Calculating the pH of a Buffer Solution Containing Acetic Acid and Sodium Hydroxide

A buffer solution is a solution that resists changes in pH when small amounts of acids or bases are added. In this article, we will calculate the pH of a buffer prepared by mixing 20 ml of 0.1M NaOH solution with 40 ml of 0.2M CH3COOH (acetic acid) solution. This process will involve the use of the Henderson-Hasselbalch equation, a fundamental tool in Programming and SEO optimization for chemistry and biochemistry applications.

Components Identification and Initial Conditions

The weak acid component of our buffer solution is acetic acid (CH3COOH). Sodium hydroxide (NaOH) is added to the acetic acid to form its conjugate base, acetate ion (CH3COO-). Here are the steps to calculate the pH of the resulting buffer solution:

Step 1: Identifying the Components

Acetic acid (CH3COOH) serves as the weak acid (HA), and sodium hydroxide (NaOH) acts as a source of hydroxide ions (OH-) that react with acetic acid to form acetate ions (CH3COO-), the conjugate base (A-).

Step 2: Calculating the Initial Moles

First, we calculate the moles of acetic acid and sodium hydroxide using their respective concentrations and volumes.

Moles of acetic acid (CH3COOH):

Concentration 0.2 mol/L, Volume 0.040 L

Moles of CH3COOH Concentration × Volume

0.2 mol/L × 0.040 L 0.008 mol

Moles of sodium hydroxide (NaOH):

Concentration 0.1 mol/L, Volume 0.020 L

Moles of NaOH Concentration × Volume

0.1 mol/L × 0.020 L 0.002 mol

Step 3: Reaction Between Acetic Acid and Sodium Hydroxide

The reaction between acetic acid and sodium hydroxide can be written as:

CH3COOH NaOH → CH3COO- H2O

After the reaction:

Moles of CH3COOH remaining:

0.008 - 0.002 0.006 mol

Moles of CH3COO- produced:

0 0.002 0.002 mol

Step 4: Calculate the Final Concentrations

We now determine the concentrations of CH3COOH and CH3COO- in the final solution.

Total Volume 20 ml 40 ml 60 ml 0.060 L

Concentration of acetic acid (HA):

Concentration Moles / Volume

0.006 mol / 0.060 L 0.1 M

Concentration of acetate (A-):

Concentration Moles / Volume

0.002 mol / 0.060 L ≈ 0.0333 M

Step 5: Using the Henderson-Hasselbalch Equation

The pKa of acetic acid is approximately 4.76. Using the Henderson-Hasselbalch equation:

pH pKa log([A-/HA])

Substituting the values:

pH 4.76 log((0.0333/0.1))

log((0.0333/0.1) ≈ log(0.333) ≈ -0.477

Substituting back into the equation:

pH 4.76 - 0.477 ≈ 4.283

Final Answer: The pH of the buffer solution is approximately 4.28.