Understanding the Calculation of Enthalpy of Solution or Dissolution

Enthalpy of solution quantifies heat change when a solute dissolves in a solvent. It is crucial for thermodynamic analysis.

This article explores detailed formulas, common values, and real-world applications for precise enthalpy calculations.

• Calculate the enthalpy of solution for 1 mole of NaCl dissolving in water at 25°C.
• Determine the enthalpy change when 0.5 moles of KNO3 dissolve in 100 g of water.
• Find the enthalpy of dissolution for CaCl2 given lattice energy and hydration enthalpy values.
• Estimate the heat absorbed or released when 2 moles of NH4Cl dissolve in 200 mL of water.

Comprehensive Tables of Common Enthalpy of Solution Values

Below are extensive tables listing enthalpy of solution values for frequently studied ionic compounds and molecular solutes in water at standard conditions (25°C, 1 atm). These values are essential for reference in calculations and experimental design.

Fundamental Formulas for Calculating Enthalpy of Solution or Dissolution

The enthalpy of solution (ΔH_sol) represents the net heat change when a solute dissolves in a solvent. It can be calculated using thermodynamic principles involving lattice enthalpy and hydration enthalpy or directly from calorimetric data.

1. Basic Enthalpy of Solution Equation

The general expression for enthalpy of solution is:

• ΔH_sol: Enthalpy of solution (kJ/mol)
• ΔH_lattice: Lattice enthalpy (kJ/mol), energy required to break ionic lattice into gaseous ions
• ΔH_hydration: Hydration enthalpy (kJ/mol), energy released when gaseous ions are solvated by water molecules

Both ΔH_lattice and ΔH_hydration are typically expressed per mole of solute dissolved.

2. Calculation from Calorimetric Data

When experimental data is available, enthalpy of solution can be calculated from the heat absorbed or released during dissolution:

• q: Heat absorbed or released by the solution (J or kJ)
• n: Number of moles of solute dissolved (mol)

The negative sign accounts for the convention that heat released by the system is negative, so ΔH_sol is positive for endothermic dissolution and negative for exothermic.

3. Heat Calculation from Temperature Change

If the temperature change (ΔT) of the solvent is measured, the heat q can be calculated as:

• m: Mass of solvent (g)
• C_p: Specific heat capacity of solvent (J/g·°C)
• ΔT: Temperature change of solvent (°C)

This formula assumes negligible heat loss to surroundings and no phase change in solvent.

4. Relationship with Gibbs Free Energy and Entropy

For a complete thermodynamic description, enthalpy of solution relates to Gibbs free energy (ΔG) and entropy (ΔS) changes:

• ΔG: Gibbs free energy change (kJ/mol)
• ΔH: Enthalpy change (kJ/mol)
• T: Absolute temperature (K)
• ΔS: Entropy change (kJ/mol·K)

While ΔH_sol quantifies heat exchange, ΔG determines spontaneity of dissolution.

5. Lattice Enthalpy Estimation via Born-Haber Cycle

Lattice enthalpy can be indirectly calculated using the Born-Haber cycle, which combines several thermodynamic steps:

• Sublimation of solid metal
• Ionization of metal atoms
• Bond dissociation of non-metal molecules
• Electron affinity of non-metal atoms
• Formation of ionic lattice

The lattice enthalpy is the energy released when gaseous ions form the ionic solid, and is a key component in calculating ΔH_sol.

Detailed Explanation of Variables and Typical Values

• ΔH_lattice: Usually positive, representing energy input to break ionic bonds. Typical values range from +600 to +3000 kJ/mol depending on ionic charges and sizes.
• ΔH_hydration: Negative, as energy is released when ions interact with solvent molecules. Values depend on ion charge density; e.g., Mg²⁺ hydration enthalpy ~ -1900 kJ/mol.
• ΔH_sol: Net result; can be positive (endothermic) or negative (exothermic) depending on balance of lattice and hydration enthalpies.
• q: Heat measured in calorimetry, typically in joules or kilojoules.
• n: Moles of solute, calculated from mass and molar mass.
• m: Mass of solvent, usually water, in grams.
• C_p: Specific heat capacity of solvent; for water, approximately 4.18 J/g·°C.
• ΔT: Temperature change observed during dissolution.

Real-World Applications and Case Studies

Case Study 1: Enthalpy of Solution of Sodium Chloride in Water

Sodium chloride (NaCl) is a common ionic compound with an enthalpy of solution of approximately +3.9 kJ/mol, indicating a slightly endothermic dissolution process. This case study demonstrates calculation using calorimetric data.

Given:

• Mass of NaCl dissolved: 5.85 g
• Mass of water: 100 g
• Temperature change observed: -1.2 °C (temperature decreases)
• Specific heat capacity of water: 4.18 J/g·°C
• Molar mass of NaCl: 58.44 g/mol

Step 1: Calculate moles of NaCl dissolved

Step 2: Calculate heat absorbed or released by water

Negative q indicates heat is absorbed from the surroundings (endothermic process).

Step 3: Calculate enthalpy of solution per mole

This experimental value is close to the literature value of +3.9 kJ/mol, validating the method.

Case Study 2: Enthalpy of Solution of Calcium Chloride in Water

Calcium chloride (CaCl₂) dissolves exothermically with a ΔH_sol of approximately -81.3 kJ/mol. This case illustrates calculation from lattice and hydration enthalpies.

Given:

• Lattice enthalpy of CaCl₂: +2258 kJ/mol
• Hydration enthalpy of Ca²⁺: -1650 kJ/mol
• Hydration enthalpy of Cl^–: -364 kJ/mol (per ion)

Step 1: Calculate total hydration enthalpy

Step 2: Calculate enthalpy of solution

The calculated value (-120 kJ/mol) is more exothermic than the literature value (-81.3 kJ/mol), which can be attributed to approximations in hydration enthalpy values and experimental conditions.

Additional Considerations and Advanced Topics

Several factors influence the enthalpy of solution beyond basic thermodynamics:

• Temperature Dependence: Enthalpy values vary with temperature; Van’t Hoff equation can be used to estimate changes.
• Solvent Effects: Different solvents have distinct hydration enthalpies and heat capacities, affecting ΔH_sol.
• Ion Pairing and Complex Formation: In concentrated solutions, ion interactions alter enthalpy values.
• Pressure Effects: Usually minor but can be significant in high-pressure systems.

Advanced computational methods, such as molecular dynamics and quantum chemistry, are increasingly used to predict enthalpy of solution with high accuracy.

Summary of Key Points for Practical Calculations

• Use accurate molar masses and precise temperature measurements for calorimetric calculations.
• Consult reliable thermodynamic databases for lattice and hydration enthalpy values.
• Account for heat losses and calibration errors in experimental setups.
• Apply the Born-Haber cycle for ionic compounds when direct measurements are unavailable.
• Consider solvent properties and solution concentration effects for real-world applications.

Recommended External Resources for Further Study

• NIST Chemistry WebBook – Comprehensive thermodynamic data.
• American Chemical Society – Thermodynamics of Solutions
• LibreTexts – Enthalpy of Solution
• ScienceDirect – Enthalpy of Solution Overview