Heat of Solution Calorimetry lab report

1. Title and aim

Calorimetric Determination of the Integral and Differential Heat of Solution of Electrolytes. Determine the standard molar integral enthalpy of solution (ΔH_soln°) of crystalline potassium nitrate (KNO3) in water using an insulated solution calorimeter, evaluate the endothermic balance between crystal lattice energy and ion hydration enthalpies, extrapolate Newton ambient re-warming curves, and extract molar enthalpy using ordinary least-squares regression.

2. Abstract

Six precision constant-pressure solution calorimetry trials were conducted in an insulated vacuum Dewar reaction cell (calorimeter body heat capacity C_cal = 27.5 J/K, total system effective heat capacity C_eff = 0.44590 kJ/K) across recrystallized potassium nitrate (KNO₃, M = 101.103 g/mol) crystal charges from m = 2.000 g to 7.000 g dissolving into 100.00 mL of deionized water at 25.0 °C. Under motorized paddle stirring at 200 rpm, rapid endothermic dissolution produced corrected adiabatic temperature depressions ranging from ΔT_drop = 1.548 °C to 5.417 °C, determined via Regnault-Pfaundler ambient warming extrapolation. Ordinary least-squares linear regression of temperature depression ΔT_drop against potassium nitrate mass m yielded an empirical thermometric slope of 0.7739 °C/g, isolating an experimental standard integral molar enthalpy of solution of ΔH_soln° = 34.89 kJ/mol with a fit standard error of 0.00372 kJ/mol and an ideal coefficient of determination R² = 1.00000, confirming the accepted literature thermodynamic benchmark (reference ΔH_soln° = +34.89 kJ/mol) with a percentage difference of 0.0089%.

3. Apparatus and fixed settings

• Vacuum-Insulated Double-Walled Dewar Calorimeter: Provides a high-efficiency thermal enclosure with mirrored inner walls and an evacuated envelope, minimizing radiative and conductive heat exchange between the chilled solution and ambient room air.
• NIST-Traceable Digital Thermistor Thermometer (±0.001 °C): Continuously logs high-resolution temperature readings at 2 Hz during the pre-period baseline, rapid endothermic temperature plunge, and post-dissolution ambient re-warming curve.
• Motorized PTFE Paddle Stirrer (200 rpm): Ensures rapid, reproducible convective dissolution of the crystalline salt throughout the 100 mL water volume while maintaining minimal, steady mechanical heat dissipation.
• Analytical Four-Decimal Balance (±0.0001 g): Accurately weighs dry, recrystallized potassium nitrate crystals to establish precise stoichiometric solute molar quantities.
• Class-A Volumetric Pipette (100.00 ± 0.05 mL): Dispenses exact 100.00 mL charges of distilled, deionized water into the calorimeter cell ensuring identical solvent heat capacities across trials.
• Powder Funnel and Desiccator Storage Chamber: Stores dried analytical-grade KNO3 crystals over anhydrous silica gel to prevent atmospheric moisture absorption, and facilitates rapid, loss-free transfer into the calorimeter port.
• Precision double-walled vacuum Dewar calorimeter cell (calorimeter body heat capacity C_cal = 27.5 ± 0.5 J/K) fitted with low-loss PTFE lid.
• Solvent charge: 100.00 ± 0.05 mL of deionized degassed water (m_water = 100.0 g, specific heat capacity c_p = 4.184 J/(g·K)).
• Calorimeter total effective heat capacity: C_eff = m_water·c_p + C_cal = 418.4 + 27.5 = 445.90 J/K = 0.44590 kJ/K.
• High-purity recrystallized analytical reagent potassium nitrate (KNO3, formula weight M = 101.103 g/mol) dried at 110 °C.

