How to Calculate pH After Diluting a Base

Understanding pH and Dilution of Bases

The pH scale measures how acidic or basic a solution is, with values ranging from 0 (very acidic) to 14 (very basic), and a pH of 7 being neutral. When we dilute a base, we reduce its concentration, which consequently affects its pH.

To calculate the pH of a diluted base, we can use the following steps:

1. Determine the initial concentration of the base (in moles per liter, M).
2. Calculate the new concentration after dilution using the dilution formula:

\[ C_1V_1 = C_2V_2 \]

Where:

• \( C_1 \) = initial concentration
• \( V_1 \) = initial volume
• \( C_2 \) = final concentration
• \( V_2 \) = final volume

3. Calculate the pOH using the formula:

   \[ pOH = -\log[OH^-] \]

4. Convert pOH to pH:

   \[ pH + pOH = 14 \]

Example 1: Diluting Sodium Hydroxide (NaOH)

Problem: You have 0.5 M NaOH and you dilute it by adding 200 mL of water to 100 mL of the solution. What is the new pH?

Step 1: Calculate the new concentration (C2)

• Initial concentration (C1) = 0.5 M
• Initial volume (V1) = 100 mL = 0.1 L
• Volume of water added = 200 mL = 0.2 L
• Final volume (V2) = 100 mL + 200 mL = 300 mL = 0.3 L

Using the dilution formula:
[
C_2 = \frac{C_1V_1}{V_2} = \frac{(0.5 \text{ M})(0.1 \text{ L})}{0.3 \text{ L}} = 0.1667 \text{ M}
]

Step 2: Calculate the pOH

• The concentration of hydroxide ions [OH⁻] = 0.1667 M

[
pOH = -\log(0.1667) \approx 0.78
]

Step 3: Calculate the pH

[
pH = 14 - pOH = 14 - 0.78 \approx 13.22
]

Conclusion:

The pH of the diluted NaOH solution is approximately 13.22.

Example 2: Diluting Ammonium Hydroxide (NH₄OH)

Problem: You have 0.2 M NH₄OH and you dilute it by adding 500 mL of water to 250 mL of the solution. What is the new pH?

Step 1: Calculate the new concentration (C2)

• Initial concentration (C1) = 0.2 M
• Initial volume (V1) = 250 mL = 0.25 L
• Volume of water added = 500 mL = 0.5 L
• Final volume (V2) = 250 mL + 500 mL = 750 mL = 0.75 L

Using the dilution formula:
[
C_2 = \frac{C_1V_1}{V_2} = \frac{(0.2 \text{ M})(0.25 \text{ L})}{0.75 \text{ L}} = 0.0667 \text{ M}
]

Step 2: Calculate the pOH

• The concentration of hydroxide ions [OH⁻] = 0.0667 M

[
pOH = -\log(0.0667) \approx 1.18
]

Step 3: Calculate the pH

[
pH = 14 - pOH = 14 - 1.18 \approx 12.82
]

Conclusion:

The pH of the diluted NH₄OH solution is approximately 12.82.

By following these steps, you can accurately calculate the pH of any diluted base. Whether in a laboratory setting or for practical applications, understanding these calculations is fundamental in chemistry.