Q. how to calculate enthalpy of solution

Q: What is the enthalpy of solution?

The enthalpy of solution, written \\Delta H_{soln} , is the heat change when specified amount of solute dissolves in solvent at constant pressure. It is often reported per mole of solute, e.g. \\Delta H_{soln} in kJ·mol^{-1}.

Q: How do you calculate \\Delta H_{soln} from calorimetry experiment?

Measure temperature change \\Delta T . Calculate heat absorbed by solution: = m C_p \\Delta T . Then \\Delta H_{soln\;per\;mol} = -\dfrac{+ q_{cal}}{n_{solute}} . Sign convention: negative if heat released.

Q: How do you include the calorimeter heat capacity?

Account for calorimeter with q_{cal} = C_{cal} \\Delta T . Total heat is q_{total} = m C_p \\Delta T + C_{cal} \\Delta T . Then divide by moles: \\Delta H_{soln} = -\dfrac{q_{total}}{n} .

Q: How to get \\Delta H_{soln} using Hess's law?

Use known step enthalpies and add. For ionic solids: \\Delta H_{soln} = -\\Delta H_{lattice} + \sum \\Delta H_{hydration} . More generally: \\Delta H_{soln} = \sum \\Delta H_f(\text{products}) - \sum \\Delta H_f(\text{reactants}) .

Q: How do you convert heat measured in J to kJ·mol^{-1}?

Convert joules to kilojoules by dividing by 1000. Then divide by moles of solute: \text{kJ·mol}^{-1} = \dfrac{q\;(\text{kJ})}{n\;(\text{mol})} .

Q: What if the solution volume or density changes significantly?

Use actual solution mass and heat capacity. If density or specific heat differ from solvent, measure or look up C_p and mass. Use = m_{solution} C_{p,solution} \\Delta T for accurate heat.

Q: How to handle dilution enthalpies or nonideal behavior?

For concentration-dependent enthalpies, report \\Delta H at specified molarity. Use calorimetry at those concentrations or integrate differential heats: \\Delta H = \int_{c_1}^{c_2} \bar{H}_{mix}(c)\,dc when datexist.

Q: How accurate are tabulated \\Delta H_{soln} values?

Tabulated values assume standard conditions and concentrations. Deviations arise from temperature, ionic strength, and nonideality. Expect experimental uncertainty and consult primary sources for conditions.

Answer

Quick explanation and formulas for enthalpy of solution. Definition: enthalpy change when 1 mol of solute dissolves. In general
\[ \Delta H_{\mathrm{soln}} = H_{\mathrm{solution}} – \bigl(H_{\mathrm{solute}} + H_{\mathrm{solvent}}\bigr). \]
For ionic solids, using lattice and hydration enthalpies:
\[ \Delta H_{\mathrm{soln}} = U_{\mathrm{lattice}} + \Delta H_{\mathrm{hydration}}, \]
where \(U_{\mathrm{lattice}}\) is the energy required to separate the solid into gaseous ions (positive) and \(\Delta H_{\mathrm{hydration}}\) is the (negative) enthalpy released when ions are solvated. Experimentally by calorimetry: measure the temperature change \(\Delta T\) of the solution. The heat gained by the solution is \(q_{\mathrm{soln}} = m_{\mathrm{soln}} c_{\mathrm{soln}} \Delta T\). The molar enthalpy of solution is
\[ \Delta H_{\mathrm{soln}} = -\frac{q_{\mathrm{soln}}}{n_{\mathrm{solute}}} = -\frac{m_{\mathrm{soln}} c_{\mathrm{soln}} \Delta T}{n_{\mathrm{solute}}}. \]
Sign convention: if the solution warms \(\Delta T > 0\), then \(\Delta H_{\mathrm{soln}} < 0\) (exothermic).

Detailed Explanation

Definition. The enthalpy of solution is the enthalpy change when one mole of solute dissolves in a large amount of solvent at constant pressure. It is usually reported as the molar enthalpy change \( \Delta H_{\text{soln}} \) with units J mol^{-1} or kJ mol^{-1}.

General calorimetric method. To determine \( \Delta H_{\text{soln}} \) experimentally by solution calorimetry, follow these steps.

Step 1. Measure masses and initial temperatures. Record the mass of solvent (usually water), the mass of solute, and the initial temperature of the solvent before dissolving.

Step 2. Dissolve the solute and record the final temperature. Stir until the solute is fully dissolved and record the equilibrium temperature of the solution.

Step 3. Compute the temperature change. Compute the temperature change of the solution as \( \Delta T = T_{\text{final}} – T_{\text{initial}} \). Note that \( \Delta T \) can be negative or positive.

Step 4. Compute the heat absorbed or released by the solution. Use the heat capacity approximation for the solution (often approximated by that of water, \( c \approx 4.18\ \mathrm{J\,g^{-1}\,K^{-1}} \), unless a more accurate value is available). The heat absorbed by the bulk solution is

\[ q_{\text{soln}} = m_{\text{soln}}\, c_{\text{soln}}\, \Delta T, \]

where \( m_{\text{soln}} \) is the total mass of the solution (solvent plus solute), \( c_{\text{soln}} \) is the specific heat capacity of the solution, and \( \Delta T \) is the temperature change.

Step 5. Convert the heat to the enthalpy change of the dissolving system. By energy conservation, the heat gained by the solution equals minus the heat change of the dissolving system. Therefore the molar enthalpy of solution is

\[ \Delta H_{\text{soln}} = -\frac{q_{\text{soln}}}{n_{\text{solute}}}, \]

where \( n_{\text{solute}} \) is the number of moles of solute that dissolved. The sign convention is such that a positive \( \Delta H_{\text{soln}} \) means the dissolution is endothermic, and a negative \( \Delta H_{\text{soln}} \) means it is exothermic.