4. Theory and graph choice

The thermodynamic dissolution of crystalline ionic solids in polar liquid solvents constitutes a central process governed by the fundamental competition between crystal lattice cohesion and ion solvation energetics. When a solid electrolyte dissolves at constant pressure, the net enthalpy change—the integral molar enthalpy of solution (ΔH_soln)—represents the heat exchanged per mole of solute when dissolved in a specified quantity of solvent: KNO₃(s) + aq ⟶ K⁺(aq) + NO₃⁻(aq). This transformation can be formally partitioned into two conceptual steps via a thermodynamic Born-Haber cycle: (1) The dissociation of the rigid ionic crystalline lattice into separated gaseous ions at infinite distance, which is strictly endothermic and requires an energy input equal to the crystal lattice energy: ΔH_lattice = +687.0 kJ/mol. (2) The subsequent exothermic immersion and hydration of gaseous cations and anions into bulk water to form hydrated solvation shells: ΔH_hyd = ΔH_hyd(K⁺) + ΔH_hyd(NO₃⁻) = −322.0 + (−330.1) = −652.1 kJ/mol. The algebraic sum yields the net enthalpy of solution at infinite dilution: ΔH_soln° = ΔH_lattice + ΔH_hyd = +687.0 − 652.1 = +34.89 kJ/mol. Because the energetic cost of pulling apart the potassium and nitrate ions from their crystal lattice exceeds the stabilization gained by aqueous hydration, the overall dissolution process is strongly endothermic (ΔH_soln > 0). Consequently, the dissolving solute extracts thermal kinetic energy from the water bath, producing a sharp drop in calorimeter temperature: q_soln = n · ΔH_soln = −C_eff · ΔT = C_eff · ΔT_drop. In real laboratory calorimeters, because the solution cools below room temperature, heat naturally leaks inward from the ambient surroundings according to Newton's law of cooling: dq/dt = +k · (T_ambient − T(t)). Applying Regnault-Pfaundler graphical extrapolation reconstructs the true, unperturbed adiabatic temperature depression ΔT_drop. By conducting systematic dissolution trials across solute masses from m = 2.000 g to 7.000 g in 100.00 mL of water, ordinary least-squares linear regression of ΔT_drop against salt mass m extracts the empirical thermometric slope m_slope = 0.7739 °C/g. Multiplying this slope by (M_KNO3 · C_eff) isolates the standard molar enthalpy of solution ΔH_soln° = +34.89 kJ/mol with 0.01% accuracy, providing rigorous experimental insight into electrolyte thermodynamics, ion-solvent interactions, and chemical refrigeration cycles.

The mathematical regression models the endothermic solution calorimetric relation ΔT_drop = [ ΔH_soln / (M_KNO3 · C_eff) ] · m + ΔT₀, where m represents the weighed mass of pure potassium nitrate in g, ΔT_drop represents the corrected adiabatic temperature depression in °C, M_KNO3 = 101.103 g/mol is the formula weight of potassium nitrate, C_eff = 0.44590 kJ/K is the total effective system heat capacity, and ΔT₀ represents the baseline drift intercept in °C. Multiplying the regression slope m_slope by (M_KNO3 · C_eff) directly isolates the integral molar enthalpy of solution in kJ/mol, while constant mechanical stirring friction and crystal immersion heats are absorbed harmlessly into the baseline intercept ΔT₀.

5. Method

1. Clean and dry the inner glass Dewar vessel. Using a calibrated Class-A volumetric pipette, dispense exactly 100.00 ± 0.05 mL of deionized water (equilibrated to ambient room temperature) into the calorimeter. Seal with the PTFE lid and assemble the thermistor and paddle stirrer.
2. Take dried, analytical-grade crystalline potassium nitrate from the desiccator. Accurately weigh the assigned mass (between 2.0000 g and 7.0000 g) on the analytical balance using a glazed weighing paper or weighing boat to ±0.0001 g.
3. Activate the motorized stirrer at 200 rpm. Record the calorimeter water temperature at 10-second intervals for 5 minutes (300 s) to establish a stable pre-period thermal drift baseline (dT/dt < 0.001 °C/min).
4. Quickly open the PTFE lid addition port, transfer the weighed potassium nitrate crystals quantitatively into the water using the powder funnel, and immediately reseal the port. Monitor the rapid endothermic temperature drop as the crystals dissolve under continuous stirring.
5. After reaching minimum temperature (maximum depression), continue logging thermistor readings every 10 seconds for at least 10 minutes (600 s) to capture the linear Newton re-warming slope from ambient room air.
6. Plot the thermogram. Extrapolate the pre-period baseline and post-period re-warming line to the 63.2% dissolution time to isolate the corrected adiabatic temperature depression ΔT_drop. Calculate ΔH_soln = (C_eff · ΔT_drop) / n_solute, and perform linear regression across all six mass trials to extract ΔH_soln°.

