Understanding the Calculation of Mixtures of Acidic and Basic Solutions (Final pH)

Calculating the final pH of mixed acidic and basic solutions is essential in chemistry. This process determines the resulting hydrogen ion concentration after mixing.

This article explores detailed formulas, common values, and real-world examples for accurate pH calculation. It provides expert-level insights for precise chemical analysis.

• Calculate the final pH when mixing 0.1 M HCl and 0.1 M NaOH in equal volumes.
• Determine the pH after mixing 50 mL of 0.2 M acetic acid with 50 mL of 0.1 M NaOH.
• Find the final pH of a solution made by mixing 100 mL of 0.05 M H2SO4 with 100 mL of 0.1 M KOH.
• Calculate the pH when 25 mL of 0.1 M NH3 is mixed with 75 mL of 0.05 M HCl.

Comprehensive Tables of Common Values for pH Calculation in Acid-Base Mixtures

Fundamental Formulas for Calculating Final pH of Acid-Base Mixtures

Calculating the final pH after mixing acidic and basic solutions requires understanding the chemical equilibria and stoichiometry involved. The following formulas and explanations cover the essential calculations.

1. Moles of Acid and Base

First, calculate the moles of acid and base before mixing:

• C_acid: Concentration of the acid (mol/L)
• V_acid: Volume of the acid solution (L)
• C_base: Concentration of the base (mol/L)
• V_base: Volume of the base solution (L)

2. Determining the Limiting Reactant and Excess Moles

Neutralization occurs between H⁺ and OH^– ions. Calculate the difference:

The species with the higher moles is in excess and determines the final pH.

3. Total Volume After Mixing

4. Calculating Final Concentration of Excess Species

Calculate the concentration of the excess species after mixing:

5. Final pH for Strong Acid-Strong Base Mixtures

For strong acids and bases, complete dissociation is assumed. The final pH depends on the excess concentration:

• If acid is in excess:
pH = -log₁₀(C_excess)
• If base is in excess:
pOH = -log₁₀(C_excess)
pH = 14 – pOH
• If moles_acid = moles_base (neutralization):

pH = 7 (at 25°C, assuming pure water)

6. Final pH for Weak Acid-Strong Base or Weak Base-Strong Acid Mixtures (Buffer Solutions)

When mixing a weak acid with a strong base or vice versa, a buffer solution forms. Use the Henderson-Hasselbalch equation:

• pK_a: Acid dissociation constant (logarithmic)
• [A^–]: Concentration of conjugate base
• [HA]: Concentration of weak acid

Calculate moles of acid and base, determine moles of conjugate base formed, and calculate concentrations after mixing.

7. Calculating pH for Polyprotic Acids

For acids with multiple dissociation steps (e.g., H2SO4, H2CO3), consider each dissociation equilibrium. The first dissociation often dominates the pH calculation.

Use the following general equilibrium expression for the first dissociation:

Calculate [H⁺] by solving the quadratic equation derived from the mass balance and equilibrium expressions.

8. Water Autoionization Consideration

In very dilute solutions or near neutralization points, consider water autoionization:

This affects pH calculations when acid and base concentrations are very low.

Detailed Real-World Examples of Final pH Calculation in Acid-Base Mixtures

Example 1: Mixing Equal Volumes of 0.1 M HCl and 0.1 M NaOH

Consider mixing 50 mL of 0.1 M hydrochloric acid (strong acid) with 50 mL of 0.1 M sodium hydroxide (strong base). Calculate the final pH.

• Calculate moles of acid and base:
moles_acid = 0.1 mol/L × 0.050 L = 0.005 mol
moles_base = 0.1 mol/L × 0.050 L = 0.005 mol
• Since moles_acid = moles_base, complete neutralization occurs.
• Total volume:
V_total = 0.050 L + 0.050 L = 0.100 L
• Final pH:

At neutralization, pH = 7 (assuming 25°C and no other species).

Example 2: Mixing 50 mL of 0.2 M Acetic Acid with 50 mL of 0.1 M NaOH

Calculate the final pH when 50 mL of 0.2 M acetic acid (weak acid, pKa = 4.76) is mixed with 50 mL of 0.1 M sodium hydroxide (strong base).

• Calculate moles:
moles_acid = 0.2 mol/L × 0.050 L = 0.010 mol
moles_base = 0.1 mol/L × 0.050 L = 0.005 mol
• Neutralization reaction:

NaOH neutralizes part of acetic acid:

CH₃COOH + OH^– → CH₃COO^– + H₂O
• Calculate moles of remaining acid and formed conjugate base:
moles_CH3COOH_remaining = 0.010 – 0.005 = 0.005 mol
moles_CH3COO^– = 0.005 mol
• Total volume:
V_total = 0.050 L + 0.050 L = 0.100 L
• Calculate concentrations:
[CH₃COOH] = 0.005 mol / 0.100 L = 0.05 M
[CH₃COO^–] = 0.005 mol / 0.100 L = 0.05 M
• Apply Henderson-Hasselbalch equation:
pH = 4.76 + log₁₀(0.05 / 0.05) = 4.76 + 0 = 4.76

The final pH is 4.76, indicating a buffer solution.

Additional Considerations and Advanced Calculations

For more complex mixtures, such as polyprotic acids or weak acid-weak base systems, iterative or numerical methods may be required to solve equilibrium equations. Software tools or spreadsheets can assist in these calculations.

Temperature also affects dissociation constants (Ka, Kb) and water ionization constant (Kw), so adjustments may be necessary for non-standard conditions.

• Use temperature-corrected Ka and Kw values for precise pH calculations.
• Consider ionic strength and activity coefficients in concentrated solutions.
• For polyprotic acids, calculate stepwise dissociation equilibria.

Recommended External Resources for Further Study

• LibreTexts: Acid-Base Equilibria
• Chemguide: pH Calculations
• ACS Publications: Acid-Base Titrations and pH Calculations
• NIST Chemistry WebBook