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Acid-Base Titration Curve Simulator

Simulate titration curves for strong and weak acids/bases. Visualize pH changes, identify equivalence points, and explore buffer regions.

Weak acid-strong base. Buffer region visible. Equivalence above pH 7.

Analyte (Solution Being Titrated)

Titrant (Solution Being Added)

Range for the titration curve

At half-equivalence, pH = pKa = 4.76

More points = smoother curve (20-500)

No Titration Results Yet

Enter your titration parameters on the left and click "Simulate Titration" to generate a pH vs. volume curve with key points marked.

This simulator supports:

  • • Strong acid + Strong base (e.g., HCl + NaOH)
  • • Weak acid + Strong base (e.g., CH₃COOH + NaOH)
  • • Strong base + Strong acid (e.g., NaOH + HCl)
  • • Weak base + Strong acid (e.g., NH₃ + HCl)

Equivalence Point Detection

If you're working through an acid-base titration curve simulator problem and trying to find where the equivalence point falls, here's what trips most students up: they assume the equivalence point is always at pH 7. That's only true for strong acid + strong base. Titrate acetic acid with NaOH and equivalence lands near pH 8.7—well above neutral—because the conjugate base (acetate) hydrolyzes and makes the solution basic.

The equivalence point is where moles of titrant exactly equal moles of analyte. The volume to reach it comes from stoichiometry: V_eq = (C_analyte × V_analyte) / C_titrant. This formula doesn't care about acid strength—it's purely about mole matching. But the pH at equivalence depends entirely on what's left in solution: neutral salt (strong-strong), conjugate base (weak acid + strong base), or conjugate acid (weak base + strong acid).

On the titration curve, equivalence appears at the steepest part of the S-curve. The near-vertical section is where a single drop of titrant swings pH by several units. That's your indicator's target zone. Choose an indicator whose color-change range overlaps with that steep section, not just "around pH 7."

Half-Equivalence pH = pKa

The half-equivalence point is the single most useful feature of a weak acid titration curve. When exactly half the acid has been neutralized, [HA] = [A⁻]. Plug that into Henderson–Hasselbalch: pH = pKa + log(1) = pKa + 0 = pKa. So reading the pH at half-equivalence directly gives you pKa. No calculation needed beyond reading a graph.

This is how experimental pKa values get measured. Titrate an unknown weak acid with standardized NaOH, find the equivalence volume, go to half that volume on your curve, read the pH. That pH is pKa. It's elegant and it works because the math guarantees the ratio is exactly 1:1 at that point.

The half-equivalence region is also the flat part of the titration curve—it's where buffer capacity peaks. Adding titrant here barely changes pH because the buffer system (HA/A⁻ in equal amounts) absorbs it. This plateau is absent in strong acid + strong base titrations because there's no buffer pair.

Strong-into-Weak Curve Shape

Titrating a weak acid with strong base produces a distinctive curve with four regions. First, the initial pH—higher than a strong acid of the same concentration because weak acids partially dissociate. Second, the buffer region—a gradual rise as titrant converts HA to A⁻, creating a buffer. Third, the equivalence region—a steep jump past pH 7 because the conjugate base is basic. Fourth, the post-equivalence region—excess NaOH dominates and pH climbs slowly toward 13-14.

Compare this to strong acid + strong base: no buffer plateau, equivalence at exactly pH 7, and the steep section is more vertical (larger pH jump in fewer drops). The weak-acid curve looks "softer" because the buffer region cushions the rise. The weaker the acid (higher pKa), the higher the initial pH and the more obvious the buffer shelf.

Curve region summary:

Initial: pH from √(Ka × C) calculation

Buffer zone: pH = pKa ± ~1 (flat region)

Half-equiv: pH = pKa exactly

Equivalence: pH from Kb hydrolysis (> 7)

Post-equiv: pH from excess [OH⁻]

Polyprotic Acid Inflections

Polyprotic acids (H₂SO₃, H₃PO₄, citric acid) have multiple ionizable protons, each with its own pKa. This produces multiple equivalence points on the titration curve—one for each proton removed. The curve shows distinct S-shaped steps, each separated by a buffer region around the corresponding pKa.

For phosphoric acid: the first equivalence removes H₃PO₄ → H₂PO₄⁻ (near pKa₁), the second removes H₂PO₄⁻ → HPO₄²⁻ (near pKa₂), and the third removes HPO₄²⁻ → PO₄³⁻ (near pKa₃). Each step doubles the titrant volume from the previous equivalence. The steps are only visible as separate inflections if the pKa values are well-separated (at least 3-4 units apart).

When pKa values are too close together (within 2 units), the individual steps merge into one blurred transition and you can't resolve separate equivalence points from the curve. This is why sulfuric acid's second proton (pKa₂ ≈ 1.99) doesn't always produce a clean second step—it's too close to the strong first ionization.

NaOH into Acetic Acid Run

Problem: Titrate 25.0 mL of 0.10 M acetic acid (pKa ≈ 4.76) with 0.10 M NaOH. Find key pH values.