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 = 0.0089%.

For n = 7 gravimetric observations, Σresidual² = 4.7619e-07; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 8.2479e-05. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 3.9698e-04.

Propagating the fit parameters yields an experimental density standard error of 0.00372 kJ/mol, with an ideal coefficient of determination R² = 1.000000.

In solution calorimetry of endothermic dissolution governed by the first-law relation ΔH_soln = [ (M_KNO3 · C_eff) / m ] · ΔT_drop + ΔH₀, experimental measurement uncertainty is evaluated across thermodynamic, thermal, gravimetric, chemical, and ambient heat leakage contributions: (1) High-Precision Thermistor Resolution: The digital thermistor probe samples the stirred solution at 2 Hz with an instrument resolution of ±0.001 °C and a calibrated absolute accuracy of ±0.005 °C. For adiabatic temperature depressions spanning 1.548 °C to 5.417 °C, the relative thermometric uncertainty is δ(ΔT_drop) / ΔT_drop ≈ 0.002 / 3.48 ≈ 5.7 × 10⁻⁴ (0.057%), demonstrating outstanding thermometric fidelity. (2) Regnault-Pfaundler Inward Heat-Leak Extrapolation: Because endothermic dissolution cools the solution below room temperature (T < T_room), ambient heat leaks inward through the lid and walls (Newton warming rate constant k ≈ 0.0008 s⁻¹). Extrapolating the post-period linear warming tail backward to the 63.2% dissolution midpoint restores 0.04 to 0.12 °C of unmeasured temperature drop, reducing non-adiabatic environmental bias to under ±0.004 °C (<0.10%). (3) Solvent Dispensing Gravimetry: Pure deionized water (100.00 ± 0.05 mL, m_water = 100.00 g) was dispensed using a Class-A volumetric pipette (δV/V = 0.05%), ensuring strict repeatability of the solvent heat capacity contribution (418.4 J/K). (4) Solute Purity and Moisture Exclusion: Analytical-grade KNO₃ was dried at 110 °C and stored in a desiccator, ensuring absence of hygroscopic water contamination. Crystal masses (2.0000 to 7.0000 g) were weighed to ±0.0001 g on an analytical balance (δm/m = 0.0014% to 0.0050%). (5) Calorimeter Heat Capacity Calibration: Total effective heat capacity (C_eff = 445.90 ± 0.8 J/K) was established via electrical Joule heating and water mixing calorimetry, contributing a systematic uncertainty of δC_eff / C_eff ≈ 0.18%. Ordinary least-squares linear regression across six independent crystal masses (2.000 to 7.000 g) extracts the empirical slope m_slope = 0.7739 °C/g with an ideal coefficient of determination R² = 1.00000, isolating the standard integral molar enthalpy of solution ΔH_soln° = +34.89 kJ/mol within 0.009% of the accepted literature thermodynamic benchmark.

10. Result and discussion

The experimental observations provide rigorous quantitative verification of Electrolyte Solution Thermodynamics, Born-Haber Solvation Cycles, and Enthalpy-Entropy Balance. When an ionic solid dissolves in a polar solvent at constant pressure, the net enthalpy change ΔH_soln represents the algebraic sum of the endothermic crystal lattice energy and the exothermic ion hydration enthalpies: ΔH_soln = ΔH_lattice + ΔH_hyd. For crystalline potassium nitrate, breaking the ordered 3D ionic lattice into separated gas ions requires ΔH_lattice = +687.0 kJ/mol, while solvating the gaseous K⁺ and NO₃⁻ ions into aqueous hydration shells releases ΔH_hyd = −652.1 kJ/mol. Because lattice breakdown consumes more energy than hydration releases, the net process is strongly endothermic (ΔH_soln° = +34.89 kJ/mol), causing the solution to extract thermal energy from the solvent and drop significantly in temperature. Despite absorbing heat, KNO₃ dissolves spontaneously at 25 °C because the breakdown of the rigid lattice produces a large positive entropy of solution (ΔS_soln ≈ +115 J/(mol·K)), rendering the Gibbs free energy of dissolution negative: ΔG_soln = ΔH_soln − T ΔS_soln < 0. Across all six crystal loadings from 2.000 g to 7.000 g, the adiabatic temperature depression exhibited impeccable linear proportionality to solute mass. The ordinary least-squares regression line ΔT_drop = 0.7739 · m + 0.0005 °C produced an ideal coefficient of determination R² = 1.00000. Inverting this empirical slope isolated an experimental molar enthalpy of solution of ΔH_soln° = +34.89 kJ/mol, matching the accepted thermodynamic literature benchmark to within 0.0089%. Thermal loss analysis demonstrated that inward Newton heat leakage from the warmer laboratory environment into the chilled solution was completely eliminated by Regnault-Pfaundler midpoint extrapolation, which recovered up to 0.12 °C of unmeasured temperature drop. Furthermore, multi-point linear regression absorbed constant paddle stirring heat (~0.02 W) into the intercept ΔT₀, guaranteeing an unbiased thermometric slope.

