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# Free Energy of Dissolution

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Have you ever needed to disinfect a wound or a sore and used salt water for it? In making salt water, you have dissolved a substance in a solvent, leading to energy being released. Within chemistry, we study this release of energy to determine how systems change.

• First, we’ll define the free energy of dissolution.

• Then, we’ll relate it to Gibbs Free Energy and Enthalpy.

• Next, we’ll look at the free energy of dissolution equation.

• Lastly, we’ll go over examples of free energy of dissolution

## The Free Energy of Dissolution

The free energy of dissolution, ΔG°soln, (also called the 'delta G naught of solution') is a measure of the behavior of a solute/solvent combination under standard conditions- there are two possibilities:

• If ΔG°soln is less than zero, ΔG°soln < 0, then dissolution is thermodynamically favorable and the solute dissolves into the solvent.
• If ΔG°soln is greater than zero, ΔG°soln > 0, then dissolution is thermodynamically unfavorable and the solute does not dissolve into the solvent.
Standard Conditions - standard thermodynamic conditions for compounds when listed in a table of thermodynamic data. Typically standard conditions are 1 atmosphere (atm) and 25°C.A solute is a substance that is in a solvent. A solute can either totally dissolve into a solvent, partially dissolve into a solvent or not dissolve at all into a solvent.A solvent is a substance that interacts with a solute.

We note that a process that is thermodynamically favorable, ΔG°soln < 0, will be one that is exothermic (a process that releases energy in the form of heat). On the other hand, a process that is thermodynamically unfavorable, ΔG°soln > 0, will be one that is endothermic (a process that absorbs energy in the form of heat).

The process described by the free energy of dissolution can be analyzed in molecular detail. If we consider a solute/solvent combination in which, ΔG°soln < 0, it must be that the solute dissolves into the solvent. If we take for instance an ionic salt as solute that is soluble in a given solvent, ions within the solute must separate from each other and disperse into the solvent. This means that the ionic lattice breaks down, resulting in the ions that made up the lattice being able to be surrounded by solvent molecules. If we used water as a solvent then many of the hydrogen bonds originally within water (solvent) will be displaced by ion-dipole interactions with the ionic salt (solute).

Ion-dipole interactions result from a charged ion (+, cation, or -, anion) and a non-charged molecule bearing a permanent dipole being attracted to one another.

In our case, the positively charged ions of the ionic salt will interact with the negative ends of our water molecules. In contrast, the negatively charged ions of the ionic salt will interact with the positive ends of our water molecules.

These interactions lead to the dissolution of ionic salts, like magnesium chloride, MgCl2, resulting in the formation of an aqueous salt solution.

Figure 1: Ion-Dipole interactions between magnesium cation and water. Daniela Lin, Study Smarter Originals.

The ion-dipole interactions occur in figure 1 because the positively charged Mg2+ cations and the negative ends of water molecules (oxygen atoms in red) are attracted to each other. Meanwhile, the same thing happens for Cl- anions being attracted to the positive end of the permanent dipole in water molecules.

Figure 2: Ion-dipole interactions between the chloride anion, Cl-, and water.

Please refer to our “Solutions and Mixtures” or “Ion-Dipole Forces” article for more information regarding solutions or ion-dipole interactions "Solutions and Mixtures” or “Ion-Dipole Forces” article.

## The Free Energy of Dissolution Equation

The magnesium chloride/water dissolution process is an example of a spontaneous reaction.

Spontaneous reactions favor the forward reaction or the formation of products.

You can confirm this by watching how easily magnesium chloride dissolves in water to form an aqueous salt solution.

We can use the free energy of dissolution equation, ΔG°soln = ΔH°soln - TΔS°soln, to confirm this mathematically; where the heat of formation is, ΔH°soln, the temperature, T, is in Kelvins and the entropy of solution is, ΔS°soln. We note that the dimensions of, ΔH°soln, is in kiloJoules (kJ), and the dimensions for the entropy of solution is, ΔS°soln, is in kiloJoules per Kelivin per mole [kJ/(K•mol)].

What does the sign of the term, ΔG°soln, say about the dissolution process?

