| # | V(NaOH) / mL | Temp / °C | Group | Remove |
|---|---|---|---|---|
| No data recorded yet. Add NaOH and click Record Data Point | ||||
⚙️ Axis Customisation
V, T or V T or V;T — one pair per line. Lines beginning with # are treated as comments.
Thermometric Titration
A comprehensive reference for CAPE Chemistry Unit 2 and University-level Analytical Chemistry
1. Introduction
Thermometric titration is an analytical technique in which the endpoint of a titration is determined by monitoring the temperature change of the reaction mixture. Rather than relying on a colour indicator or pH electrode, this method exploits the enthalpy change of the chemical reaction occurring between titrant and analyte.
As titrant is added, temperature rises (for exothermic reactions) until the equivalence point is reached. Beyond this point, no further reaction occurs, and the temperature falls due to dilution and heat loss to the surroundings. The equivalence point is located by extrapolating both the rising and falling portions of the temperature–volume curve to their intersection.
2. Reactions in This Simulator
Reaction 1: NaOH + Hydrochloric Acid
This is a 1:1 (monoprotic) neutralisation. The equivalence volume of NaOH equals the volume of HCl that contains the same number of moles as the NaOH solution. The standard enthalpy of neutralisation for a strong acid–strong base pair is approximately −57.6 kJ mol⁻¹ (per mole of water formed).
Reaction 2: NaOH + Sulfuric Acid
Sulfuric acid is a diprotic acid — each molecule provides two H⁺ ions. Therefore, two moles of NaOH are required for every mole of H₂SO₄. The equivalence volume of NaOH is therefore twice what would be needed for an equimolar HCl solution.
| Property | HCl / NaOH | H₂SO₄ / NaOH |
|---|---|---|
| Acid type | Monoprotic strong acid | Diprotic strong acid |
| Molar ratio (acid:base) | 1 : 1 | 1 : 2 |
| ΔH per mol H₂O | −57.6 kJ mol⁻¹ | −57.6 kJ mol⁻¹ |
| ΔH per mol acid | −57.6 kJ mol⁻¹ | −115.2 kJ mol⁻¹ |
| Net ionic equation | H⁺ + OH⁻ → H₂O | 2H⁺ + 2OH⁻ → 2H₂O |
3. Temperature Model & Calculations
3.1 Predicting the Equivalence Volume
where n = 1 for HCl, n = 2 for H₂SO₄
3.2 Temperature Rise Before Equivalence
As NaOH is added up to the equivalence point, the temperature rises. Assuming perfect insulation (styrofoam cup):
ΔT = q / (mtotal × Cp)
T = Tinitial + ΔT
where: mtotal = (Vacid + VNaOH) g [density ≈ 1 g/mL]
Cp = 4.18 J g⁻¹ °C⁻¹ (specific heat of water)
3.3 Temperature After Equivalence
Beyond the equivalence point, no further heat is produced. The temperature falls because room-temperature NaOH dilutes the warm solution, and there is ongoing heat loss to the surroundings:
where k is a heat loss coefficient dependent on insulation quality (adjustable in this simulator as the "Heat Loss Factor" slider).
3.4 Calculating Enthalpy of Neutralisation
ΔHneut = −q / nH₂O [kJ mol⁻¹]
4. Graphical Analysis — Finding the Equivalence Point
Because real experiments involve heat losses, the peak temperature is lower than the theoretical maximum. The correct equivalence point is found by extrapolating two best-fit lines:
- A rising line through points before the equivalence point
- A falling line through points after the equivalence point
- The intersection of these two extrapolated lines gives the corrected equivalence point
In this simulator, you manually select the rising and falling points, and the app calculates the best-fit lines using linear regression, then computes their intersection.
Linear Regression Formula
Intercept b = (Σy − mΣx) / n
Best-fit line: T = mV + b
Intersection: Veq = (b₂ − b₁) / (m₁ − m₂), Teq = m₁Veq + b₁
5. Experimental Sources of Error
| Source of Error | Effect | Mitigation |
|---|---|---|
| Heat loss to surroundings | Peak temperature lower than theoretical | Use styrofoam cup; use graphical extrapolation |
| Slow thermal equilibration | Readings lag behind actual temperature | Stir after each addition; allow time before reading |
| Dilution effect | Concentration decreases as V increases | Use concentrated titrant; account in model |
| Heat capacity of thermometer | Absorbs some heat from solution | Use thin electronic temperature probe |
| Incomplete dissociation | Slightly less heat evolved | Use standard strong acid/base pairs for benchmarking |
6. Key Thermochemical Data
| Quantity | Value |
|---|---|
| ΔHneut (strong acid + strong base) | −57.6 kJ mol⁻¹ (per mol H₂O) |
| Specific heat capacity of water (Cp) | 4.18 J g⁻¹ °C⁻¹ |
| Density of dilute aqueous solutions | ≈ 1.00 g mL⁻¹ |
| Standard conditions | 298 K, 100 kPa |
| Net ionic equation | H⁺(aq) + OH⁻(aq) → H₂O(l) |