Weak Triprotic Acid Titration Curve Simulator

Weak triprotic acid titration curve simulator tool simulates the complete pH titration curve for a weak triprotic acid (H₃A) being titrated by a strong monobasic base (like NaOH). This is the classic titration performed in general and analytical chemistry for polyprotic acids such as Phosphoric Acid (H₃PO₄) and Citric Acid.

Unlike simple calculators that use approximations, this simulator uses a numerically stable systematic solver (a bisection method) to solve the full charge balance equation. This makes it highly accurate across all buffer regions, even for acids with overlapping pKa values (like citric acid).

It generates a high-precision, interactive graph and calculates the precise volume and pH for all three equivalence points.

How to Use This Tool

1. Analyte (Weak Triprotic Acid):
   • Concentration (M): Enter the initial molarity of your acid (e.g., 0.1).
   • Volume (mL): Enter the volume of acid in your beaker (e.g., 25).
   • Analyte pKa₁, pKa₂, pKa₃: Enter the three acid dissociation constants for your acid. Note: These values must be in increasing order (pKa₁ < pKa₂ < pKa₃). The defaults are for Phosphoric Acid (2.15, 7.20, 12.35).
2. Titrant (Strong Base):
   • Concentration (M): Enter the molarity of your titrant (e.g., 0.1).
3. Generate Curve:
   • Click the "Generate/Update Curve" button to plot the titration.
4. Analyze Your Results:
   • The Results section will automatically populate with the exact titrant volume and pH for all three equivalence points.
   • You can also use the "Check pH at specific volume" tool to find the exact pH at any point along the curve.

Understanding the Chemistry: The 7 Regions of a Triprotic Titration

A triprotic titration is a sequence of three separate acid-base reactions. Your graph is a visual representation of all seven distinct chemical regions.

1. Region 1: The Initial Point (Vb = 0)
   • What's in the beaker: Only the weak acid H₃A and water.
   • pH Calculation: The pH is determined by the first dissociation: H₃A ⇌ H⁺ + H₂A⁻. This is governed by pKa₁.
2. Region 2: The First Buffer Region (0 < Vb < Veq₁)
   • Reaction: H₃A + OH⁻ → H₂A⁻ + H₂O
   • What's in the beaker: A buffer system containing the acid H₃A and its conjugate base H₂A⁻.
   • pH Calculation: The pH is centered around pKa₁. At the halfway point (Vb = Veq₁ / 2), pH ≈ pKa₁.
3. Region 3: The First Equivalence Point (Vb = Veq₁)
   • What's in the beaker: The solution contains (almost) exclusively the first amphiprotic species, H₂A⁻.
   • pH Calculation: The pH is determined by H₂A⁻ acting as both an acid (donating to HA²⁻) and a base (accepting to H₃A). The pH is calculated with a robust amphiprotic formula (approximated by pH ≈ (pKa₁ + pKa₂) / 2).
4. Region 4: The Second Buffer Region (Veq₁ < Vb < Veq₂)
   • Reaction: H₂A⁻ + OH⁻ → HA²⁻ + H₂O
   • What's in the beaker: A new buffer system containing H₂A⁻ and its conjugate base HA²⁻.
   • pH Calculation: The pH is centered around pKa₂. At the second halfway point (Vb = (Veq₁ + Veq₂) / 2), pH ≈ pKa₂.
5. Region 5: The Second Equivalence Point (Vb = Veq₂)
   • What's in the beaker: The solution contains (almost) exclusively the second amphiprotic species, HA²⁻.
   • pH Calculation: The pH is determined by HA²⁻ acting as both an acid and a base. It's calculated with another robust amphiprotic formula (approximated by pH ≈ (pKa₂ + pKa₃) / 2).
6. Region 6: The Third Buffer Region (Veq₂ < Vb < Veq₃)
   • Reaction: HA²⁻ + OH⁻ → A³⁻ + H₂O
   • What's in the beaker: The final buffer system containing HA²⁻ and its conjugate base A³⁻.
   • pH Calculation: The pH is centered around pKa₃. At the third halfway point (Vb = (Veq₂ + Veq₃) / 2), pH ≈ pKa₃.
7. Region 7: The Third Equivalence Point & Excess Base
   • At Veq₃: All acid has been neutralized. The solution contains only the weak base A³⁻. The pH is determined by its reaction with water (A³⁻ + H₂O ⇌ HA²⁻ + OH⁻), which is governed by pKb₁ (where pKb₁ = 14 - pKa₃).
   • Past Veq₃: The pH is determined solely by the concentration of the excess strong base (NaOH) titrant.

A Note on Extreme Dilutions and Model Scope

This tool is designed for common laboratory concentrations (e.g., 0.01 M to 1 M). You may notice that at extreme dilutions (e.g., 0.0001 M or less), the shape of the curve changes dramatically.

This is correct chemical behavior! At such low concentrations, the acid's effect on pH is so small that it is "squashed" by the natural pH of water (the autoionization, Kw). This is why the pH at the start and end of a very dilute titration will be much closer to 7.

While our core systematic solver for the buffer regions is robust even at these dilutions, the simple quadratic functions used for the Initial Point and the Final Equivalence Point (Veq₃) do not include the effect of water. Therefore, in these non-practical, ultra-dilute scenarios, the calculated pH at the very beginning or end of the curve may differ slightly from the true value, as the "jumps" themselves become chemically indistinct.

Related Tools

• Monoprotic Acid-Base Titration Simulator: For simpler titrations involving only one proton, such as Acetic Acid with NaOH or Ammonia with HCl.
• Weak Diprotic Acid Titration Simulator: For diprotic acids like Oxalic Acid.
• Weak Diprotic Base Titration Simulator: For titrating bases like Carbonate (CO₃²⁻) with a strong acid.