# Chapter 9.5: Enthalpies of Solution

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 Howard University General Chemistry: An Atoms First Approach Unit 1: Atomic Theory      Unit 2: Molecular Structure        Unit 3: Stoichiometry          Unit 4: Thermochem & Gases Unit 5:  States of Matter         Unit 6: Kinetics & Equilibria        Unit 7: Electro & Thermo Chemistry       Unit 8: Materials

### Learning Objectives

• To understand Enthalpies of Solution and be able to use them to calculate the Heat absorbed or emitted when making solutions.

## Enthalpies of Solution and Dilution

Physical changes, such as melting or vaporization, and chemical reactions, in which one substance is converted to another, are accompanied by changes in enthalpy. Two other kinds of changes that are accompanied by changes in enthalpy are the dissolution of solids and the dilution of concentrated solutions.

The dissolution of a solid can be described as follows:

$$solute\left ( s \right ) + solvent\left ( l \right )\rightarrow soulution\left ( l \right ) \tag{9.5.1}$$

The values of ΔHsoln for some common substances are given in Table 9.5.1 . The sign and the magnitude of ΔHsoln depend on specific attractive and repulsive interactions between the solute and the solvent; these factors will be discussed in Chapter 13. When substances dissolve, the process can be either exothermic (ΔHsoln < 0) or endothermic (ΔHsoln > 0), as you can see from the data in Table 9.5.1.

Table 9.5.1 Enthalpies of Solution at 25°C of Selected Ionic Compounds in Water (in kJ/mol)

 Anion Cation Fluoride Chloride Bromide Iodide Hydroxide lithium 4.7 −37.0 −48.8 −63.3 −23.6 sodium 0.9 3.9 −0.6 −7.5 −44.5 potassium −17.7 17.2 19.9 20.3 −57.6 ammonium −1.2 14.8 16.8 13.7 — silver −22.5 65.5 84.4 112.2 — magnesium −17.7 −160.0 −185.6 −213.2 2.3 calcium 11.5 −81.3 −103.1 −119.7 −16.7 Nitrate Acetate Carbonate Sulfate lithium −2.5 — −18.2 −29.8 sodium 20.5 −17.3 −26.7 2.4 potassium 34.9 −15.3 −30.9 23.8 ammonium 25.7 −2.4 — 6.6 silver 22.6 — 22.6 17.8 magnesium −90.9 — −25.3 −91.2 calcium −19.2 — −13.1 −18.0

Substances with large positive or negative enthalpies of solution have commercial applications as instant cold or hot packs. Single-use versions of these products are based on the dissolution of either calcium chloride (CaCl2, ΔHsoln = −81.3 kJ/mol) or ammonium nitrate (NH4NO3, ΔHsoln = +25.7 kJ/mol). Both types consist of a plastic bag that contains about 100 mL of water plus a dry chemical (40 g of CaCl2 or 30 g of NH4NO3) in a separate plastic pouch. When the pack is twisted or struck sharply, the inner plastic bag of water ruptures, and the salt dissolves in the water. If the salt is CaCl2, heat is released to produce a solution with a temperature of about 90°C; hence the product is an “instant hot compress.” If the salt is NH4NO3, heat is absorbed when it dissolves, and the temperature drops to about 0° for an “instant cold pack.”

A similar product based on the precipitation of sodium acetate, not its dissolution, is marketed as a reusable hand warmer (Figure 9.5.1). At high temperatures, sodium acetate forms a highly concentrated aqueous solution. With cooling, an unstable supersaturated solution containing excess solute is formed. When the pack is agitated, sodium acetate trihydrate [CH3CO2Na·3H2O] crystallizes, and heat is evolved:

$$Na^{+}\left ( aq \right )+ CH_{3}CO_{2}^{-}\left ( aq \right ) + H_{2}O\left ( l \right ) \rightarrow CH_{3}CO_{2}Na\cdot \bullet H_{2}O\left ( s \right ) \quad \quad \Delta H = - \Delta H_{soln} = - 19.7 \; kJ/mol \tag{9.5.2}$$

A bag of concentrated sodium acetate solution can be carried until heat is needed, at which time vigorous agitation induces crystallization and heat is released. The pack can be reused after it is immersed in hot water until the sodium acetate redissolves.

Figure 9.5.1 An Instant Hot Pack Based on the Crystallization of Sodium Acetate The hot pack is at room temperature prior to agitation (left). Because the sodium acetate is in solution, you can see the metal disc inside the pack. After the hot pack has been agitated, the sodium acetate crystallizes (right) to release heat. Because of the mass of white sodium acetate that has crystallized, the metal disc is no longer visible.

The amount of heat released or absorbed when a substance is dissolved is not a constant; it depends on the final concentration of the solute. The ΔHsoln values given previously and in Table 8.2.2 for example, were obtained by measuring the enthalpy changes at various concentrations and extrapolating the data to infinite dilution.

Because ΔHsoln depends on the concentration of the solute, diluting a solution can produce a change in enthalpy. If the initial dissolution process is exothermic (ΔH < 0), then the dilution process is also exothermic. This phenomenon is particularly relevant for strong acids and bases, which are often sold or stored as concentrated aqueous solutions. If water is added to a concentrated solution of sulfuric acid (which is 98% H2SO4 and 2% H2O) or sodium hydroxide, the heat released by the large negative ΔH can cause the solution to boil. Dangerous spattering of strong acid or base can be avoided if the concentrated acid or base is slowly added to water, so that the heat liberated is largely dissipated by the water. Thus you should never add water to a strong acid or base; a useful way to avoid the danger is to remember: Add water to acid and get blasted!

### Summary

The enthalpy of solution (ΔHsoln) is the heat released or absorbed when a specified amount of a solute dissolves in a certain quantity of solvent at constant pressure.

### Key Takeaway

• Enthalpy is a state function whose change indicates the amount of heat transferred from a system to its surroundings or vice versa, at constant pressure.

### Conceptual Problems

Please be sure you are familiar with the topics discussed in Essential Skills 4 (Section 9.9) before proceeding to the Conceptual Problems.

1. Describe the distinction between ΔHsoln and ΔHf.

2. Does adding water to concentrated acid result in an endothermic or an exothermic process?

3. The following table lists ΔHosoln values for some ionic compounds. If 1 mol of each solute is dissolved in 500 mL of water, rank the resulting solutions from warmest to coldest.

Compound ΔHosoln(kJ/mol)
KOH −57.61
LiNO3 −2.51
KMnO4 43.56
NaC2H3O2 −17.32

### Numerical Problems

Please be sure you are familiar with the topics discussed in Essential Skills 4 (Section 9.9 ) before proceeding to the Numerical Problems.

### Contributors

• Anonymous

Modified by Joshua Halpern

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