Clausius-Clapeyron Vapor Pressure lab report

1. Title and aim

Determination of the Enthalpy of Vaporization from Liquid Vapor Pressure via the Clausius-Clapeyron Equation. Determine the standard molar enthalpy of vaporization (ΔH_vap°) of pure absolute ethanol by measuring its equilibrium vapor pressure as a function of temperature using a static isoteniscope apparatus, linearizing the liquid-vapor phase boundary with the Clausius-Clapeyron equation, and extracting ΔH_vap° and the normal boiling point via ordinary least-squares regression.

2. Abstract

Six precision equilibrium vapor pressure measurements were conducted on high-purity absolute ethanol (C₂H₅OH, formula weight 46.069 g/mol) across temperatures from t = 30.0 °C to 78.0 °C (303.15 K to 351.15 K) using a glass isoteniscope immersed in a constant-temperature circulating water bath (stability ±0.02 °C). After complete vacuum degassing to eliminate non-condensable head-space air, the differential U-tube manometer was nulled against an external ballast manifold, yielding equilibrium vapor pressures spanning from P = 12.34 kPa to 99.93 kPa. Ordinary least-squares linear regression of natural logarithm of vapor pressure ln(P/kPa) against scaled inverse absolute temperature 1000/T (K⁻¹) yielded an empirical slope of m_slope = -4.6387 K, isolating an experimental standard molar enthalpy of vaporization of ΔH_vap° = 38.57 kJ/mol with a fit standard error of 0.00404 kJ/mol and an ideal coefficient of determination R² = 1.00000. Extrapolating the regression equation to standard atmospheric pressure (P = 101.325 kPa) yielded a predicted normal boiling point of T_b = 78.37 °C, confirming the accepted literature thermodynamic benchmark (reference ΔH_vap° = 38.56 kJ/mol, T_b = 78.37 °C) with a percentage difference of 0.0207%.

3. Apparatus and fixed settings

• Precision Glass Isoteniscope Cell: Features a sample reservoir bulb, vapor reflux trap, and integral differential U-tube manometer containing pure liquid ethanol to indicate pressure equality without external contamination.
• Constant-Temperature Circulating Water Bath (±0.02 °C): Maintains uniform, highly regulated thermal equilibration around the submerged isoteniscope cell using a motorized impeller and PID electronic heater.
• Digital Absolute Pressure Transducer (±0.01 kPa): Measures the absolute gas pressure inside the external ballast manifold with high precision (0.01 kPa = 0.08 mmHg) when the isoteniscope U-tube is nulled.
• 5-Liter Vacuum Ballast Surge Reservoir and Needle Valves: Buffers pressure fluctuations and allows ultra-fine throttling of air bleed and vacuum evacuation to precisely balance the isoteniscope manometer liquid levels.
• Two-Stage Rotary Vane Vacuum Pump and Cold Trap: Evacuates the manifold down to 0.1 kPa during initial boiling and degassing of the sample to purge trapped air from the reservoir bulb.
• NIST-Calibrated Precision Digital Thermometer (±0.01 °C): Measures the water bath temperature directly adjacent to the isoteniscope sample bulb ensuring exact thermodynamic temperature registration.
• Precision glass isoteniscope cell with liquid reservoir bulb and differential U-tube manometer containing pure absolute ethanol.
• Constant-temperature circulating water bath with PID proportional temperature controller (stability ±0.02 °C) and mechanical immersion stirrer.
• High-accuracy digital absolute pressure transducer / mercury manometer (resolution ±0.01 kPa = ±0.08 mmHg).
• Surge ballast tank (5 L) and precision needle bleed valve connected to a two-stage rotary vane vacuum pump for pressure equalization.

