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## AP®︎/College Chemistry

### Course: AP®︎/College Chemistry > Unit 9

Lesson 3: Free energy of dissolution# Free energy of dissolution

The dissolution of a solid can be thought of as occurring in three hypothetical steps: (1) the breaking apart of the solid, (2) the spreading out of the solvent, and (3) the interaction of the dissolved solid with the solvent. As shown in this video, we can predict the signs of the enthalpy and entropy changes for each of these steps and relate this information to the solubility of the solid. Created by Jay.

## Want to join the conversation?

- Re: energy release in hydration/solvation - would it be possible to get some additional mechanistic detail behind enthalpy of hydration/solvation? Happy to watch another video if a good one comes to mind!(1 vote)
- When a water soluble chemical like sodium chloride dissolves in water the water molecules disrupt the ionic bonds of the lattice and pull ions from the lattice individually. This requires the breaking of bonds and thus an input of energy. The water now forms ion-dipole bonds with the loose ions in a solvation shell and thus releases energy. The solvation shell is essentially a layer of solvent molecules which surround the dissolved solutes. The energy change for the dissolution process is the difference between the energy put into the reaction and the energy released from the reaction.

Hope that helps.(2 votes)

## Video transcript

- [Instructor] The term
dissolution refers to the dissolving of one
substance in a solvent. The dissolve substance
is now called a salute and the solute plus the
solvent form a solution. If the standard change in
free energy, delta G naught is less than zero, the dissolution is
thermodynamically favorable. So, if we were to put this substance in a solvent like water, the substance would dissolve
and it would form a solution. However, if delta G naught
is greater than zero, the dissolution is
thermodynamically unfavorable. So, if we try to dissolve
the substance in water, it wouldn't dissolve and therefore we would just see it on the bottom of the beaker. Since we're talking about
potentially making a solution, sometimes you see a
subscript soln written next to delta G naught. So, this would be delta
G naught of solution. We could also call this the
free energy of dissolution. We can calculate delta
G naught of solution by taking the standard change
and enthalpy of the solution and from that subtracting
the absolute temperature, times the standard change
in entropy of the solution. So, let's look in more
detail at what determines the signs for delta H
naught and delta S naught. We can think about the
disillusion of a solid in three hypothetical steps. The first step involves
breaking up the solid. Let's think about the change in enthalpy, delta H one, for this first step. Solids are held together
by attractive forces. For example, if we had an ionic solid, it would be ionic bonds or electrostatic
interactions holding together the opposite charges. So, if our goal is to pull
apart or break apart the solid, it would take energy to overcome
these attractive forces. Therefore, delta H one would be positive. Next, let's think about
the change in entropy. Delta S one for the first step. When the solid is broken up, the particles have a greater
number of possible positions and an increased number of
possible positions means an increase in number
of possible microstates. An increase in the number of microstates means an increase in entropy. Therefore, breaking up the solid means an increase in entropy and delta S one will be positive. Step two is the preparation of the solvent to receive the salute. And let's think about
the change in enthalpy for this second step. The solvent particles are held together by intermolecular forces. For water molecules, the most important intermolecular
force is hydrogen bonding. The goal of this theoretical second step is to break apart the solvent particles and to move them far apart from each other so there's enough room to
fit in a solute particle. Since it takes energy to overcome the intermolecular forces holding the solvent particles together, delta H two is positive. Next, let's think about
the change in entropy, delta S two for this second step. When the water molecules are pulled apart, there's an increase in the
number of possible positions of the water molecules. And like the first step,
an increase in the number of possible positions means an increase in the number of microstates, which means an increase in entropy. Therefore, delta S two is positive. The third step is called solvation, which refers to the interaction of the solute and the solvent. So, imagine there's an attractive force between this white solute particle and these four blue solvent particles. If the solvent is water, this
process is called hydration. And if we think about,
say a positive cation, interacting with water, since opposite charges attract, the positive cation is
attracted to the negative end of the water molecule. Since we have a positively
charged ion interacting with water, which is a polar
molecule with a dipole moment, this type of interaction is called an ion dipole interaction. And let's think about
the change in enthalpy for this third step. When the solute comes
together with the solvent, energy is released, therefore delta H three is negative. One way to think about
why this is negative is to consider the ion dipole
interactions on the right. Since it would take energy to break these ion dipole interactions, when those ion dipole interactions form, energy must be given off. Next, let's think about
the change in entropy. Delta S three for the third step. Because the water molecules are attracted to the ions in solution, the water molecules have a
decreased freedom of movement and therefore there are
fewer positions possible for the water molecules. A decrease in the number
of possible positions means a decrease in the
number of microstates, which means a decrease in entropy. Therefore, for the third step,
delta S three is negative. Now that we've talked about the signs for delta H and delta S for
each of the three steps, let's think about how they
influence the overall changes in delta H naught of solution and delta S naught of solution. And let's start with delta
H naught of solution, which is equal to the sum of the changes in enthalpy for the three steps. So, delta H one, plus delta
H two, plus delta H three. We've already seen that
delta H one is positive, delta H two is positive, and
delta H three is negative. So, adding delta H one
and delta H two together, it gives us a positive value. And since we're adding a
negative in delta H three, it's the magnitude of delta H three that determines if the overall
delta H naught of solution is positive or negative. If the magnitude of delta
H one, plus delta H two is greater than the
magnitude of delta H three, delta H naught of
solution will be positive. However, if the magnitude of delta H three is greater than the magnitude of delta H one plus delta H two, delta H naught of
solution will be negative. Therefore, it's possible for
