Diprotic Acid Titration Curve Simulator - Weak Diprotic Acid vs Strong Base

This tool provides a precise, interactive simulation of the titration of a weak diprotic acid (like oxalic acid or carbonic acid) with a strong monoprotic base (like NaOH). It is designed for chemistry students and lab professionals who need to visualize and calculate the properties of a polyprotic titration without relying on error-prone approximations.

By inputting your specific concentrations and pKa values, you can instantly generate a high-fidelity titration curve, identify both equivalence points, and calculate the exact pH at any point during the titration.

The Theory: Understanding the Diprotic Titration Curve

A diprotic acid, represented as H₂A, is an acid that can donate two protons (H⁺ ions) in a stepwise manner.

1. H₂A + H₂O ⇌ HA⁻ + H₃O⁺ (governed by Ka₁)
2. HA⁻ + H₂O ⇌ A²⁻ + H₃O⁺ (governed by Ka₂)

When you titrate this acid with a strong base like sodium hydroxide (NaOH), the base removes these protons one by one. This results in a titration curve with two distinct "S" shaped regions and two equivalence points.

The curve is defined by several key regions and points:

• Initial Point (0 mL titrant added): The pH is determined solely by the first dissociation of the weak acid, H₂A, in water.
• First Buffer Region: As the strong base is added, it converts H₂A into its conjugate base, HA⁻. This creates a buffer system (H₂A / HA⁻).
• First Half-Equivalence Point (V = ½ Veq₁): At this point, the concentration of [H₂A] equals [HA⁻]. According to the Henderson-Hasselbalch equation, pH = pKa₁.
• First Equivalence Point (V = Veq₁): All the H₂A has been converted to HA⁻. The solution now contains only the amphiprotic species HA⁻. The pH is not simply (pKa₁ + pKa₂)/2 (an approximation that often fails); it is calculated using the full equilibrium equation for an amphiprotic species, which this tool does automatically.
• Second Buffer Region: Past the first equivalence point, the strong base begins converting HA⁻ into A²⁻, creating a second buffer system (HA⁻ / A²⁻).
• Second Half-Equivalence Point (V = Veq₂ - ½ Veq₁): At this point, [HA⁻] equals [A²⁻]. The pH = pKa₂.
• Second Equivalence Point (V = Veq₂): All the HA⁻ has been converted to A²⁻. The solution now contains only the weak base A²⁻. The pH is calculated from the hydrolysis of this weak base (using Kb₁ = Kw / Ka₂).
• Excess Base Region: Beyond the second equivalence point, the pH is determined almost entirely by the concentration of the excess strong base (NaOH) added.

How to Use This Simulator

Follow these simple steps to generate and analyze your titration curve.

1. Enter Analyte Parameters:
   • Concentration (M): The initial molarity of your weak diprotic acid (H₂A).
   • Volume (mL): The initial volume of your acid.
   • Analyte pKa₁: The pKa value for the first proton.
   • Analyte pKa₂: The pKa value for the second proton. (Note: pKa₁ must be less than pKa₂).
2. Enter Titrant Parameters:
   • Concentration (M): The molarity of your strong base titrant (e.g., NaOH).
3. Select Indicator (Optional):
   • Choose a chemical indicator from the dropdown menu. Its effective pH range will be shaded on the graph, helping you see if it's a suitable choice for one of the equivalence points.
4. Generate & Analyze the Graph:
   • Click the "Generate Curve" button.
   • The tool will plot the full titration. You can hover your mouse over the line to see the specific pH at any volume.
   • The 1st Equivalence Point is marked with a red dashed line, and the 2nd Equivalence Point is marked with a blue dashed line.
   • The precise volume and pH for both equivalence points are displayed in the "Results" boxes.
5. Calculate Specific pH (Precision Tool):
   • To find the pH at an exact volume, type the titrant volume (in mL) into the "Check pH at specific volume" box and click "Calculate".
   • This uses the same robust, systematic calculation engine as the graph to give you a high-precision pH value.
6. Download Your Results:
   • Click "Download As JPG" (in light or dark mode) to save a high-resolution image of your graph and results, perfect for lab reports or presentations.

A Note on Accuracy

This calculator is designed for high accuracy. Unlike simple textbook approximations (like the Henderson-Hasselbalch equation), it uses a systematic bisection method to solve the full charge-balance equilibrium equation for the buffer regions. It also uses the full quadratic formulas to find the pH at the equivalence points, ensuring it provides correct data even for challenging cases (like very strong, very dilute, or closely-spaced pKa values) where simpler methods fail.

Looking for a Different Titration?

This tool is specifically for Weak Diprotic Acids vs. Strong Bases.

If you are titrating a simple acid or base with only one proton (e.g., Acetic Acid with NaOH, or Ammonia with HCl), please use our Monoprotic Acid-Base Titration Simulator. It is designed to handle all four common monoprotic scenarios (Weak/Strong, Strong/Weak, Strong/Strong, and inverse titrations).

Simulate titrating a weak base (like Carbonate ion) with a strong acid (like HCl) using Weak Diprotic Base Titration Curve Simulator.

Simulate titrating a strong acid (like Sulfuric Acid) with a strong base (like NaOH) using the Strong Diprotic Acid Titration Curve Simulator.

Simulate titrating a weak triprotic acid (like Phosphoric Acid) with a strong base (like NaOH) using the Weak Triprotic Acid Titration Curve Simulator.