Thermal Analysis Freezing Point Glass Cell
Double-walled vacuum-jacketed glass tube with internal PTFE mechanical paddle stirrer for controlled cooling.
Chemical & Process Engineering / SLE Eutectic Phase Diagram
FREE TO EXPLORELABORATORY 37 · CHEMICAL & PROCESS ENGINEERING
Solid-Liquid Phase Equilibrium (SLE) & Simple Eutectic Phase Diagram Construction
Construct the solid-liquid equilibrium (SLE) phase diagram for a binary naphthalene-biphenyl organic eutectic mixture using thermal analysis cooling curves across solute mole fractions x_B from 0.04 to 0.24, evaluate freezing point depression ΔT_f, determine the cryoscopic limiting slope, and extract the eutectic point coordinates. Explore interactive transport phenomena, unit operations simulation, and chemical engineering telemetry.
TRANSPORT PHENOMENA · UNIT OPERATIONS · PROCESS CONTROL · REACTION ENGINEERING
Your virtual chemical and process engineering laboratory.
FREEZING POINT DEPRESSION ΔT_F—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Solute Mole Fraction x_B = 0.12 mol/mol.
Adjust Solute Mole Fraction x_B, then execute chemical process trial.
Chemical and process engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity transport phenomena and unit operations modeling.
Process engineering assumptions and boundary condition limits
The transport and thermodynamic models apply within the specified calibrated operating window (0.04 to 0.24 mol/mol). Evaluated using an automated thermal analysis cooling cell with 4-wire Pt100 RTD sensor (±0.02 °C) and programmable air-jacketed cooling mantle. Pure naphthalene: T_mA = 80.20 °C, ΔH_fus,A = 18.98 kJ/mol; pure biphenyl: T_mB = 69.20 °C, ΔH_fus,B = 18.58 kJ/mol.
Process apparatus & industrial sensors.
Precision 4-Wire Pt100 RTD Sensor & Data Logger
Measures melt temperature with 0.01 °C resolution and 5 Hz sampling rate to record cooling curve inflection points.
Thermostatic Silicone Oil Heating Bath
Melts organic mixtures up to 100.0 °C and maintains uniform liquid temperature before cooling.
Controlled Ambient Air-Jacketed Cooling Jacket
Provides steady, reproducible convective heat removal rate of 1.5 to 2.0 °C/min during solidification.
Variable-Speed Reciprocating Stirrer Motor
Maintains continuous 120 RPM vertical agitation to eliminate thermal stratification and minimize supercooling.
High-Precision Analytical Balance (0.0001 g)
Weighs naphthalene and biphenyl components gravimetrically to establish exact synthetic mole fractions.
FOLLOW THE METHOD
A reason behind every step.
Construct the solid-liquid equilibrium (SLE) phase diagram for a binary naphthalene-biphenyl organic eutectic mixture using thermal analysis cooling curves across solute mole fractions x_B from 0.04 to 0.24, evaluate freezing point depression ΔT_f, determine the cryoscopic limiting slope, and extract the eutectic point coordinates. Standardized parameter settings: 0.04, 0.08, 0.12, 0.16, 0.2, 0.24 mol/mol.
01
Sensor Calibration & Pure Component Baseline
Calibrate the Pt100 RTD sensor against distilled ice point (0.00 °C) and boiling water (100.00 °C); record cooling curve of pure naphthalene to verify T_mA = 80.20 °C.
02
Gravimetric Mixture Preparation
Weigh exactly 10.000 g of naphthalene and add calculated mass of biphenyl to synthesize x_B = 0.04 into the freezing tube.
03
Complete Liquefaction in Oil Bath
Immerse sample tube in 95.0 °C silicone oil bath until solids are completely melted; stir gently to ensure homogeneous liquid mixing.
04
Cooling Cell Transfer & Stirring Activation
Transfer tube to the air-jacketed cooling assembly; start reciprocating stirrer at 120 RPM and begin logging temperature versus time at 2 Hz.
05
Cooling Curve Inflection & Liquidus Determination
Identify the liquidus freezing point T_f from the cooling curve slope change (inflection from sensible cooling to crystal latent heat plateau); compute ΔT_f = T_mA - T_f.
06
Composition Step Progression & Eutectic Logging
Add subsequent increments of biphenyl to achieve x_B = 0.08, 0.12, 0.16, 0.20, and 0.24, repeating the melt-cool protocol to determine cryoscopic slope S.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates SLE Eutectic Phase Diagram mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
ΔT_f = S · x_B = 58.5000 · x_B
| # | Biphenyl Solute Mole Fraction x_B (mol/mol) | Freezing Point Depression ΔT_f (°C) | Biphenyl solute mole fraction x_B (mol/mol) | Freezing point depression ΔT_f (°C) | Remove |
|---|
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CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
According to the Gibbs Phase Rule at constant pressure (F = C - P + 1), the degrees of freedom F at a binary eutectic point are:
The Schröder–van Laar equation models solid-liquid equilibrium under which assumption?
In a cooling curve, the onset of crystallization of the primary component appears as:
The cryoscopic limiting slope S = dT_f / dx_B in a dilute ideal binary solution is equal to:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
Solid-liquid equilibrium (SLE) phase diagrams are foundational to chemical engineering crystallization, melt purification, pharmaceutical co-crystal formulation, metallurgy, and thermal energy storage phase-change materials (PCMs). When two chemical species are completely miscible in the liquid melt but mutually immiscible in the solid crystalline state, they form a simple binary eutectic system. The classic chemical engineering model system is the binary mixture of naphthalene (component A, pure melting point T_mA = 80.20 °C) and biphenyl (component B, pure melting point T_mB = 69.20 °C). In this system, adding solute B to pure liquid A depresses the liquidus temperature—the temperature at which the first pure crystal of component A nucleates from the melt. According to the Schröder–van Laar equation derived from chemical potential equality between pure solid A and liquid solution A: ln(γ_A · x_A) = -[ΔH_fus,A / R] · [1/T - 1/T_mA], where ΔH_fus,A is the standard enthalpy of fusion (18.98 kJ/mol for naphthalene) and γ_A is the liquid-phase activity coefficient. In the dilute solute regime (x_B = 1 - x_A << 1), the liquid behaves nearly ideally (γ_A ≈ 1.00), and expanding the reciprocal temperature term in a first-order series yields the linear cryoscopic freezing point depression relation: ΔT_f = T_mA - T = S · x_B, where the cryoscopic limiting slope is given by S = R · T_mA^2 / ΔH_fus,A = 58.5000 °C (K). Continued addition of solute B depresses the liquidus until it intersects the second liquidus curve of component B at the eutectic point (T_eutectic ≈ 39.4 °C, x_B,eutectic ≈ 0.45), where both solid A and solid B crystallize simultaneously at a unique invariant temperature. In this laboratory experiment, an instrumented thermal analysis freezing point apparatus records time-temperature cooling curves across biphenyl mole fractions from 0.04 to 0.24 to identify the liquidus break temperatures, confirm the linear cryoscopic slope S = 58.5000 °C, and construct the complete SLE phase boundary.
ΔT_f = S · x_B = 58.5000 · x_B
Evaluated using an automated thermal analysis cooling cell with 4-wire Pt100 RTD sensor (±0.02 °C) and programmable air-jacketed cooling mantle. Pure naphthalene: T_mA = 80.20 °C, ΔH_fus,A = 18.98 kJ/mol; pure biphenyl: T_mB = 69.20 °C, ΔH_fus,B = 18.58 kJ/mol.