Introduction to Buffer Solutions

Buffer solutions play a crucial role in maintaining a stable pH in various chemical and biological systems. A classic example is the ammonia-ammonium chloride buffer. This article will guide you through the process of calculating the pH of a buffer solution made by mixing 0.2 M NH3 with 0.5 M NH4Cl, and then determining the pH change after adding 20 mL of 0.02 M NaOH to 60 mL of the buffer. We will accomplish this using the Henderson-Hasselbalch (HH) equation and common chemical principles.

Understanding the Initial Buffer Solution

To calculate the pH of the initial buffer, we need to utilize the Henderson-Hasselbalch (HH) equation. The HH equation for a weak base and its conjugate acid is given as:

HH Equation:

pH pKa log([A-]/[HA])

where [A-] is the concentration of the conjugate base (NH3), and [HA] is the concentration of the weak acid (NH4Cl).

In this case, [NH3] 0.2 M, and [NH4Cl] 0.5 M. Before applying the equation, we need to determine the pKa of the ammonium ion (NH4 ).

The pKa value can be found using the relationship between pKa and pKb for the conjugate acid-base pair. The NH4 is the conjugate acid of NH3, and the pKb of NH3 can be found in many chemistry references or notes. For ammonia, pKb 4.75. The relationship between pKa and pKb is given by:

pKa pKb 14

Substituting the pKb value:

pKa 14 - pKb

Therefore, pKa 14 - 4.75 9.25

Calculating the Initial pH of the Buffer

Now, using the HH equation:

pH 9.25 log([0.2]/[0.5])

pH 9.25 log(0.4)

pH 9.25 - 0.398 8.852

Effect of Adding NaOH to the Buffer

When 20 mL of 0.02 M NaOH is added to 60 mL of the buffer, NaOH will act as a base and neutralize some of the NH4 ions. We need to follow these steps to determine the new pH:

Calculate the moles of OH- added. Update the moles of NH4 and NH3 in the buffer. Calculate the new concentrations of NH3 and NH4 in moles per liter. Use the HH equation to find the new pH. Compare the new pH with the initial pH to determine the change in pH.

Step-by-Step Calculation

Step 1: Calculate the moles of OH- Added

The volume of NaOH added is 20 mL, and its molarity is 0.02 M. First, convert the volume to liters:

20 mL 0.020 L

Moles of OH- Molarity × Volume

Moles of OH- 0.02 M × 0.020 L 0.0004 moles

Step 2: Update the Moles of NH4 and NH3

The original volume of the buffer is 60 mL, and its molarity for NH4Cl is 0.5 M, and for NH3 is 0.2 M. Convert to moles in the original buffer:

Moles of NH4 0.5 M × 0.060 L 0.030 moles

Moles of NH3 0.2 M × 0.060 L 0.012 moles

The addition of OH- will neutralize some of the NH4 to form NH3. The moles of NH4 will decrease by 0.0004 moles, and the moles of NH3 will increase by 0.0004 moles:

New moles of NH4 0.030 moles - 0.0004 moles 0.0296 moles

New moles of NH3 0.012 moles 0.0004 moles 0.0124 moles

Step 3: Calculate the New Concentrations in Moles per Liter

The new volume of the buffer after adding NaOH is 60 mL 20 mL 80 mL 0.080 L.

New concentration of NH4 0.0296 moles / 0.080 L 0.37 M

New concentration of NH3 0.0124 moles / 0.080 L 0.155 M

Step 4: Use the HH Equation to Find the New pH

Substitute the new concentrations into the HH equation:

pH 9.25 log([0.155]/[0.37])

pH 9.25 log(0.4189)

pH 9.25 - 0.377 8.873

Step 5: Determine the Change in pH

The change in pH New pH - Initial pH

Change in pH 8.873 - 8.852 0.021

Conclusion

By following the above steps, we determined that the pH of the buffer solution changes from 8.852 to 8.873 after adding 20 mL of 0.02 M NaOH to 60 mL of the initial buffer. This small change in pH demonstrates the buffering capacity of the solution, which helps maintain a stable pH in the presence of added base.