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 hydrogen ion concentration of the solution? Is the solution acidic or basic?

Step-by-Step Solution

Answer

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

Step 1: Understand the relationship between pH and pOH

Remember that for any aqueous solution, the sum of the pH and pOH is always equal to 14. This is expressed by the equation: \( \text{pH} + \text{pOH} = 14 \). In the problem, the pH is given as 10.5.

Step 2: Calculate the pOH

Use the relationship mentioned above to find the pOH. Since \( \text{pH} = 10.5 \), we can calculate the pOH as follows: \( \text{pOH} = 14 - 10.5 = 3.5 \).

Step 3: Calculate the hydroxide ion concentration

The hydroxide ion concentration \( [\text{OH}^-] \) can be found using the formula \( [\text{OH}^-] = 10^{-\text{pOH}} \). Plug in the pOH value: \( [\text{OH}^-] = 10^{-3.5} \).

Step 4: Calculate the hydrogen ion concentration

Use the relationship between \([\text{H}^+ ]\) and \([\text{OH}^-]\), expressed as \([\text{H}^+] \times [\text{OH}^-] = 1 \times 10^{-14}\). Solve for \([\text{H}^+]\): \[ [\text{H}^+] = \frac{1 \times 10^{-14}}{[\text{OH}^-]} \]. Substitute \([\text{OH}^-] = 10^{-3.5}\) into the equation: \[ [\text{H}^+] = \frac{1 \times 10^{-14}}{10^{-3.5}} = 10^{-10.5} \approx 3.16 \times 10^{-11} \].

Step 5: Determine if the solution is acidic or basic

A solution is acidic if its pH is below 7, and basic if its pH is above 7. With a pH of 10.5, this solution is basic.

Key Concepts

pH Calculations

Calculating pH is essential in understanding the acidity or alkalinity of a solution. The pH scale ranges from 0 to 14 and is used to measure the concentration of hydrogen ions in a solution. A lower pH means higher acidity, while a higher pH indicates a more basic or alkaline solution. The formula to determine pH is \( ext{pH} = - ext{log}[ ext{H}^+] \).

Knowing the pH allows you to calculate the pOH using the relationship:

• \( ext{pH} + ext{pOH} = 14 \)

For example, if the pH is 10.5, you can find the pOH by subtracting the pH from 14:

\( ext{pOH} = 14 - ext{pH} \)

This step helps in determining the hydrogen and hydroxide ion concentrations.

The pH value provides a quick way to assess whether a solution is acidic or basic. Understanding these concepts enables better manipulation and prediction of chemical reactions in different solutions. Break it down, and practice will make calculating pH feel like second nature!
It's a fundamental skill in acid-base chemistry.

Hydrogen Ion Concentration

Hydrogen ion concentration \([ ext{H}^+]\) is vital in determining how acidic a solution is. The concentration of hydrogen ions influences the pH, which can be calculated using the formula: \[ [ ext{H}^+] = 10^{- ext{pH}} \].

However, sometimes you may be dealing with the concentration of hydroxide ions.In such cases, use the relationship between \([ ext{H}^+]\) and \( [ ext{OH}^-] \):

• \( [ ext{H}^+] \times [ ext{OH}^-] = 1 imes 10^{-14} \)

This lets you calculate \([ ext{H}^+] \) if you know \( [ ext{OH}^-] \).

For example, if \( [ ext{OH}^-] \) is \( 10^{-3.5} \), then \([ ext{H}^+] \) can be determined as follows:

• \( [ ext{H}^+] = \frac{1 imes 10^{-14}}{10^{-3.5}} \approx 3.16 imes 10^{-11} \)

Understanding \([\text{H}^+]\) is crucial in predicting the reactivity and behavior of a solution. It helps determine whether the environment is suitable for specific reactions. Getting comfortable with this concept will deepen your understanding of acid-base balance.

Basic Solutions

A basic solution has a pH greater than 7. Such solutions contain more hydroxide ions \([\text{OH}^-]\) than hydrogen ions \([\text{H}^+]\). For example, a solution with a pH of 10.5 is considered basic.

This means the solution is more alkaline, often associated with compounds like Mg(OH)\(_2\).

Basic solutions have several key properties:

• They feel slippery to the touch.
• They can turn red litmus paper blue.
• Often used in cleaning products to neutralize acids.

Understanding whether a solution is basic helps in its application and role in chemical reactions. Recognizing the pH allows you to make predictions about chemical behavior and its suitability for certain processes.
Appreciating these fundamental aspects of basic solutions is essential for grasping broader acid-base chemistry concepts.