delta H naught of solution to be positive or negative, depending on the
substance being dissolved. An example of a substance
that has a positive value for delta H naught of
solution is sodium chloride. At 25 degrees Celsius, delta H naught of solution
for sodium chloride is positive 3.9 kilojoules
per mole of reaction. An example of a substance
that has a negative value for delta H naught of solution
is magnesium chloride. At 25 degrees Celsius, delta H naught of solution
for magnesium chloride is equal to negative 160.0
kilojoules per mole of reaction. The main reason why these two substances have such different enthalpies of solution has to do with the third step. So, the value of delta H three. So, let's take a look
at some diagrams showing the ion dipole interaction of the cation of both of these substances
in aqueous solution, interacting with water molecules. For sodium chloride, we
would have a sodium cation in solution with a one plus charge. And for magnesium chloride, it would be an Mg two
plus cation interacting with the water molecules. Because the Mg two plus
cation has a higher charge than the sodium cation
and because it's smaller, the Mg two plus cation exerts
a greater electric force on the water molecules, and because the magnesium
two plus cation exerts a greater electric force
on the water molecules, more energy is released when
the magnesium two plus cation is hydrated compared to when the sodium one
plus cation is hydrated. And since more energy is
given off in the third step for the hydration of the
magnesium two plus cation, that's enough to turn the overall delta H naught
of solution negative. Therefore, the dissolution
of magnesium chloride is an exothermic process. For sodium chloride, when the
sodium cation is hydrated, not as much energy is released. Therefore, the overall delta
H of solution is positive and the dissolution of sodium chloride is an endothermic process. Next, let's think about
delta S naught of solution. Delta S naught of solution is equal to delta S one, plus delta S two, plus delta S three. Delta S one, the change in entropy for the first step, we saw was positive. Delta S two was also positive, but delta S3 was negative. Therefore, just like we
saw for delta H naught, the sign for delta S naught
depends on the magnitude of delta S one, plus delta S
two, compared to delta S three. If delta S one, plus delta S two is greater in magnitude
than delta S three, delta S naught of
solution will be positive. However, if the magnitude of delta S three is greater than the
magnitude of delta S one, plus delta S two, delta S naught of
solution will be negative. An example of a substance
that has a positive value for delta S naught of
solution is sodium chloride. At 25 degrees Celsius, delta S naught of solution is equal to positive 43.4 joules per
Kelvin mole of reaction. An example of a substance
that has a negative value for delta S naught of solution
is magnesium chloride. At 25 degrees Celsius, delta S naught of solution is equal to negative 114.7 joules
per Kelvin mole of reaction. The main reason for the
difference in entropies for these two substances has
to do with the third step. So, the magnitude of delta S three. So, once again, let's take a look at the diagrams showing the hydration of the cations in aqueous solution. We've already talked about
the fact that the smaller and more positive
magnesium two-plus cation has a greater electric force on its surrounding water molecules than the sodium one plus cation does on its surrounding water molecules. The stronger electric force
means a decreased freedom of movement of water molecules around the magnesium two plus cation, and a decreased freedom of movement means a decreased number of
possible microstates, which means a greater decrease in entropy. So, the hydration of the
magnesium two plus cation leads to a greater decrease in
entropy for step three, which outweighs the positive
values for steps one and two. And that gives an overall negative value for delta S naught of solution, therefore dissolving magnesium chloride in water results in a decrease in entropy. Since the sodium cation has a weaker electrostatic
attraction for water molecules, the decrease in entropy is not as much. And therefore, the
magnitude of the third term does not overcome the magnitude
of the first two terms, which means the overall
delta S naught of solution is positive and dissolving sodium chloride in water results in an
increase in entropy. We've just looked at
delta H naught of solution and delta S naught of
solution for two salts, sodium chloride and magnesium chloride. Let's calculate delta G naught of solution for both salts at 25 degrees Celsius. Let's start with the dissolution of solid sodium chloride and water to form sodium cations
and chloride anions. 25 degrees Celsius is 298 Kelvin so we can plug that into our equation. And we can also plug in the
values for delta H naught and delta S naught. So, both of them were positive values for the dissolution of sodium chloride. Kelvin cancels out and gives
us delta G naught of solution is equal to negative 9.0
kilojoules per mole of reaction. Since delta G naught is negative, the dissolution of solid sodium chloride is a thermodynamically favorable process, which means at 25 degrees Celsius, sodium chloride is soluble in water. Notice how in this case, the favorable positive
entropy term outweighs the unfavorable positive enthalpy term to give a negative value
for delta G naught. Therefore, for the dissolution
of sodium chloride, the increase in entropy
drives the dissolution. Next, let's do the same calculation for the dissolution of solid
magnesium chloride and water to form the magnesium two plus cation and two chloride anions. We've already seen how the
increased positive charge of the Mg two plus cation in solution gave us a negative
value for delta H naught and a negative value for delta S naught. So, plugging in all our numbers and a temperature of 298 Kelvin, Kelvin cancels out and gives
us delta G naught of solution is equal to negative 125.8
kilojoules per mole of reaction. Since, delta G naught
of solution is negative, the dissolution of magnesium chloride is a thermodynamically favorable process. So, at room temperature
of 25 degrees Celsius, magnesium chloride is soluble in water. However, this time it's the
favorable negative value for the enthalpy term that outweighs the unfavorable negative value for the entropy term to give
a negative value overall for delta G naught of solution. So, this time it's the
decrease in enthalpy that drives the dissolution. Delta G naught has been negative
for both sodium chloride and for magnesium chloride. However, those are just the two examples that I chose for this video, it's certainly possible
to get a positive value for delta G naught of solution, which would mean an insoluble salt, and because it can be very
difficult to predict the signs for delta H naught and for delta S naught for a particular salt, it's even more difficult to
predict if delta G naught is positive or negative
for that particular salt. Therefore, it's often
necessary to do a calculation to see if delta G naught
is positive or negative.