Understanding pH Calculation in Diluted Solutions

The pH of a solution is a measure of its acidity or alkalinity. It is defined as the negative logarithm of the hydrogen ion concentration, [H ]. This article will guide you through the process of calculating the pH of a resulting solution when a given quantity of a specific pH solution is diluted with water. We will use the given example and apply the principles of pH calculation to determine the new pH after dilution.

Step-by-Step Calculation

Let's start by understanding the initial conditions:

Initial volume of the solution: 50 mL Initial pH of the solution: 4.301 Volume of water added: 200 mL

To find the pH of the resulting solution, we need to follow several steps:

1. Calculate the Concentration of Hydrogen Ions in the Original Solution

The relationship between pH and the concentration of hydrogen ions is given by the formula:

[H ] 10^{-text{pH}}

For a pH of 4.301, we can calculate:

[H ] 10^{-4.301} approx 4.98 times 10^{-5},text{M}

2. Calculate the Total Number of Moles of Hydrogen Ions in the Original Solution

The volume of the original solution is 50 mL or 0.050 L. Therefore, the moles of hydrogen ions are:

text{moles of } H [H ] times text{volume} 4.98 times 10^{-5},text{M} times 0.050,text{L} approx 2.49 times 10^{-6},text{moles}

3. Calculate the Total Volume of the Diluted Solution

The total volume after dilution is:

text{Total volume} 50,text{mL} 200,text{mL} 250,text{mL} 0.250,text{L}

4. Calculate the New Concentration of Hydrogen Ions After Dilution

The new concentration of [H ] in the diluted solution is:

[H ] frac{text{moles of } H }{text{total volume}} frac{2.49 times 10^{-6},text{moles}}{0.250,text{L}} approx 9.96 times 10^{-6},text{M}

5. Calculate the New pH of the Diluted Solution

Finally, we can find the pH of the diluted solution:

text{pH} -log[H ] -log(9.96 times 10^{-6}) approx 5.00

Thus, the pH of the resulting solution after dilution is approximately 5.00.

General Principles of pH Calculation During Dilution

The pH of a solution changes upon dilution. For example, if a solution with a pH of 4.301 is diluted, the concentration of hydrogen ions also changes. Here is a summary of how pH changes with dilution:

For Acid Solutions:

When diluted two times, pH increases by a value of 0.3010. When diluted four times, pH increases by a value of 0.6020. When diluted five times, pH increases by a value of 0.6990. When diluted ten times, pH increases by a value of 1.000. When diluted one hundred times, pH increases by a value of 2.000.

For Strong Bases:

When diluted two times, pH decreases by a value of 0.3010. When diluted four times, pH decreases by a value of 0.6020. When diluted five times, pH decreases by a value of 0.6990. When diluted ten times, pH decreases by a value of 1.000. When diluted one hundred times, pH decreases by a value of 2.000.

Conclusion

This article has provided a detailed explanation of how to calculate the pH of a resulting solution when a specific volume of a pH solution is diluted. By understanding the relationships between pH, hydrogen ion concentration, and dilution, you can effectively predict and control the properties of your solutions.