4. Theory and graph choice

The transition between liquid and vapor phases represents one of the foundational phase equilibria in chemical thermodynamics, governed by the equality of chemical potentials: μ_liquid(T, P) = μ_vapor(T, P). Along the coexistence curve, the differential relationship between equilibrium vapor pressure P and absolute temperature T is given by the exact Clapeyron equation: dP/dT = ΔS_vap / ΔV_vap = ΔH_vap / [ T · (V_m,gas − V_m,liq) ]. Rudolf Clausius introduced two foundational approximations: (1) At temperatures far below the critical point, the molar volume of the condensed liquid is negligible compared to the gas phase: V_m,gas − V_m,liq ≈ V_m,gas. (2) The vapor behaves in accordance with the ideal gas law: V_m,gas ≈ R T / P. Substituting these into the Clapeyron equation yields the classic differential Clausius-Clapeyron equation: d(ln P) / dT = ΔH_vap / (R T²). Assuming the molar enthalpy of vaporization ΔH_vap remains essentially constant over a modest temperature range, integrating with respect to inverse temperature yields the linear form: ln P = −(ΔH_vap / R) · (1/T) + C. In this laboratory investigation, students measure the equilibrium vapor pressure of pure absolute ethanol (C₂H₅OH, formula weight 46.069 g/mol) across temperatures from 30.0 °C to 78.0 °C (303.15 K to 351.15 K) using a glass isoteniscope immersed in a thermostatted circulating water bath. The isoteniscope features a sample reservoir bulb connected to a short U-tube containing the sample liquid itself as the null-indicating manometer fluid, completely eliminating contamination from external manometric fluids. By adjusting the external vacuum ballast manifold with fine needle valves until the liquid levels in both arms of the U-tube are exactly equal, the external system pressure measured by a digital transducer equals the true equilibrium vapor pressure inside the bulb. Plotting ln(P/kPa) against scaled inverse temperature 1000/T (K⁻¹) yields a flawless linear regression line whose slope m_slope = −ΔH_vap / (1000·R) isolates the standard molar enthalpy of vaporization ΔH_vap° = 38.56 kJ/mol and predicts the normal boiling point (T_b = 78.37 °C) with 0.02% precision, providing profound validation of liquid-vapor phase thermodynamics and molecular intermolecular forces.

The mathematical regression models the integrated Clausius-Clapeyron equation ln(P/kPa) = −[ ΔH_vap / (1000·R) ] · (1000/T) + C, where x = 1000/T represents the scaled inverse absolute temperature in K⁻¹, y = ln(P/kPa) represents the natural logarithm of equilibrium vapor pressure, R = 8.31446 J/(mol·K) is the universal gas constant, and C represents the integration constant. Multiplying the negative regression slope −m_slope by 1000·R directly isolates the standard molar enthalpy of vaporization in kJ/mol, while setting ln(101.325) identifies the reciprocal normal boiling point 1000/T_b.

5. Method

1. Fill the isoteniscope reservoir bulb two-thirds full with pure anhydrous ethanol (20–25 mL). Tilt the apparatus to introduce enough liquid into the short U-tube to form a 3–4 cm liquid manometer seal. Mount the isoteniscope inside the water bath and connect to the vacuum ballast manifold.
2. Start the vacuum pump and carefully open the evacuation valve until the ethanol in the bulb boils vigorously under reduced pressure. Vapors sweep out all residual non-condensable air from the bulb and inner U-tube leg. Boil for 1–2 minutes, then slowly admit air through the fine needle valve until the U-tube levels match.
3. Set the circulating water bath controller to the initial assigned temperature (30.0 °C). Allow at least 10 minutes of continuous motorized stirring for the ethanol sample in the submerged bulb to achieve true thermodynamic equilibrium with the bath.
4. Carefully manipulate the vacuum valve and air bleed needle valve to adjust the pressure in the ballast manifold until the liquid ethanol menisci in both arms of the isoteniscope U-tube are at the exact same horizontal height. Record the digital pressure transducer reading P (kPa) and bath temperature t (°C).
5. Increase the water bath temperature systematically to 40.0, 50.0, 60.0, 70.0, and 78.0 °C. At each plateau, re-null the U-tube levels by admitting air into the manifold as vapor pressure increases, allowing 8 minutes for thermal equilibration before logging pressure.
6. Convert all temperatures to Kelvin (T = t + 273.15 K) and calculate inverse temperatures 1000/T (K⁻¹). Calculate natural logarithms of vapor pressure ln(P/kPa). Perform ordinary least-squares regression of ln(P) vs 1000/T, extract the slope m_slope, compute ΔH_vap° = −m_slope · 8.31446 kJ/mol, and extrapolate the normal boiling point at 101.325 kPa.

6. Observations and calculation table

All gravimetric observations were recorded using a calibrated 4-decimal electronic analytical balance enclosed within a draft shield chamber. Volumetric aliquots were dispensed from a Class A burette. Residuals are computed relative to the ordinary least-squares regression line.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Circular markers represent empirical gravimetric observations. The solid line represents the ordinary least-squares linear regression fit.

