Problem 56 - Chemistry and Chemical Reactivity

Question

A saturated solution of milk of magnesia, \(\mathrm{Mg}(\mathrm{OH})_{2},\) has a pH of \(10.5 .\) What is the hydronium ion concentration of the solution? Is the solution acidic or basic?

Step-by-Step Solution

Answer

The hydronium ion concentration is \(3.16 \times 10^{-11} \, \text{M}\) and the solution is basic.

Step 1: Understanding pH and Hydronium Ion Concentration

pH is the negative logarithm of the hydronium ion concentration, \\[\text{pH} = -\log [\text{H}_3\text{O}^+]\] \For a pH of 10.5, we can find the hydronium ion concentration by rearranging the formula: \\[[\text{H}_3\text{O}^+] = 10^{-\text{pH}}\] \Next, we'll calculate the hydronium ion concentration for a pH of 10.5.

Step 2: Calculating the Hydronium Ion Concentration

To find the hydronium ion concentration for a pH of 10.5, substitute the value into the equation, \\[[\text{H}_3\text{O}^+] = 10^{-10.5}\] \Using a calculator, solve for \\[[\text{H}_3\text{O}^+] = 3.16 \times 10^{-11} \, \text{M}\]This is the concentration of hydronium ions in the solution.

Step 3: Determining Solution Type (Acidic or Basic)

Remember, a solution is acidic if the pH is less than 7, neutral if pH equals 7, and basic if pH is greater than 7. Since the given pH is 10.5, which is greater than 7, this solution is basic.

Key Concepts

Acidic and Basic Solutions

Understanding whether a solution is acidic or basic is important in chemistry. A solution's pH tells you how acidic or basic it is. The pH scale ranges from 0 to 14:

• If the pH is less than 7, the solution is acidic.
• If the pH is exactly 7, the solution is neutral.
• If the pH is greater than 7, the solution is basic.

A pH of 10.5, as in the case of magnesium hydroxide, means the solution is basic. Basic solutions often feel slippery and can neutralize acids. Recognizing the pH range helps in predicting the chemical behavior of substances in various applications.

Logarithmic Calculations in Chemistry

Logarithms may seem complex, but they are very helpful in chemistry. The pH of a solution is derived from the hydronium ion concentration using the logarithmic formula: \( ext{pH} = - ext{log} [ ext{H}_3 ext{O}^+]\). This equation shows the negative relationship between pH and the concentration of hydronium ions. To find the hydronium ion concentration from pH, use: \([ ext{H}_3 ext{O}^+] = 10^{- ext{pH}}\).For example, if the pH is 10.5, the concentration becomes \(3.16 \times 10^{-11} \, \text{M}\). These calculations help determine the strength and characteristics of a solution, enabling better understanding and handling of chemical reactions.

Magnesium Hydroxide Solubility

Magnesium hydroxide, also known as milk of magnesia, has interesting solubility properties. It is sparingly soluble in water, producing a basic solution. This solubility produces hydroxide ions, increasing the solution's pH.

• Milk of magnesia is often used as an antacid because it neutralizes stomach acid.
• Its high pH makes it suitable for relieving acid-related discomforts.

Understanding magnesium hydroxide's solubility helps explain why its solutions are basic. This knowledge supports its practical applications in both health and industrial contexts, where controlling pH is essential.