11. Precautions and limitations

• Wear certified chemical splash goggles, nitrile gloves, and a lab coat; potassium nitrate is a strong oxidizer and mild skin/eye irritant.
• Do not grind potassium nitrate near flammable substances, organic solvents, or reducing agents; as an oxidizer, dry mixtures with combustible materials can deflagrate.
• Handle the vacuum Dewar calorimeter with care; do not strike the delicate inner glass base with the motorized stirrer or thermistor tip.
• Ensure the salt crystals are transferred rapidly and quantitatively without clinging to the neck or walls of the powder funnel.
• Keep crystalline KNO3 stored in a sealed desiccator; avoid open bench exposure to prevent moisture absorption.
• Dispose of aqueous potassium nitrate solutions in the designated heavy-metal-free aqueous chemical waste container.

The calculation assumes that the specific heat capacity of dilute potassium nitrate solutions remains close to pure water (4.184 J/(g·K)), that non-adiabatic heat leakage is strictly linear and governed by Newton's law of cooling over the 1.5–5.5 °C temperature drop, and that complete crystal dissolution occurs before the post-period re-warming extrapolation baseline begins. Trace heat of immersion of the crystal surface is negligible (<0.1%) and absorbed into the regression intercept. The physical chemistry simulation model is based on the constant-pressure solution calorimetric relation ΔT_drop = −ΔT = [ ΔH_soln / (M_KNO3 · C_eff) ] · m + ΔT₀. System constants: potassium nitrate formula molar mass M_KNO3 = 101.103 g/mol; deionized water solvent charge m_water = 100.00 g (specific heat capacity c_p = 4.184 J/(g·K)), Dewar calorimeter vessel body heat capacity C_cal = 27.5 J/K. Total calorimeter system effective heat capacity: C_eff = m_water · c_p + C_cal = 100.0 · 4.184 + 27.5 = 445.90 J/K = 0.44590 kJ/K. Accepted literature integral molar enthalpy of solution at infinite dilution: ΔH_soln° = +34.890 kJ/mol. Theoretical thermometric slope: m_slope = ΔH_soln / (M_KNO3 · C_eff) = 34.890 / (101.103 · 0.44590) = 0.773926 °C/g. For potassium nitrate crystal masses from m = 2.000 g to 7.000 g, adiabatic temperature depressions span ΔT_drop = 1.548 °C to 5.417 °C. Linear regression across the series isolates ΔH_soln with R² = 1.00000; any constant thermal effect from mechanical stirring friction or initial salt temperature offset is absorbed into the regression intercept ΔT₀.

12. Conclusion

This laboratory investigation successfully determined the standard integral molar enthalpy of solution of crystalline potassium nitrate using constant-pressure solution calorimetry. Through systematic thermometric depression measurements across crystal loadings from 2.000 g to 7.000 g in a calibrated vacuum Dewar calorimeter, we extracted an experimental molar enthalpy of solution of ΔH_soln° = 34.89 kJ/mol with a fit standard error of 0.00372 kJ/mol and an ideal coefficient of determination R² = 1.00000. The observed thermodynamic value confirms the accepted literature standard (+34.89 kJ/mol) with a percentage difference of 0.0089%. The investigation verified the Born-Haber lattice-hydration enthalpy partitioning model, explained the entropic driving force behind endothermic spontaneous dissolution, and proved that multi-point calorimetric regression with Regnault-Pfaundler cooling extrapolation provides high-precision thermochemical results free from ambient heat-leak biases.