Practical notes. Include calorimeter heat capacity if known: then use \( q_{\text{total}} = m_{\text{soln}} c_{\text{soln}} \Delta T + C_{\text{cal}} \Delta T \) and replace \( q_{\text{soln}} \) above by \( q_{\text{total}} \). Correct for heat losses if necessary, and use the precise specific heat for the solution when available.

Relation for ionic solids. For an ionic solid, you can relate lattice and hydration contributions. If \( \Delta H_{\text{latt}}^{\text{sep}} \) is the positive enthalpy required to separate the ions into the gas phase (i.e., the energy to break the lattice), and \( \Delta H_{\text{hyd}} \) is the enthalpy released when the gaseous ions are hydrated, then

\[ \Delta H_{\text{soln}} = \Delta H_{\text{latt}}^{\text{sep}} + \Delta H_{\text{hyd}}. \]

Equivalently, if \( \Delta H_{\text{latt}}^{\text{form}} \) denotes the lattice enthalpy defined as the enthalpy of formation of the solid from gaseous ions (typically negative), then

\[ \Delta H_{\text{soln}} = \Delta H_{\text{hyd}} – \Delta H_{\text{latt}}^{\text{form}}. \]

Worked numerical example. Suppose 2.00 g of a solute (molar mass 80.04 g mol^{-1}) is dissolved in 100.0 g of water. The measured temperature falls from 25.00°C to 22.00°C. Approximate the solution specific heat as 4.18 J g^{-1} K^{-1} and neglect the calorimeter heat capacity. Compute \( \Delta H_{\text{soln}} \) in kJ mol^{-1}.

Step A. Compute moles of solute.

\[ n_{\text{solute}} = \frac{2.00\ \mathrm{g}}{80.04\ \mathrm{g\ mol^{-1}}} = 0.02499\ \mathrm{mol}. \]

Step B. Compute total solution mass and temperature change.

\[ m_{\text{soln}} = 100.0\ \mathrm{g} + 2.00\ \mathrm{g} = 102.0\ \mathrm{g}. \]

\[ \Delta T = 22.00\ ^{\circ}\mathrm{C} – 25.00\ ^{\circ}\mathrm{C} = -3.00\ \mathrm{K}. \]

Step C. Compute heat absorbed by the solution.

\[ q_{\text{soln}} = m_{\text{soln}}\, c\, \Delta T = 102.0 \times 4.18 \times (-3.00) = -1279\ \mathrm{J}. \]

Step D. Compute molar enthalpy of solution.

\[ \Delta H_{\text{soln}} = -\frac{q_{\text{soln}}}{n_{\text{solute}}} = -\frac{-1279\ \mathrm{J}}{0.02499\ \mathrm{mol}} = 5.12\times 10^{4}\ \mathrm{J\ mol^{-1}} = 51.2\ \mathrm{kJ\ mol^{-1}}. \]

Interpretation. The positive value \( \Delta H_{\text{soln}} = +51.2\ \mathrm{kJ\ mol^{-1}} \) indicates the dissolution is endothermic under these conditions.

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Chemistry FAQs

What is the enthalpy of solution?

The enthalpy of solution, written \( \\Delta H_{soln} \), is the heat change when specified amount of solute dissolves in solvent at constant pressure. It is often reported per mole of solute, e.g. \( \\Delta H_{soln} \) in kJ·mol^{-1}.

How do you calculate \( \\Delta H_{soln} \) from calorimetry experiment?

Measure temperature change \( \\Delta T \). Calculate heat absorbed by solution: \( = m C_p \\Delta T \). Then \( \\Delta H_{soln\;per\;mol} = -\dfrac{+ q_{cal}}{n_{solute}} \). Sign convention: negative if heat released.

How do you include the calorimeter heat capacity?

Account for calorimeter with \( q_{cal} = C_{cal} \\Delta T \). Total heat is \( q_{total} = m C_p \\Delta T + C_{cal} \\Delta T \). Then divide by moles: \( \\Delta H_{soln} = -\dfrac{q_{total}}{n} \).

How to get \( \\Delta H_{soln} \) using Hess's law?

Use known step enthalpies and add. For ionic solids: \( \\Delta H_{soln} = -\\Delta H_{lattice} + \sum \\Delta H_{hydration} \). More generally: \( \\Delta H_{soln} = \sum \\Delta H_f(\text{products}) - \sum \\Delta H_f(\text{reactants}) \).

How do you convert heat measured in J to kJ·mol^{-1}?

Convert joules to kilojoules by dividing by 1000. Then divide by moles of solute: \( \text{kJ·mol}^{-1} = \dfrac{q\;(\text{kJ})}{n\;(\text{mol})} \).

What if the solution volume or density changes significantly?

Use actual solution mass and heat capacity. If density or specific heat differ from solvent, measure or look up \( C_p \) and mass. Use \( = m_{solution} C_{p,solution} \\Delta T \) for accurate heat.

How to handle dilution enthalpies or nonideal behavior?

For concentration-dependent enthalpies, report \( \\Delta H \) at specified molarity. Use calorimetry at those concentrations or integrate differential heats: \( \\Delta H = \int_{c_1}^{c_2} \bar{H}_{mix}(c)\,dc \) when datexist.

How accurate are tabulated \( \\Delta H_{soln} \) values?