ΔG°soln, tells you the direction of a chemical reaction and whether or not it's spontaneous or non-spontaneous.

ΔG°soln < 0 exergonic reaction = spontaneous

ΔG°soln > 0 endergonic reaction = non-spontaneous

• If our Gibbs free energy sign is negative, our reaction is spontaneous, favoring product formation. In comparison, if our Gibbs free energy sign is positive, our reaction is non-spontaneous, favoring reactant formation.
• The overall sign of our Gibbs free energy equation tells us which direction is favored in our chemical reaction or if our solute will dissolve into our solvent easily.
• If our sign is positive, then our reaction is endergonic or non-spontaneous. This signifies that our chemical reaction will not readily dissolve, as reactant formation is favored.

Now you might be wondering what exergonic or endergonic reactions are. Here’s a graphical explanation below to help you visualize the situation:

Figure 3: Exergonic vs. Endergonic reactions. Daniela Lin, Study Smarter Originals.

Exergonic means that energy is released to the surroundings, as the bonds being made are stronger than those that are being broken. Exergonic reactions can also occur when multiple weak bonds are formed so that the energy of the sum total of the bonds formed is greater than the energy of the bonds broken. Notice, that the term exergonic (specifically for chemical reactions) is related to exothermic (which pertains to all thermodynamic processes).

By comparison, endergonic signifies that energy is absorbed from the surroundings by the chemical reaction as it proceeds to products. The energy absorbed by the system facilitates the breaking of stronger bonds which are then replaced by the weaker bonds arising from solute ions interacting with the solvent. Notice, that the term endergonic (specifically for chemical reactions) is related to endothermic (which pertains to all thermodynamic processes).

## Standard Free Energy of Dissolution

We can use the standard free energy dissolution equation to figure out if a substance will dissolve under standard conditions:

ΔG°soln = ΔH°soln - TΔS°soln

where, ΔG°soln, is the standard free energy of dissolution, ΔH°soln, is the standard enthalpy change of dissolution, ΔS°soln, is the standard entropy change of dissolution and the temperature, T, is given in Kelvins.

Some other essential things to know are:

• Enthalpy, for a chemical substance, is equivalent to the potential energy that is stored as heat within the chemical bonds of a compound.

• Entropy is a measure of the randomness or disorder of a system.

You can calculate the standard free energy of dissolution using the equation shown above, as the free energy of dissolution is the same as the change in Gibbs free energy $$(\Delta G^\circ)$$ when applied to a solute that fully dissolves in a solvent. Another formula that can be utilized to calculate the standard free energy of solution, ΔG°soln, using the standard free energy of solution from products, ΔG°soln(products), and the standard free energy of solution of reactants, ΔG°soln(reactants), is:

ΔG°soln = Σ nΔG°soln(products) - Σ mΔG°soln(reacatants)

where, Σ, is the summation symbol, n, and, m, are the stoichiometric coefficients of the balanced equation for products and reactants, respectively.

Thermodynamic tables listing data for the Gibbs free energies, enthalpies and entropies of ionic substances can be used with the understanding that these were usually obtained from electrochemistry experiments. For reactions involving multiple states of matter, it is controversial to mix thermodynamic data for reactions that occur in the gas phase with those that produce ionic species and occur in solution, as often the reaction conditions are not equivalent. Exceptions can, however, can be found; take for example the following electrochemical reaction run at standard conditions (1 atm, 1 mole of reactants and products and 25°C) involving multiple states of matter:

$$Zn \left( s \right) +Cl_2 \left( g \right) \rightarrow Zn^{2+} \left( aq \right) +2Cl^- \left( aq\right)$$

Here, we note that the reactants involve a reactant that is a solid, Zn (s), and a reactant that is a gas, Cl2 (g), while on the products side we have a solution of ions. We can, in this case, still calculate the standard free energy from the standard free energies of formation of the reactants and products, using data from thermodynamic tables, because as we list the standard free energies of formation below the reactants and product for this chemical equation we find that:

$$\hspace{1cm}Zn \left( s \right) +Cl_2 \left( g \right) \rightarrow Zn^{2+} \left( aq \right) +2Cl^- \left( aq\right)$$

$$ΔG^\circ _f \colon \hspace{1cm}0 \hspace{1cm}0 \hspace{1cm}-147 \hspace{1cm}2(-131) \hspace{1cm}kJ/mol$$

Thus,

ΔG°soln = [ 0 kJ + 0 kJ/mol] - [(-147 kJ/mol) + 2•(-131 kJ/mol)] = -409 kJ/mol

Notice, that in this case, we can mix thermodynamic data because the reactants are elements in their reference form and as such will have standard free energies of formation of value zero.