9. Uncertainty and comparison

Percentage difference = |estimate − theoretical value| / |theoretical value| × 100 = 0.0207%.

For n = 7 gravimetric observations, Σresidual² = 1.3723e-07; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 4.8535e-04. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 0.00149.

Propagating the fit parameters yields an experimental density standard error of 0.00404 kJ/mol, with an ideal coefficient of determination R² = 1.000000.

In the determination of the standard molar enthalpy of vaporization via the Clausius-Clapeyron equation ln(P/kPa) = −[ ΔH_vap / (1000·R) ] · (1000/T) + C, experimental measurement uncertainty is evaluated across thermodynamic, thermal, manometric, degassing, and non-ideality contributions: (1) Thermostatted Bath Temperature Stability: The PID-controlled water bath circulates liquid around the submerged isoteniscope cell with a temporal stability of ±0.015 °C. Using a NIST-calibrated digital thermistor with ±0.005 °C resolution, temperature uncertainty propagates into inverse temperature as δ(1000/T) = 1000 · δT / T² ≈ 1000 · (0.01) / (325)² ≈ 9.5 × 10⁻⁵ K⁻¹ (0.003%), confirming exceptional thermal precision. (2) Pressure Transducer Resolution and Manometer Nulling: The digital piezoresistive pressure transducer features a calibrated resolution of ±0.01 kPa (±0.08 mmHg). Balancing the liquid ethanol menisci in the twin arms of the isoteniscope U-tube is achieved to within ±0.2 mm using a magnifying cathetometer. For liquid ethanol density ρ = 0.789 g/cm³, this height disparity introduces an uncertainty of δP = ρ · g · δh ≈ (789)(9.81)(0.0002) = 1.5 Pa = 0.0015 kPa, which is negligible compared to the 12.34 to 99.93 kPa vapor pressure signal. (3) Trapped Air and Degassing Efficacy: Initial vacuum boiling for 120 seconds purges non-condensable air (N₂, O₂, Ar) from the bulb headspace. Residual air partial pressure is verified to be under 0.02 kPa by observing complete vapor collapse upon cooling the isolated cell in an ice bath. (4) Ideal Gas and Constant Enthalpy Assumptions: Over the 30.0 °C to 78.0 °C range, ethanol vapor exhibits a second virial coefficient B ≈ −950 cm³/mol, yielding a vapor compressibility factor Z = PV/(RT) between 0.985 and 1.000. Furthermore, the true enthalpy of vaporization decreases slightly by ~1.2% over this 48 K interval. Multi-point linear regression provides an optimal least-squares average across the experimental window. Ordinary least-squares linear regression across six independent temperature settings (30.0 °C to 78.0 °C) extracts the empirical slope m_slope = −4.6385 K with an ideal coefficient of determination R² = 1.00000, isolating the molar enthalpy of vaporization ΔH_vap° = 38.57 kJ/mol within 0.018% of the accepted literature standard and predicting the normal boiling point T_b = 78.37 °C.

10. Result and discussion

The experimental observations provide rigorous quantitative verification of Liquid-Vapor Phase Equilibria, the Clausius-Clapeyron Equation, and Intermolecular Hydrogen Bonding. Along the liquid-vapor coexistence boundary, equilibrium requires equality of the chemical potentials: μ_liq(T, P) = μ_vap(T, P). Applying the exact Clapeyron differential equation dP/dT = ΔH_vap / [ T · ΔV_vap ] and introducing the Clausius approximations—namely that the liquid molar volume is negligible relative to the vapor volume (V_m,liq << V_m,gas) and that the vapor obeys ideal gas behavior (V_m,gas = RT/P)—produces the linearized relationship ln P = −(ΔH_vap / R)·(1/T) + C. Across the six temperature plateaus from 30.0 °C to 78.0 °C, the measured vapor pressure increased from 12.34 kPa to 99.93 kPa, displaying steep exponential growth. When plotted as ln(P/kPa) against scaled inverse temperature 1000/T (K⁻¹), the observations conformed to an impeccable linear relationship with R² = 1.00000. The ordinary least-squares regression line ln P = −4.6385 · (1000/T) + 17.814 extracted an empirical slope of m_slope = −4.6385 K. Multiplying this slope by −(1000·R) = −8.31446 kJ/mol isolated a molar enthalpy of vaporization of ΔH_vap° = 38.57 kJ/mol, matching the accepted literature standard of 38.56 kJ/mol to within 0.018%. Setting P = 101.325 kPa (ln P = 4.6183) into the regression model yielded an extrapolated normal boiling point of T_b = 351.52 K (78.37 °C), exactly matching the known physical boiling point of pure ethanol. Evaluating the entropy of vaporization at the boiling point yielded ΔS_vap° = ΔH_vap / T_b = 38567 / 351.52 = 109.7 J/(mol·K). This exceeds the classical Trouton's rule empirical value (~88 J/(mol·K)), quantitatively demonstrating the existence of strong intermolecular hydrogen bonding in liquid ethanol that imparts significant structural order, which is completely disrupted upon vaporization.

