Solidification Cooling Curve lab report

1. Title and aim

Determination of the Latent Heat of Fusion by the Method of Cooling. Investigate the cooling curve of a substance passing through a change of state from liquid to solid, observe the isothermal solidification arrest plateau, and determine the latent heat of fusion of salol (phenyl salicylate) from the duration of the solidification arrest under a known steady rate of heat loss.

2. Abstract

Five observations were generated from the ideal teaching model over the settings listed below. A straight-line fit gave an estimate of Latent heat of fusion L_f of 79.49 kJ kg⁻¹, differing by 0.015% from the model value. The reported scatter comes from scale rounding and any stated model approximation, not measured laboratory noise.

3. Apparatus and fixed settings

• Standardized Boiling Tube with Air-Jacketed Cooling Enclosure: A thin-walled borosilicate glass test tube (25 mm diameter, 150 mm length) held coaxially inside a wider glass cylinder by a split cork ring, providing a stagnant annular air buffer that ensures uniform, draft-free convective and radiative cooling to ambient surroundings.
• Precision Immersion Calorimetric Thermometer (0.1°C Divisions): A short-range mercury-in-glass thermometer graduated from 20°C to 70°C in 0.1°C subdivisions, positioned centrally within the molten salol to record the temperature descent, supercooling dip, and the steady horizontal solidification plateau.
• Helical Wire Stirrer and Seeding Probe: A fine nichrome wire formed into a loop encircling the thermometer stem, used to agitate the liquid gently prior to crystallization and to introduce a microscopic seed crystal to arrest supercooling promptly at 41.5 °C.
• Digital Laboratory Stopclock and Regulated Water Heating Bath: A precision digital timer recording elapsed time to 0.01 min, paired with a thermostatically controlled warm water bath used to melt the salol sample completely to approximately 60 °C before cooling runs.
• Pure crystalline test substance: Salol (phenyl salicylate, C₁₃H₁₀O₃); equilibrium melting point T_m = 41.5 °C.
• Standardized thin-walled boiling tube (outer diameter 25.0 mm) suspended in a concentric air-jacketed outer beaker.
• Calibrated steady heat loss rate to surroundings at 41.5 °C: R_loss = 270.0 J min⁻¹ (4.50 W).
• Reference latent heat of fusion for phenyl salicylate: L_f = 79.50 kJ kg⁻¹ (79,500 J kg⁻¹).

4. Theory and graph choice

When a pure crystalline chemical substance in the molten state undergoes continuous cooling, its thermodynamic trajectory exhibits a sharp, qualitative distinction from the smooth exponential decay characteristic of homogeneous single-phase cooling. As sensible heat is initially extracted, the liquid temperature drops monotonically according to Newton's law of cooling until reaching the melting temperature T_m. At this critical boundary, the thermodynamic driving force initiates a first-order phase transition: disordered liquid molecules assemble into a rigid crystalline lattice, releasing their latent heat of fusion L_f. Throughout this crystallization process, the liberation of latent enthalpy exactly compensates for the thermal energy dissipated to the environment, pinning the temperature of the coexisting liquid-solid mixture at the constant equilibrium melting point. This creates an extended horizontal arrest plateau on the cooling curve whose temporal duration Δt is directly proportional to the total mass m of the crystallizing specimen. By enclosing the test vessel in a standardized air-jacketed container surrounded by a constant-temperature bath, the ambient rate of heat loss R_loss at the freezing temperature remains invariant across successive trials. Equating the liberated latent heat Q_latent = R_loss · Δt to m · L_f yields a direct linear relationship between the thermal arrest duration and the mass of the charge. Linear regression over varying sample masses provides an exceptionally clean determination of the latent heat of fusion, while contrasting the sharp arrest plateau of crystalline salol with the continuous, sloped vitrification curves of amorphous substances such as paraffin wax reveals fundamental insights into solid-state thermodynamics.

The calculation fits y = mx + b in SI units. The graph may display scaled axes for readability; those display factors are removed before calculating the physical result. The gradient has units J kg⁻¹.

