Understanding the Calculation of the Heat of Dissolution (ΔH of dissolution)

The heat of dissolution quantifies energy change when a solute dissolves in a solvent. It is essential for thermodynamic analysis.

This article explores detailed formulas, common values, and real-world applications of ΔH of dissolution for expert understanding.

• Calculate the heat of dissolution for NaCl dissolving in water at 25°C.
• Determine ΔH of dissolution for KNO3 given lattice and hydration enthalpies.
• Find the heat absorbed when 50 g of NH4Cl dissolves in 100 mL of water.
• Estimate ΔH of dissolution for CaCl2 using calorimetric data.

Comprehensive Table of Common Heat of Dissolution Values

Fundamental Formulas for Calculating the Heat of Dissolution (ΔH of dissolution)

The heat of dissolution (ΔH_dissolution) represents the enthalpy change when one mole of solute dissolves in a solvent. It can be calculated using several thermodynamic relationships depending on available data.

1. Basic Definition

ΔH_dissolution = H_solution – (H_solute + H_solvent)

• H_solution: Enthalpy of the final solution
• H_solute: Enthalpy of the pure solute
• H_solvent: Enthalpy of the pure solvent

This direct approach is often impractical; thus, indirect methods using lattice and hydration enthalpies are preferred.

2. Using Lattice and Hydration Enthalpies

The heat of dissolution can be approximated by the difference between lattice enthalpy and hydration enthalpy:

ΔH_dissolution = ΔH_lattice + ΔH_hydration

• ΔH_lattice: Energy required to break the ionic lattice into gaseous ions (endothermic, positive)
• ΔH_hydration: Energy released when gaseous ions are solvated by solvent molecules (exothermic, negative)

Both values are typically expressed in kJ/mol.

3. Calorimetric Measurement Approach

When experimental calorimetric data is available, ΔH of dissolution can be calculated by:

ΔH_dissolution = – (m × C × ΔT) / n

• m: Mass of solvent (g)
• C: Specific heat capacity of solvent (J/g·°C)
• ΔT: Temperature change of solvent (°C)
• n: Number of moles of solute dissolved (mol)

The negative sign accounts for the exothermic or endothermic nature of the process relative to the temperature change.

4. Van’t Hoff Equation for Temperature Dependence

To understand how ΔH of dissolution varies with temperature, the Van’t Hoff equation is used:

ln K = – (ΔH / R) × (1/T) + (ΔS / R)

• K: Equilibrium constant of dissolution
• ΔH: Enthalpy change (J/mol)
• R: Universal gas constant (8.314 J/mol·K)
• T: Temperature (K)
• ΔS: Entropy change (J/mol·K)

Plotting ln K vs. 1/T allows determination of ΔH from the slope.

5. Hess’s Law Application

Using Hess’s Law, the heat of dissolution can be derived from known enthalpies of related reactions:

ΔH_dissolution = ΔH_hydration – ΔH_lattice

Note that this is consistent with the lattice and hydration enthalpy approach but emphasizes the use of Hess’s Law to combine enthalpy changes.

Detailed Explanation of Variables and Typical Values

• ΔH_lattice: Typically positive, ranging from +500 to +3000 kJ/mol depending on ionic bond strength. For example, NaCl has ~+787 kJ/mol.
• ΔH_hydration: Negative values, often between -400 to -4000 kJ/mol, depending on ion charge density and solvent polarity. Na+ hydration enthalpy is about -406 kJ/mol.
• m: Mass of solvent, usually in grams; water is common with density ~1 g/mL.
• C: Specific heat capacity of solvent; for water, 4.18 J/g·°C.
• ΔT: Measured temperature change during dissolution, can be positive or negative.
• n: Number of moles of solute, calculated from mass and molar mass.
• R: Universal gas constant, 8.314 J/mol·K.
• T: Absolute temperature in Kelvin (K = °C + 273.15).
• K: Equilibrium constant, dimensionless, related to solubility.
• ΔS: Entropy change, typically positive for dissolution due to increased disorder.

Real-World Application Examples of Heat of Dissolution Calculations

Example 1: Calculating ΔH of Dissolution for Sodium Chloride (NaCl) in Water

Given:

• Lattice enthalpy of NaCl = +787 kJ/mol
• Hydration enthalpy of Na+ = -406 kJ/mol
• Hydration enthalpy of Cl- = -363 kJ/mol

Step 1: Calculate total hydration enthalpy:

ΔH_hydration = ΔH_{hydration, Na+} + ΔH_{hydration, Cl-} = -406 + (-363) = -769 kJ/mol

Step 2: Calculate ΔH of dissolution:

ΔH_dissolution = ΔH_lattice + ΔH_hydration = 787 + (-769) = +18 kJ/mol

This positive value indicates an endothermic dissolution process, consistent with experimental data (~+3.9 kJ/mol, slight discrepancy due to approximations).

Example 2: Calorimetric Determination of ΔH of Dissolution for Ammonium Chloride (NH4Cl)

Experimental data:

• Mass of NH4Cl dissolved: 5.0 g
• Mass of water: 100 g
• Specific heat capacity of water: 4.18 J/g·°C
• Temperature drop observed: 3.5 °C
• Molar mass of NH4Cl: 53.49 g/mol

Step 1: Calculate moles of NH4Cl dissolved:

n = 5.0 g / 53.49 g/mol = 0.0935 mol

Step 2: Calculate heat absorbed by water (q):

q = m × C × ΔT = 100 g × 4.18 J/g·°C × 3.5 °C = 1463 J = 1.463 kJ

Step 3: Calculate ΔH of dissolution per mole:

ΔH_dissolution = – q / n = -1.463 kJ / 0.0935 mol = -15.65 kJ/mol

The negative sign indicates an endothermic process (temperature drop). Literature values for NH4Cl dissolution are approximately +14.8 kJ/mol, showing good agreement.

Additional Considerations and Advanced Insights

Several factors influence the heat of dissolution beyond lattice and hydration enthalpies:

• Ion size and charge density: Smaller, highly charged ions have larger hydration enthalpies, affecting ΔH.
• Solvent properties: Polarity, dielectric constant, and temperature impact solvation energy.
• Concentration effects: At higher concentrations, ion pairing and activity coefficients alter enthalpy values.
• Temperature dependence: ΔH varies with temperature, requiring Van’t Hoff analysis for precise modeling.

Advanced computational methods, such as molecular dynamics simulations and quantum chemical calculations, provide deeper insight into dissolution thermodynamics, complementing experimental data.

Summary of Key Points for Expert Application

• ΔH of dissolution is critical for understanding solubility, reaction energetics, and process design.
• It can be calculated via lattice and hydration enthalpies, calorimetry, or equilibrium constant analysis.
• Accurate data for lattice and hydration enthalpies are essential; consult authoritative databases like NIST and PubChem.
• Calorimetric methods require precise temperature and mass measurements, with corrections for heat losses.
• Van’t Hoff plots enable temperature-dependent enthalpy determination, important for industrial and environmental applications.

For further reading and authoritative data, visit:

• NIST Chemistry WebBook
• PubChem Database
• ChemEurope: Heat of Solution