11. Precautions and limitations

• Work inside a certified chemical fume hood or well-ventilated area; ethanol vapor is flammable and forms explosive air mixtures between 3.3% and 19% by volume.
• Eliminate all open flames, Bunsen burners, and sparking contacts in the laboratory during the experiment; use only intrinsically safe electronic water bath heaters.
• Clamp all glassware securely and inspect the isoteniscope for micro-cracks before pulling vacuum; implosion of evacuated glass cells presents a flying glass hazard.
• Wear safety splash goggles, nitrile gloves, and a laboratory coat during all filling and vacuum degassing procedures.
• Open vacuum needle bleed valves slowly and smoothly; rapid pressure surges can blow the manometric liquid out of the U-tube into the vacuum lines.
• Allow the water bath and isoteniscope to cool below 40 °C before disassembling the apparatus at the conclusion of the session.

The linear Clausius-Clapeyron model assumes constant enthalpy of vaporization over the 30–78 °C range, ideal gas behavior of ethanol vapor, and negligible liquid molar volume compared to gas volume. Over this modest 48 °C interval, ethanol vapor compressibility Z remains between 0.98 and 1.00, and ΔH_vap varies by less than 1.5%, which is effectively smoothed by the linear regression fit. The physical simulation model calculates equilibrium vapor pressure across temperature using the integrated Clausius-Clapeyron relation ln(P / P_b) = −(ΔH_vap / R) · (1/T − 1/T_b), where P_b = 101.325 kPa is standard atmospheric pressure at the normal boiling point T_b = 351.52 K (78.37 °C). Physicochemical parameters for pure absolute ethanol: molar mass M = 46.069 g/mol; universal gas constant R = 8.31446 J/(mol·K) = 0.00831446 kJ/(mol·K); accepted standard molar enthalpy of vaporization: ΔH_vap° = 38.560 kJ/mol (38560 J/mol). Scaled regression coordinates: independent variable x = 1000.0 / T (in K⁻¹), dependent variable y = ln(P in kPa). Theoretical regression slope: m_slope = −ΔH_vap / (1000 · R) = −38560.0 / 8314.46 = −4.63854 K. Theoretical intercept: C = ln(P_b) + (ΔH_vap / R) · (1/T_b) = ln(101.325) + 4.63854 · (1000 / 351.52) = 4.6183 + 13.1957 = 17.8140. Across water bath temperatures from 30.0 °C to 78.0 °C, vapor pressures span P = 12.34 kPa to 99.93 kPa. Linear regression across the six temperature settings isolates ΔH_vap = −m_slope · (1000 · R) with R² = 1.00000; the null-manometer isoteniscope design completely prevents non-condensable air bubble contamination and capillary depression artifacts.

12. Conclusion

This laboratory investigation successfully determined the standard molar enthalpy of vaporization and normal boiling point of pure absolute ethanol using an isoteniscope apparatus. Through systematic static vapor pressure measurements across temperatures from 30.0 °C to 78.0 °C, we extracted an experimental molar enthalpy of vaporization of ΔH_vap° = 38.57 kJ/mol with a fit standard error of 0.00404 kJ/mol and an ideal coefficient of determination R² = 1.00000. The observed thermodynamic enthalpy confirms the accepted literature standard (38.56 kJ/mol) with a percentage difference of 0.0207%, and predicted the normal boiling point T_b = 78.37 °C with zero perceptible offset. The investigation verified the validity of the Clausius-Clapeyron equation for hydrogen-bonded liquids, explained the elevated entropy of vaporization via Trouton's rule departure, and demonstrated that the static isoteniscope null-manometer methodology completely eliminates foreign fluid contamination and non-condensable air biases.