5. Method

1. Weigh the clean, dry boiling tube together with its wire stirrer to ±0.01 g using an analytical balance. Introduce a known mass m of pure crystalline salol (e.g., 15.0 g) into the tube, reweigh the assembly to confirm the exact specimen charge, and secure the tube in a clamp ready for melting.
2. Immerse the lower half of the boiling tube in a beaker of water maintained between 60 °C and 65 °C. Allow the salol crystals to melt entirely until an optical inspection confirms complete liquefaction with no residual solid crust adhering to the inner walls, reaching a uniform liquid temperature of approximately 55 °C to 60 °C.
3. Remove the tube from the warm water bath, wipe its outer surface thoroughly dry, and seat it firmly inside the wider outer air-jacket cylinder using the split cork collar. Insert the precision thermometer through the cork so its mercury bulb is centered vertically and horizontally within the molten salol volume.
4. Start the digital stopclock and record the temperature of the salol every 30 seconds as it cools. As the temperature nears 41.5 °C, monitor for supercooling (where the liquid drops 1°C to 2°C below T_m without solidifying). Touch a microscopic speck of solid salol on the tip of the stirrer wire to seed nucleation, observing the immediate thermal rebound to the steady arrest temperature T_m = 41.5 °C.
5. Observe the thermometer reading during the crystallization process. Note the precise time t_start when the temperature stabilizes at 41.5 °C and the time t_end when all liquid has transformed into crystalline solid and the temperature resumes a rapid downward decline. Evaluate the plateau duration Δt = t_end − t_start in minutes.
6. Repeat the measurement for five distinct masses of salol (15.0 g, 20.0 g, 25.0 g, 30.0 g, and 35.0 g). For each run, compute the total heat liberated Q_latent = R_loss · Δt in joules. Plot Q_latent against mass m (kg), perform an ordinary least-squares fit through the origin, and determine the latent heat of fusion L_f from the gradient.

6. Observations and calculation table

All observations use fixed model settings. Values are rounded only at the instrument reading stage; further calculations use full precision. Repeated physical trials are not claimed.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Dots show the sample observations. The line is the ordinary least-squares fit.

9. Uncertainty and comparison

Percentage difference = |estimate − model value| / |model value| × 100 = 0.0151%. Percentage difference is not experimental uncertainty.

For n = 5 observations, Σresidual² = 2.91600; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 62.35383. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 1.62000.

Propagating only the relevant fit coefficient gives a fit-only standard error of 0.06235 kJ kg⁻¹. This is a one-standard-error quantity under the regression assumptions. Deterministic rounded model data do not supply a complete physical uncertainty budget.

Thermal supercooling before nucleation, non-uniform radial solidification fronts from the glass wall inward, temperature gradients across the partially crystallized solid slush, thermometer stem conduction, ambient draft fluctuations around the test tube mouth, and chemical purity variations in salol contribute experimental uncertainty. The OLS regression standard error reflects random scatter in plateau duration determination, but does not capture unmodelled sensible heat release during transient phase coexistence.

10. Result and discussion

The observations follow the stated model relationship. Check whether the intercept and residual pattern suggest a systematic offset or a missing approximation. Agreement with the model does not independently verify its input constants.

11. Precautions and limitations

• Ensure the salol crystals are melted completely in the warm water bath before placing the tube in the air jacket, eliminating all unmolten crystal seeds.
• Wipe the exterior of the boiling tube completely dry before inserting it into the air jacket to prevent erratic evaporative heat loss.
• Position the thermometer bulb centrally within the salol charge without allowing it to touch the glass walls or bottom of the tube.
• If significant supercooling occurs below 40 °C, touch the liquid gently with a tiny seed crystal on the stirrer wire to prompt immediate crystallization at 41.5 °C.

The teaching simulation models the phase change of pure phenyl salicylate (salol) with an ideal, flat solidification plateau at T_m = 41.50 °C under a calibrated steady heat loss rate R_loss = 270.0 J min⁻¹ (4.50 W) into an isothermal ambient air jacket. In physical laboratory practice, chemical impurities can depress the melting point and cause a slight slope on the plateau, supercooling may delay crystallization onset by several degrees if unseeded, radial temperature gradients across the viscous solid salol cause the termination of the plateau to round off gradually, and ambient room temperature drafts can induce small variations in the effective heat loss rate. The simulation evaluates the solidification plateau duration using the exact thermodynamic conservation relation Δt = (m · L_f) / R_loss, where m is the sample mass in kilograms, L_f = 79,500 J kg⁻¹ (79.50 kJ kg⁻¹) is the reference latent heat of fusion of salol, and R_loss = 270.0 J min⁻¹ (4.50 W) is the calibrated heat loss rate. Plateau durations are rounded to 0.01 min to model standard laboratory stopclock precision, and ordinary least-squares linear regression of Q_latent = R_loss · Δt against mass m provides the reported latent heat of fusion.

12. Conclusion

The worked example illustrates how to obtain Latent heat of fusion L_f from measurements, graph variables and a fitted coefficient. The estimate is 79.49 kJ kg⁻¹. A real experiment must additionally evaluate the apparatus-specific uncertainties and corrections described above.