Saturated Vapor Pressure lab report

1. Title and aim

Determination of the Saturated Vapor Pressure and Enthalpy of Vaporization of a Volatile Liquid. Measure the saturated vapor pressure of pure ethyl alcohol (ethanol) across temperatures from 20.0 °C to 80.0 °C using an immersed vapor pressure tube and precision mercury manometer, verify the Clausius-Clapeyron equation ln(P) = −(ΔH_vap / R)(1/T) + C, and determine the molar enthalpy of vaporization ΔH_vap.

2. Abstract

Five observations were generated from the ideal teaching model over the settings listed below. A straight-line fit gave an estimate of Molar enthalpy of vaporization ΔH_vap of 41.91 kJ mol⁻¹, differing by 0.016% 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

• Borosilicate Saturated Vapor Pressure J-Tube Assembly: A specialized glass U-tube containing an evacuated upper bulb partially filled with degassed liquid ethanol, with the liquid-vapor meniscus positioned inside the submerged bulb and communicating with a mercury column.
• Precision Liquid Mercury Manometer with Millimeter Mirror Scale: Measures the difference in mercury column heights between the vapor-filled closed limb and open atmospheric limb to register the differential gauge vapor pressure Δh to ±0.2 mmHg.
• Thermostatically Regulated Heating Water Bath with Immersion Element: Surrounds the vapor bulb in a deep water bath, heated by an adjustable electrical resistance coil to maintain steady operating temperatures between 20.0 °C and 80.0 °C.
• Motor-Driven Propeller Stirrer and Convection Shield: Provides continuous, vigorous fluid circulation throughout the heating bath, eliminating vertical thermal stratification and ensuring identical temperature across the entire vapor bulb.
• Precision Secondary Standard Immersion Thermometer (0 to 100 °C): Calibrated mercury-in-glass thermometer with 0.1 °C subdivisions, suspended directly alongside the vapor bulb to record the liquid equilibrium temperature to ±0.05 °C.
• Fortin Precision Mercurial Laboratory Barometer: Determines the ambient atmospheric pressure B in mmHg and kPa, required to convert open-limb manometer differential readings into total absolute vapor pressure P = B + Δh.
• Pure spectrophotometric grade ethyl alcohol (ethanol, C₂H₅OH, molecular weight M = 46.069 g mol⁻¹) degassed by vacuum distillation.
• Ambient atmospheric barometric pressure B = 760.0 mmHg = 101.325 kPa verified by precision Fortin laboratory barometer.
• Thermostatically regulated water bath with motorized propeller agitator maintaining thermal stability within ±0.05 °C.
• Precision mercury manometer tube with mirror-backed millimeter scale (mercury density ρ = 13,595 kg m⁻³ at 0 °C).
• Accepted literature reference molar enthalpy of vaporization for ethanol: ΔH_vap_ref = 41.92 kJ mol⁻¹ (41,920 J mol⁻¹) over 20 °C to 80 °C.

4. Theory and graph choice

When a pure volatile liquid is introduced into an evacuated closed space, molecules possessing sufficient thermal kinetic energy escape from the liquid phase into the adjacent headspace through the process of surface vaporization. Simultaneously, vapor-phase molecules collide with the liquid interface and condense. Once dynamic equilibrium is attained—the rate of vaporization equaling the rate of condensation—the pressure exerted by the vapor reaches a unique, stable value known as the saturated vapor pressure (P_sat). Saturated vapor pressure depends exclusively on the chemical nature of the substance and its thermodynamic temperature, remaining completely independent of the relative volumes occupied by the liquid and vapor phases provided both phases coexist. The fundamental thermodynamic relation governing this liquid-vapor coexistence boundary was formulated by the French engineer Émile Clapeyron in 1834 using Carnot’s thermodynamic cycle, and later given a rigorous microscopic and mathematical foundation by the German physicist Rudolf Clausius in 1850. The exact Clapeyron equation expresses the slope of the coexistence curve as dP/dT = L_v / [T (V_v − V_l)], where L_v is the latent heat of vaporization per mole and V_v and V_l are the molar volumes of the saturated vapor and liquid, respectively. Because the molar volume of a gas at moderate pressures is several orders of magnitude greater than that of the condensed liquid (V_v ≫ V_l), the liquid volume V_l may be neglected with minimal error (V_v − V_l ≈ V_v). Furthermore, approximating the vapor as an ideal gas obeying the equation of state V_v = RT/P yields the famous Clausius-Clapeyron differential equation: dP/dT = (ΔH_vap P) / (R T²), or equivalently, d(ln P) / d(1/T) = −ΔH_vap / R, where ΔH_vap is the molar enthalpy of vaporization and R = 8.31446 J mol⁻¹ K⁻¹ is the universal gas constant. Assuming the enthalpy of vaporization remains approximately constant over a moderate temperature interval, integrating this differential equation yields the linear working relationship ln(P) = −(ΔH_vap / R)(1/T) + C. In the classical precision physics laboratory, this relationship is investigated using a submerged vapor pressure tube containing pure ethyl alcohol (ethanol, C₂H₅OH) completely immersed in a stirred, thermostatically controlled liquid heating bath. The vapor pressure tube is coupled to a precision mercury manometer. By recording the equilibrium vapor pressure P across a sequence of temperatures from room temperature up to the normal boiling point (78.4 °C), and plotting ln(P) against the reciprocal absolute temperature 1/T, students obtain an exceptionally straight regression line whose negative slope m = −ΔH_vap / R directly yields the molar enthalpy of vaporization ΔH_vap = −m R, providing deep empirical insight into intermolecular cohesion and phase transition 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 K.

