions in water can be described by the water ion product (\( K_w \)), which at 25°C is \( 1.0 \times 10^{-14} \). This relationship is expressed in the equation:

\[ [H^+][OH^-] = 1.0 \times 10^{-14} \]

To find the hydroxide concentration, you divide \( 1.0 \times 10^{-14} \) by the hydronium concentration. From the exercise, with \( [H^+] = 3.02 \times 10^{-11} \) M, the hydroxide ion concentration is calculated to be approximately \( 3.31 \times 10^{-4} \) M.

This higher concentration of hydroxide ions compared to hydronium ions indicates the solution is indeed basic.

pH Calculation

The concept of pH is a simple yet powerful way to describe the acidity or basicity of a solution. pH is defined as the negative logarithm (base 10) of the hydronium ion concentration. The formula for pH is:

\[ \text{pH} = -\log([H^+]) \]

Understanding this formula helps in determining whether a solution is acidic, neutral, or basic.

• A pH less than 7 indicates acidity.
• A pH of exactly 7 defines a neutral solution.
• A pH greater than 7 signifies a basic solution.

For example, the pH value of 10.52 in the given exercise indicates a basic solution. This is substantiated by the calculated hydronium ion concentration of \( 3.02 \times 10^{-11} \) M. In practice, knowing the pH allows us to accurately assess the balance between hydronium and hydroxide ions in any aqueous solution.