Titration Point Calculator
Compute titration point using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
V_eq = (n_analyte x stoich) / C_titrant | pH_half = pKa
The equivalence volume is calculated by dividing the moles of analyte (concentration times volume) by the titrant concentration. At the half-equivalence point, pH equals pKa. Initial pH uses the weak acid approximation, and equivalence pH accounts for conjugate base hydrolysis.
Worked Examples
Example 1: Weak Acid Titration with NaOH
Problem: Titrate 25 mL of 0.1 M acetic acid (pKa = 4.76) with 0.1 M NaOH. Find the equivalence point volume and pH values at key points.
Solution: Moles of acetic acid: 0.1 M x 0.025 L = 0.0025 mol = 2.5 mmol\nEquivalence volume: 0.0025 / 0.1 = 0.025 L = 25.0 mL NaOH\nHalf-equivalence volume: 12.5 mL\nInitial pH: 0.5 x (4.76 - log(0.1)) = 0.5 x (4.76 + 1) = 2.88\nHalf-equiv pH: pKa = 4.76\nEquiv pH: conjugate base hydrolysis gives pH ~ 8.72
Result: Equivalence at 25.0 mL | Initial pH: 2.88 | Half-equiv pH: 4.76 | Equiv pH: 8.72
Example 2: Determining Unknown Acid pKa
Problem: A 0.15 M unknown weak acid (50 mL) is titrated with 0.1 M NaOH. The equivalence point is at 75 mL. At 37.5 mL NaOH, the pH reads 5.3. Find the pKa.
Solution: Moles of acid: Ct x Vequiv = 0.1 x 0.075 = 0.0075 mol\nConcentration check: 0.0075 / 0.050 = 0.15 M (confirmed)\nHalf-equivalence volume: 75 / 2 = 37.5 mL\nAt half-equivalence: pH = pKa\nTherefore pKa = 5.3\nKa = 10^(-5.3) = 5.01 x 10^(-6)
Result: pKa = 5.3 | Ka = 5.01 x 10^-6 | Equivalence volume: 75 mL
Frequently Asked Questions
What is the equivalence point in a titration and how is it determined?
The equivalence point is the exact moment when the moles of titrant added are stoichiometrically equal to the moles of analyte in the solution. At this point, all of the analyte has reacted completely with the titrant. For a strong acid-strong base titration, the equivalence point occurs at pH 7.0. For a weak acid titrated with a strong base, the equivalence point pH is above 7 because the conjugate base formed is basic. For a weak base with a strong acid, it falls below 7. The equivalence point is determined using indicators that change color at the appropriate pH, or more precisely with a pH meter by identifying the steepest inflection point on the titration curve where pH changes most dramatically per unit volume added.
What is the half-equivalence point and why is it important?
The half-equivalence point occurs when exactly half of the analyte has been neutralized by the titrant, meaning the volume of titrant added is exactly half of the equivalence volume. At this point, the concentrations of the weak acid and its conjugate base are equal ([HA] = [A-]), so the Henderson-Hasselbalch equation simplifies to pH = pKa + log(1) = pKa. This makes the half-equivalence point the most reliable experimental method for determining the pKa of an unknown weak acid. The buffer capacity is also at its maximum here, meaning the solution resists pH changes most effectively. Identifying this point on a titration curve provides direct insight into the acid dissociation constant.
How do I choose the right indicator for a titration?
An appropriate indicator must change color within the pH range of the steep portion of the titration curve near the equivalence point. For strong acid-strong base titrations (equivalence at pH 7), bromothymol blue (pH 6.0-7.6) works well. For weak acid-strong base titrations (equivalence pH 8-10), phenolphthalein (pH 8.2-10.0) is ideal. For weak base-strong acid titrations (equivalence pH 4-6), methyl orange (pH 3.1-4.4) or bromocresol green (pH 3.8-5.4) are suitable. The indicator should have a transition range that overlaps with the equivalence pH. Using the wrong indicator leads to systematic errors, as you would stop adding titrant at the wrong volume. Universal indicators or pH meters eliminate this source of error entirely.
What is the buffer region on a titration curve?
The buffer region is the relatively flat section of the titration curve surrounding the half-equivalence point, where pH changes slowly despite adding titrant. This region spans approximately from 10% to 90% of the equivalence volume, corresponding to a pH range of roughly pKa minus 1 to pKa plus 1. Within this zone, the solution contains significant amounts of both the weak acid and its conjugate base, creating a buffer system that resists pH changes. The flattest portion is at the half-equivalence point where buffering capacity is maximal. Understanding the buffer region is critical for biological and pharmaceutical applications where maintaining a stable pH is essential for protein stability, enzyme activity, and drug formulation.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How accurate are the results from Titration Point Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.