Equivalence volume:

V_eq = (0.10 × 25.0) / 0.10 = 25.0 mL

Initial pH (0 mL NaOH):

Ka ≈ 1.74 × 10⁻⁵

[H⁺] = √(1.74 × 10⁻⁵ × 0.10) = 1.32 × 10⁻³

pH = 2.88

Half-equivalence (12.5 mL):

pH = pKa = 4.76

At equivalence (25.0 mL):

All HA → A⁻. [A⁻] = 0.0025/0.050 = 0.050 M

Kb = 10⁻¹⁴/1.74 × 10⁻⁵ = 5.75 × 10⁻¹⁰

[OH⁻] = √(5.75 × 10⁻¹⁰ × 0.050) = 5.36 × 10⁻⁶

pH = 14 − 5.27 = 8.73

Notice: equivalence is at 8.73, not 7. Phenolphthalein (color change 8–10) is the right indicator here. Methyl orange would change color far too early, in the buffer region.

Endpoint Logic

• Endpoint ≠ equivalence point: Endpoint is the experimental observation (indicator color change). Equivalence is the theoretical stoichiometric point. Good technique minimizes the gap between them.

• Volume changes dilute: Total volume increases as you add titrant. Always use (V_analyte + V_titrant) as your denominator when calculating concentrations mid-titration.

• Different formulas per region: Before equivalence: buffer equation or excess acid. At equivalence: hydrolysis of salt. After equivalence: excess titrant. Using the wrong formula for the wrong region is the #1 exam error.

• Temperature and CO₂: CO₂ absorption from air makes basic solutions drift acidic over time. Kw changes with temperature, shifting the neutral point. Both affect real titrations but not idealized calculations.

