Why Is the Heat of Solution Positive or Negative?

The sign of the heat of solution tells you whether the dissolving process absorbs or releases heat. Under the standard thermodynamic convention, the enthalpy of solution is written as $\Delta H_{\mathrm{soln}}$:

• $\Delta H_{\mathrm{soln}} > 0$: dissolving is endothermic and absorbs heat.
• $\Delta H_{\mathrm{soln}} < 0$: dissolving is exothermic and releases heat.

At constant pressure, assuming only pressure–volume work, a positive enthalpy change corresponds to heat absorbed by the system. The main source of confusion is that “heat absorbed by the solution” and “heat released by the dissolving process” describe opposite energy transfers.

What does heat of solution measure?

The molar enthalpy of solution is the enthalpy change per mole of solute when a specified amount of solute dissolves in a specified solvent under specified conditions, including temperature, pressure, and final concentration. In the usual constant-pressure model, where only pressure–volume work is relevant, it is expressed as

$$\Delta H_{\mathrm{soln}} = \frac{q_p}{n}$$

Here, $q_p$ is the heat transferred to the chemical system at constant pressure, and $n$ is the amount of solute dissolved. Under these conditions, $q_p$ equals the total enthalpy change of the process.

If the dissolving process absorbs heat, then $q_p$ is positive. If it releases heat, then $q_p$ is negative.

In an idealized calorimetry experiment, where the process and the defined surroundings are the only bodies exchanging heat, you often calculate the heat gained by the water or solution. That quantity has the opposite sign:

$$q_{\mathrm{process}} = -q_{\mathrm{surroundings}}$$

Real calorimetry may require corrections for heat absorbed by the calorimeter or exchanged with the external environment. Thus, if the water warms, the water has absorbed positive heat, but the dissolving process has released negative heat.

Why does dissolving require and release energy?

Dissolving can be viewed as three energy changes:

1. Separating solute particles from one another requires energy.
2. Separating some solvent molecules to make room also requires energy.
3. Forming interactions between solute and solvent releases energy.

A schematic representation is

$$\Delta H_{\mathrm{soln}} \approx \Delta H_{\mathrm{lattice\ separation}} + \Delta H_{\mathrm{solvent\ separation}} + \Delta H_{\mathrm{solute-solvent\ formation}}$$

For an ionic solid, the first step is associated with breaking the ionic lattice. A common Hess’s-law shorthand groups the solvent-separation and solute–solvent-formation terms into a solvation term:

$$\Delta H_{\mathrm{soln}} \approx \Delta H_{\mathrm{lattice\ separation}} + \Delta H_{\mathrm{solvation}}$$

Here, $\Delta H_{\mathrm{solvation}}$ includes solvent reorganization as well as the formation of solute–solvent interactions. The lattice-separation term is positive because energy is needed to pull ions apart. The solvation term is usually negative because solvent molecules form attractive interactions with the ions. In water, this is specifically called hydration.

The overall sign depends on which effect is larger:

• If separating particles costs more energy than solvation releases, $\Delta H_{\mathrm{soln}}$ is positive.
• If solvation releases more energy than particle separation requires, $\Delta H_{\mathrm{soln}}$ is negative.

For a molecular solute, the same principle applies, although the interactions being broken and formed may include hydrogen bonds, dipole–dipole interactions, and dispersion forces rather than an ionic lattice.

What does a positive value look like?

Suppose $0.100\ \mathrm{mol}$ of a salt dissolves and the surrounding solution loses $1.84\ \mathrm{kJ}$ of heat. The solution cools, so the solution’s heat change is approximately

$$q_{\mathrm{solution}}=-1.84\ \mathrm{kJ}$$

The dissolving process gains that heat:

$$q_{\mathrm{process}}=+1.84\ \mathrm{kJ}$$

Therefore,

$$\Delta H_{\mathrm{soln}} = \frac{+1.84\ \mathrm{kJ}}{0.100\ \mathrm{mol}} =+18.4\ \mathrm{kJ\ mol^{-1}}$$

This is an endothermic dissolution. The positive sign does not mean that the solution becomes warmer; it means the dissolving process takes heat from the surroundings, making the solution cooler.

Potassium nitrate dissolving in water is a familiar example of an endothermic dissolution; ammonium nitrate is more commonly used in commercial instant cold packs.

What does a negative value look like?

Now suppose $0.100\ \mathrm{mol}$ of a substance dissolves and the surrounding solution gains $3.50\ \mathrm{kJ}$. The solution warms, so

$$q_{\mathrm{solution}}=+3.50\ \mathrm{kJ}$$

The dissolving process releases that energy:

$$q_{\mathrm{process}}=-3.50\ \mathrm{kJ}$$

Consequently,

$$\Delta H_{\mathrm{soln}} = \frac{-3.50\ \mathrm{kJ}}{0.100\ \mathrm{mol}} =-35.0\ \mathrm{kJ\ mol^{-1}}$$

This is an exothermic dissolution. Sodium hydroxide dissolving in water is a common example: strong ion–water interactions release substantial energy, and the solution temperature can rise noticeably.

Why do textbook answers sometimes use the opposite sign?

Some sources use “heat of solution” to mean the heat absorbed by the surrounding solution, rather than the enthalpy change of the dissolving process. In that usage, a warming solution may be assigned a positive heat value even though the process has a negative enthalpy change.

For example:

Quantity reported	Solution warms	Solution cools
Heat gained by solution, $q_{\mathrm{solution}}$	Positive	Negative
Heat of dissolving process, $q_{\mathrm{process}}$	Negative	Positive
Thermodynamic $\Delta H_{\mathrm{soln}}$	Negative	Positive

Always check what the symbol refers to. The safest wording is to say either “the solution absorbs $3.50\ \mathrm{kJ}$” or “the dissolution has $\Delta H_{\mathrm{soln}}=-35.0\ \mathrm{kJ\ mol^{-1}}$.”

Heat of solution is not the same as spontaneity

A positive heat of solution does not automatically mean that a substance cannot dissolve. Dissolution depends on Gibbs free energy:

$$\Delta G=\Delta H-T\Delta S$$

A process with positive $\Delta H$ can still be spontaneous if the entropy increase, represented by $T\Delta S$, is sufficiently large. For example, dispersing solute particles through a solvent can increase entropy substantially.

Conversely, a negative heat of solution does not guarantee unlimited solubility. Solubility also depends on entropy, concentration, temperature, pressure, and the nature of the solute and solvent.

Common mistakes

Confusing the solution with the process

If the water gets warmer, the water absorbed heat, but the dissolving process released heat. Their heat changes have opposite signs.

Treating every broken interaction as the whole process

Breaking the solute lattice costs energy, but new solute–solvent interactions form at the same time. The measured heat of solution is the net result.

Ignoring the amount dissolved

A total heat such as $-3.50\ \mathrm{kJ}$ is not the same as a molar enthalpy. Divide by the number of moles to obtain $\mathrm{kJ\ mol^{-1}}$.

Assuming “positive” always means warming

A positive $\Delta H_{\mathrm{soln}}$ means the dissolving process absorbs heat. The visible temperature change is usually cooling, not warming.

Forgetting the convention for lattice energy

Lattice energy may be defined as the enthalpy change when gaseous ions form a solid, which is negative under a signed thermodynamic convention, or as the positive energy required to separate the solid into gaseous ions. State the definition before combining it with hydration enthalpy.