1. Now, let us consider the following example: The dissolution of one mole of sodium chloride in one liter of water at 25°C :

$$NaCl \left( s \right) \rightarrow Na^+ \left( aq \right)+Cl^- \left( aq \right)$$

Now, looking up the standard free energies of formation of the reactants and products, from thermodynamic tables, we find that:

ΔG°soln = [ΔG°soln(Na+) + ΔG°soln(Cl-)] - ΔG°soln(NaCl) = [(-261.87 kJ/mol) + (-131.2 kJ/mol)] - (-384.0 kJ/mol) = -9.1 kJ/mol

As such, the reaction is exergonic and thus thermodynamically favorable (spontaneous), ΔG° < 0.

## Examples of the Free Energy of Dissolution

### The Free Energy for Dissolution of Magnesium Chloride

What’s the free energy of dissolution of one mole of magnesium chloride, MgCl2, dissolved into 1 liter of water at 25°C?

$$MgCl_2 \left( s \right) \rightarrow Mg^{2+} \left( aq \right) +2Cl^- \left( aq\right)$$

The standard change in Gibbs free energy of dissolution of, MgCl2, can be found by utilizing the formula for the free energy of dissolution in the following form:

ΔG°soln(MgCl2) = ΔH°soln(MgCl2) - TΔS°soln(MgCl2)

where, ΔG°soln(MgCl2), is the standard free energy of dissolution of magnesium chloride, ΔH°soln(MgCl2), is the standard enthalpy change of dissolution of magnesium chloride, ΔS°soln(MgCl2), is the standard entropy change of dissolution of magnesium chloride and the temperature, T, is given in Kelvins. Looking up the thermodynamic data from an appropriate table we find:

 Ionic Salt ΔH°soln ΔS°soln MgCl2 -160 kJ/mol -0.1147 kJ/(K•mol)

Then using the above formula for the standard free energy of dissolution of magnesium chloride, we get:

ΔG°soln(MgCl2) = -160 kJ/mol - (298 K)•(-0.1147 kJ/(K•mol)) = -125.8 kJ/mol

Thus the reaction is exergonic and spontaneous.

### The Gibbs Free Energy of Dissolution of Sodium Chloride

Now, let's ask what’s the free energy of dissolution of one mole of sodium chloride, NaCl, dissolved into 1 liter of water at 25°C?

$$NaCl \left( s \right) \rightarrow Na^{+} \left( aq \right) +Cl^- \left( aq\right)$$

The standard change in Gibbs free energy of dissolution of, NaCl, can be found by utilizing the formula for the free energy of dissolution in the following form:

ΔG°soln(NaCl) = ΔH°soln(NaCl) - TΔS°soln(NaCl)

where, ΔG°soln(NaCl), is the standard free energy of dissolution of sodium chloride, ΔH°soln(NaCl), is the standard enthalpy change of dissolution of sodium chloride, ΔS°soln(NaCl), is the standard entropy change of dissolution of sodium chloride and the temperature, T, is given in Kelvins. Looking up the thermodynamic data from an appropriate table we find:

 Ionic Salt ΔH°soln ΔS°soln NaCl +3.9 kJ/mol 0.0434 kJ/(K•mol)

Then using the above formula for the standard free energy of dissolution of sodium chloride, we get:

ΔG°soln(NaCl) = +3.9 kJ/mol - (298 K)•(0.0434 kJ/(K•mol)) = -9.1 kJ/mol

Thus the reaction is again exergonic and spontaneous.

## Free Energy of Dissolution - Key takeaways

• The free energy of dissolution is the energy released when a substance dissolves in a solvent.