Sources

Frequently Asked Questions

What is the equivalence point in a titration and how is it different from the end point?
The equivalence point is the theoretical moment when moles of titrant added exactly equal moles of analyte present—the reaction is stoichiometrically complete. The end point is the experimental moment when an indicator changes color or a pH meter detects a specific pH change. Ideally, the end point matches the equivalence point, but they can differ slightly due to indicator selection or measurement limitations. For strong acid + strong base titrations, the equivalence point occurs at pH 7.00 (at 25°C). For weak acid + strong base, equivalence occurs above pH 7 (typically pH 8-10) due to conjugate base hydrolysis. For weak base + strong acid, equivalence occurs below pH 7 (typically pH 4-6) due to conjugate acid hydrolysis. Understanding this distinction is crucial for accurate titration analysis and proper indicator selection.
Why is the equivalence point pH not always 7?
The equivalence point pH depends on the products formed at equivalence. For strong acid + strong base (e.g., HCl + NaOH), the salt formed (NaCl) is neutral and doesn't hydrolyze, so the solution is pure water and pH = 7.00 at 25°C. For weak acid + strong base (e.g., CH₃COOH + NaOH), all weak acid is converted to conjugate base (CH₃COO⁻) at equivalence. The conjugate base hydrolyzes: A⁻ + H₂O ⇌ HA + OH⁻, making the solution basic, so pH > 7 (typically 8-10). For weak base + strong acid (e.g., NH₃ + HCl), all weak base is converted to conjugate acid (NH₄⁺) at equivalence. The conjugate acid hydrolyzes: BH⁺ + H₂O ⇌ B + H₃O⁺, making the solution acidic, so pH < 7 (typically 4-6). The pH at equivalence is determined by hydrolysis of the products, not by the initial reactants.
What is the half-equivalence point and why is it important?
The half-equivalence point occurs when exactly half of the analyte has reacted with the titrant (i.e., when V_titrant = V_equivalence / 2). For a weak acid titration, at this point [HA] = [A⁻] (equal amounts of weak acid and conjugate base), so by the Henderson–Hasselbalch equation, pH = pKa. This makes the half-equivalence point extremely useful: (1) you can determine the pKa of an unknown weak acid by measuring pH at half-equivalence, (2) buffer capacity is at its maximum (both forms present in equal amounts), (3) the buffer region is most effective. For weak base titrations, at half-equivalence pOH = pKb (or pH = 14 - pKb). The half-equivalence point appears as a relatively flat region on the titration curve, making it easy to identify visually. It's a key feature that distinguishes weak acid/base titrations from strong acid/base titrations.
What is the buffer region on a titration curve and why does it appear flat?
The buffer region is the relatively flat portion of the titration curve (for weak acid/base titrations) that occurs before the equivalence point. In this region, both the weak acid and its conjugate base (or weak base and its conjugate acid) are present in significant amounts, creating a buffer system that resists pH changes. The buffer region typically spans from the initial point to just before equivalence, covering approximately pKa ± 1 pH units. During this region, pH changes slowly because the buffer system absorbs additions of titrant through equilibrium shifts (Le Chatelier's principle). The flatness comes from maximum buffer capacity when [HA] = [A⁻] (around half-equivalence) and significant capacity throughout the region. The buffer region is absent in strong acid + strong base titrations because there's no weak acid/base pair to create buffering—pH changes more dramatically throughout. Understanding the buffer region helps you predict curve shapes and select appropriate indicators.
How do I choose the right indicator for a titration?
Choose an indicator whose color change transition range overlaps with the steep portion of the titration curve near the equivalence point. The indicator's transition range (typically 2 pH units) should include or be very close to the equivalence point pH. For strong acid + strong base titrations (equivalence at pH 7): phenolphthalein (pH 8-10) or methyl red (pH 4.4-6.2) work well because the steep region spans pH 4-10. For weak acid + strong base titrations (equivalence at pH 8-10): phenolphthalein (pH 8-10) is ideal because its transition range matches the equivalence pH. For weak base + strong acid titrations (equivalence at pH 4-6): methyl orange (pH 3.1-4.4) or methyl red (pH 4.4-6.2) are better choices. Use this calculator to find the exact equivalence point pH, then select an indicator whose transition range includes that pH. Don't assume based on titration type alone—calculate equivalence pH first.
Why does the titration curve have an S-shape?
The S-shape results from how pH changes throughout the titration process: (1) Initial region: pH changes slowly because there's excess analyte. For strong acids, pH is low and relatively stable. For weak acids, pH is higher but still changes slowly. (2) Buffer region (weak acid/base only): Relatively flat section where pH changes slowly due to buffering. Both weak acid and conjugate base are present, creating resistance to pH changes. (3) Equivalence region: The steepest part of the curve—a tiny amount of titrant causes a dramatic pH change. This is where the equivalence point occurs. The steepness comes from the buffer being exhausted—no more resistance to pH changes. (4) Post-equivalence region: pH changes slowly again because excess titrant dominates. The S-shape is most pronounced in strong acid + strong base titrations (sharp vertical rise). Weak acid/base titrations show a more gradual S-shape with a visible buffer plateau before the steep rise.
How is the equivalence volume calculated and does it depend on acid/base strength?
The equivalence volume is calculated using stoichiometry: V_eq = (C_analyte × V_analyte) / C_titrant. This formula comes from the fact that at equivalence, moles of titrant = moles of analyte. Since moles = concentration × volume, we get C_analyte × V_analyte = C_titrant × V_eq. Solving for V_eq gives the formula. Importantly, the equivalence volume does NOT depend on whether acids/bases are strong or weak—it only depends on stoichiometry. A 0.1 M weak acid requires the same volume of 0.1 M strong base as a 0.1 M strong acid (assuming 1:1 stoichiometry). However, the pH at equivalence differs dramatically: weak acid gives pH > 7, strong acid gives pH = 7. This separation—volume from stoichiometry, pH from acid/base strength—is a key insight that simplifies problem-solving. The equivalence volume tells you how much titrant is needed, while acid/base strength determines what pH you'll have at that point.
What are the limitations of this titration curve simulator?
This simulator uses simplified textbook approximations designed for educational understanding: (1) Assumes complete dissociation of strong acids and bases (100% ionization). (2) Uses Kw = 1.0 × 10⁻¹⁴ (valid at 25°C, but changes with temperature). (3) Ignores activity coefficients and ionic strength effects (assumes ideal dilute solutions). (4) Uses simplified hydrolysis calculations at equivalence (approximation [OH⁻] ≈ √(Kb × C) for weak acid titrations). (5) Does not account for polyprotic acids (only monoprotic acids/bases). (6) Ignores CO₂ absorption, which can affect basic solutions. (7) Assumes 1:1 stoichiometry (one H⁺ per acid, one OH⁻ per base). Real laboratory titrations may differ due to temperature variations, ionic strength, impurities, or non-ideal behavior. Use this tool for educational understanding, homework practice, and conceptual learning—not for laboratory predictions or analytical applications requiring high accuracy.
How is the initial pH calculated for weak acids and weak bases?
For a weak acid HA with concentration C and Ka, the initial pH is calculated from the acid dissociation equilibrium: HA ⇌ H⁺ + A⁻. Using the approximation valid when Ka << C and [H⁺] << C, we get [H⁺] ≈ √(Ka × C). Then pH = -log₁₀([H⁺]). For example, 0.1 M acetic acid (Ka = 1.74 × 10⁻⁵): [H⁺] ≈ √(1.74×10⁻⁵ × 0.1) = 0.00132 M, so pH = 2.88. For a weak base B with Kb, we calculate [OH⁻] ≈ √(Kb × C) using the same approximation, then pOH = -log₁₀([OH⁻]), and pH = 14 - pOH. For example, 0.1 M ammonia (Kb = 1.78 × 10⁻⁵): [OH⁻] ≈ √(1.78×10⁻⁵ × 0.1) = 0.00133 M, pOH = 2.88, pH = 11.12. These approximations work well for typical concentrations (0.01-1 M) and Ka/Kb values (10⁻² to 10⁻⁵), which cover most textbook problems.

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