Problem 59 - Chemistry for Allied Health

Question

You have prepared \(1.00 \mathrm{~L}\) of a solution with a pH of \(5.00 .\) What is the \(\mathrm{pH}\) of the solution if \(0.100 \mathrm{~L}\) of additional water is added to it? (Hint: Calculate the moles of \(\mathrm{H}^{+}\) ions present in the solution.)

Step-by-Step Solution

Answer

The pH of the solution after adding water is approximately 5.04.

Step 1: Calculate initial moles of H⁺ ions

First, find the initial concentration of H⁺ ions in the solution. Since pH = 5.00, we use the formula \( [ ext{H}^+] = 10^{- ext{pH}} \). So, \( [ ext{H}^+] = 10^{-5} \) M. With a volume of 1.00 L, the initial moles of H⁺ ions is \( 10^{-5} ext{ moles/L} \times 1.00 ext{ L} = 10^{-5} ext{ moles} \).

Step 2: Calculate the new moles of H⁺ after dilution

Since no H⁺ ions are added or removed, the initial moles of H⁺ ions remain the same at \( 10^{-5} \) moles after the dilution.

Step 3: Calculate the new concentration of H⁺ ions

The new total volume after adding 0.100 L of water is \( 1.00 ext{ L} + 0.100 ext{ L} = 1.100 ext{ L} \). The new concentration of H⁺ ions is calculated by dividing the moles of H⁺ by the new volume: \( [ ext{H}^+] = \frac{10^{-5} ext{ moles}}{1.100 ext{ L}} \approx 9.09 \times 10^{-6} ext{ M} \).

Step 4: Calculate the new pH

Use the concentration of H⁺ ions to find the new pH: \( ext{pH} = - ext{log}_{10}(9.09 \times 10^{-6}) \approx 5.04 \).

Key Concepts

pH Calculation

Understanding pH is essential in chemistry, especially when dealing with acidic or basic solutions. The pH scale, which ranges from 0 (very acidic) to 14 (very basic), measures the acidity or basicity of a solution.
To calculate the pH, one uses the formula:

• \(\text{pH} = -\log_{10}[\text{H}^+]\)

This equation tells us that the pH is the negative logarithm of the hydrogen ion concentration \([\text{H}^+]\).
For example, if the concentration of \([\text{H}^+]\) is \(10^{-5}\), the pH is calculated as follows:

• \(\text{pH} = -\log_{10}(10^{-5}) = 5\)

It's as simple as that! Understanding this concept helps you measure how acidic or basic a solution is.

H⁺ Ion Concentration

The concentration of hydrogen ions \([\text{H}^+]\) is a crucial aspect of understanding the acidity of solutions. Higher concentrations indicate more acidic solutions.
The relationship between pH and \([\text{H}^+]\) can be reversed using the formula:

• \([\text{H}^+] = 10^{-\text{pH}}\)

For instance, if a solution has a pH of 5, the hydrogen ion concentration is:

• \([\text{H}^+] = 10^{-5} \text{ M}\)

This means there are \(10^{-5}\) moles of \([\text{H}^+]\) per liter of solution.
Understanding this concentration helps in predicting how dilution or other chemical changes will affect the pH of a solution.

Molarity of Solution

Molarity is a measure of the concentration of a solute in a solution, depicted as moles of solute per liter of solution. It is a fundamental concept for understanding how solutions behave.
The formula for calculating molarity \(M\) is:

• \(M = \frac{\text{moles of solute}}{\text{liters of solution}}\)

In the context of our problem, we initially had \(1.00\) liter of a solution with \(10^{-5}\) moles of \([\text{H}^+]\), giving us:

• \(M = \frac{10^{-5} \text{ moles}}{1.00 \text{ L}} = 10^{-5} \text{ M}\)

When \(0.100\) L of water is added, the new volume becomes \(1.100\) L, and the molarity changes to:

• \(M = \frac{10^{-5} \text{ moles}}{1.100 \text{ L}} = 9.09 \times 10^{-6} \text{ M}\)

This shows how dilution affects molarity, and subsequently, the pH of a solution can be slightly altered as well.