• The free energy of dissolution occurs when a substance like salt dissolves in a solvent like water.

• Ion-dipole interactions result from a charged ion (+, cation or -, anion) and a molecule, bearing a dipole, being attracted to each other.
• When solvent-solvent interactions are more robust than solute-solvent interactions, the solute is less likely to dissolve, leading to a positive, +ΔG°, standard Gibbs free energy change.
• A negative, -ΔG°, standard Gibbs free energy change indicates that a solute will dissolve into a solvent, with a more significant negative value indicating a greater propensity of the solute to dissolve into the solvent.

## References

1. Cooper, M. M., & Klymkowsky, M. W. (2022, April 3). 6.4: Gibbs Energy and solubility. Chemistry LibreTexts.
2. General chemistry: An atoms first approach. Chemistry LibreTexts. (2022, February 10).
3. Key, J. A. (2014, September 16). Free energy under nonstandard conditions. Introductory Chemistry 1st Canadian Edition. Retrieved August 10, 2022, from https://opentextbc.ca/introductorychemistry/chapter/free-energy-under-nonstandard-conditions/
4. Libretexts. (2022, April 25). The reaction quotient. Chemistry LibreTexts. Retrieved August 10, 2022, from https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Equilibria/Chemical_Equilibria/The_Reaction_Quotient#:~:text=The%20reaction%20quotient%20(Q)%20measures,the%20reactants%20and%20the%20products.

## Frequently Asked Questions about Free Energy of Dissolution

The free energy of equilibrium occurs when the Gibbs Free Energy equals 0. In other words, when neither the product nor reactants are favored.

For a solution to form a reaction needs to be spontaneous or the Gibbs Free energy negative. The more negative it is the more soluble something is.

You can relate Gibbs's free energy to solubility through Ksp or the solubility product constant.

The free energy concept describes how a system can change and how much work they can do.

The standard free energy deals with products and reactants when they are in their standard states (temperature, pressure, etc.). Meanwhile, non-standard Gibbs free energy is determined through experimental conditions.

## Final Free Energy of Dissolution Quiz

Question

What is the energy released when a substance dissolves in a solvent?

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Answer

free energy of dissolution

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Question

The overall sign of our Gibbs free energy equation tells us what?

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Answer

It tells us which direction is favored in our chemical reaction, or in this case if our solute is going to easily dissolve into our solvent.

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Question

Why can you use the Gibbs Free Energy equation to calculate the free energy of dissolution?

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Answer

You can calculate the free energy of dissolution using the standard Gibbs free energy equation. Because by finding the enthalpy or heat change caused by dissolution and entropy at a certain temperature, you can calculate G and find out whether the reaction favors product formation aka dissolution, or not.

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Question

What's enthalpy when compared to entropy?

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Answer

Entropy is the total change in heat within a system when pressure is constant. While enthalpy is the randomness or disorder of a system.

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Question

What type of reaction favors the forward reaction or the formation of products?

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Answer

Spontaneous

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Question

What exactly are K and Ksp and how are they related?

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Answer

The equilibrium constant, K, relates the products and reactants of a reaction at equilibrium.

The Ksp is our solubility product constant and describes how likely a solute is to dissolve into a solution. It's basically the same as K when a solid solute is dissolving into a liquid solution.

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Question

How do you form a solution?

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Answer

You combine a solute and a solvent.

A solute is a substance that dissolves into a solvent. While a solvent is a substance into which the solute dissolves, resulting in a solution.

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Question

How does the reaction quotient (Q) relate to K (equilibrium constant)?

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Answer

The reaction quotient (Q) and K (equilibrium constant) can be compared to determine if more reactants or products will be made.

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Question

How do Q (reaction quotient) and K (equilibrium constant) determine how the reaction proceeds?

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Answer

If Q=K, the reaction is in equilibrium as neither reactant nor product is favored.

If Q<K, the reaction favors the products. This is because there are fewer products than reactants. To get back to equilibrium, the system needs to make more products.

If Q>K, the reaction favors the reactants. This is because there are more products than reactants. To get back to equilibrium, the system needs to make more reactants.

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