5. Method

1. Read the laboratory Fortin mercurial barometer to 0.1 mmHg, applying temperature and brass scale corrections to determine the ambient atmospheric pressure B (baseline B = 760.0 mmHg = 101.325 kPa). Inspect the vapor pressure tube to verify that the upper bulb contains pure liquid ethanol free of trapped atmospheric air bubbles and that the mercury surfaces are clean and reflective.
2. Fill the water bath with tap water adjusted to 20.0 °C. Position the vapor bulb completely submerged beneath the liquid surface and run the motorized stirrer for at least five minutes. Confirm that the bath thermometer reading remains steady at 20.0 °C and the mercury menisci in the manometer limbs have ceased drifting. Read the heights of the mercury columns in both limbs.
3. Energize the electric heating coil to warm the bath progressively in 15.0 °C intervals (35.0 °C, 50.0 °C, 65.0 °C, 80.0 °C). Keep the propeller stirrer operating continuously at moderate speed to circulate the water evenly around the glass vapor chamber and thermometer stem.
4. Upon reaching each target temperature, adjust the heater power to maintain a stable plateau and wait for a dwell interval of at least three to four minutes. Confirm that the temperature remains constant to within ±0.05 °C and the mercury column elevation stabilizes.
5. Read the mercury column levels in both the closed vapor limb (h_closed) and open atmospheric limb (h_open) using the mirror-backed millimeter scale. Align the optical line of sight so that the mercury meniscus directly occludes its reflected image in the mirror, eliminating parallax error. Compute the gauge pressure Δh = h_open − h_closed and determine the absolute pressure P = B + Δh in kilopascals (kPa).
6. Turn off the electric heater and record repeat readings at the same temperature stations as the bath cools naturally to verify the absence of thermal hysteresis or air ingress. Convert all temperatures to absolute kelvins (T = t + 273.15 K) and compute the reciprocal temperature 1/T. Calculate the natural logarithm of vapor pressure ln(P / Pa), plot ln(P) versus 1/T, and determine the slope m to evaluate the molar enthalpy of vaporization ΔH_vap = −m R.

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 = 0.0160%. Percentage difference is not experimental uncertainty.

For n = 5 observations, Σresidual² = 1.4137e-07; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 0.47367. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 0.00148.

Propagating only the relevant fit coefficient gives a fit-only standard error of 0.00394 kJ mol⁻¹. This is a one-standard-error quantity under the regression assumptions. Deterministic rounded model data do not supply a complete physical uncertainty budget.

Volatile liquid purity (dissolved atmospheric air or trace moisture altering vapor pressure by Raoult’s law), liquid-vapor thermal equilibrium dwell time during rapid heating (~2–4 min latency), mercury meniscus curvature and capillary depression in narrow vapor tubes, barometric pressure fluctuations affecting open-tube manometer readings (±0.2 mmHg), emergent thermometer stem temperature gradient, and non-ideal vapor departures at elevated temperatures (vapor compressibility factor Z < 1 near boiling point) contribute experimental uncertainty. The OLS regression standard error evaluates random scatter in the Clausius-Clapeyron linear transform, but excludes systematic liquid impurities or temperature-dependent enthalpy variations (ΔC_p = C_{p,v} − C_{p,l}).

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 volatile liquid sample has been thoroughly degassed prior to sealing the vapor tube to prevent trapped air from exerting an extraneous partial pressure.
• Run the motorized stirrer continuously to ensure the heating bath maintains a completely uniform temperature without vertical stratification around the submerged vapor bulb.
• Wait at least three to four minutes at each temperature station before recording data to verify that dynamic liquid-vapor phase equilibrium is fully re-established.
• Use an optical magnifier aligned horizontally with the mirror backing on the manometer scale to eliminate visual parallax when sighting the mercury menisci.

The teaching model assumes the enthalpy of vaporization ΔH_vap remains constant over the 20 °C to 80 °C temperature range and that the ethanol vapor behaves as an ideal gas. In rigorous thermodynamics, ΔH_vap decreases slightly with temperature due to non-zero heat capacity differences (ΔC_p = C_p,v − C_p,l), and ethanol vapor exhibits slight non-ideality near its normal boiling point. The Clausius-Clapeyron equation provides the thermodynamic cornerstone connecting macroscopic phase equilibria with microscopic intermolecular binding forces. The measured molar enthalpy of vaporization ΔH_vap = 41.92 kJ mol⁻¹ demonstrates the substantial energetic cost of disrupting intermolecular hydrogen bonds during the liquid-to-vapor phase transition.

12. Conclusion

The worked example illustrates how to obtain Molar enthalpy of vaporization ΔH_vap from measurements, graph variables and a fitted coefficient. The estimate is 41.91 kJ mol⁻¹. A real experiment must additionally evaluate the apparatus-specific uncertainties and corrections described above.