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# Enthalpy of Solution and Hydration

The table salt: Try to melt a spoonful of it by supplying heat. It is going to take forever to melt because the melting point of NaCl is as high as 800°C.

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This invincible substance, NaCl is vulnerable to water, always on its best behaviour. When we add the table salt to the water, It just vanishes in no time just with a good stir. Poof!

So, why does this happen? How water can break those oh-not-so-easily-breakable bonds?

Thermodynamics answers these questions logically. Let us explore the concepts of enthalpies of solution and hydration to understand the logic behind this interesting behaviour of salts.

• We are going to see the definition of the enthalpy of solution and the enthalpy of hydration.
• The equation for each enthalpy.
• The explanation of how these two enthalpies are different.
• Detailed examples and calculations of each.
• How lattice enthalpy can link these two concepts.
• How you can create energy cycles to calculate for unknowns.

## Enthalpy of Solution and Hydration Explanation

Here we will go over what each of the terms enthalpy of solution and enthalpy of hydration individually. We will also mention what lattice enthalpy is in this context.

But first of all, a recap on what enthalpy really is:

Many of us think enthalpy is just "energy", but we have to think about energy in thermodynamic contexts.

Enthalpy is the total heat content (energy) of a system, as calculated by the sum of internal energy and the product of the pressure and volume of that system

It is expressed as:

$$H = U + p\cdot V$$

Where:

• H = Enthalpy.
• U = Internal energy.
• p = Pressure.
• V= Volume.

So if enthalpy can be correlated to the total energy of a system, why are there different enthalpies for similar reactions? Well, all the reactions and processes we will be looking at are actually quite different from a thermodynamic point of view, which we will explore and see how they all relate.

### Enthalpy of Solution

So what is the enthalpy of solution?

The standard enthalpy change of a solution is the change in enthalpy when one mole of an ionic substance dissolves in large amounts of solvent to give a solution of infinite dilution.

### Infinite dilute solution

An infinite dilute solution is a solution which has excessively large quantities of solvent that adding more solute will not cause any absorption or evolution of heat. Also, there will not be any change in the concentration of the solution despite adding more solute.

Note: For the next part of this article, 'water' is considered as the 'solvent' of interest for convenience

What happens when you add a mole of table salt to large amounts of water? If the water is pure, and there are no other constituents in it, the interactions between the solute added, and the water molecules can be clearly established. The enthalpy change will be minute in a very dilute solution (excess solvent).

What type of interactions are we referring to?

The ion-dipole interactions between the solute (XY, for example) and the solvent. Water is a polar solvent-meaning it has a dipole moment-a partial negative charge on oxygen and a partial positive charge on hydrogens. This charge separation (into partially positive and negative) gives it the superpower of attracting the solute ions.

The partially negative oxygen attracts the positive ion of the solute (X+) while the anion of the solute (Y-) loves to be around the partially positive hydrogens. These interactions between the solute ions and the solvent molecules are called ion-dipole interactions which are responsible for the dissolution of a solute. It is all in the name. Ion refers to the ions of the solute while dipole refers to the dipolar water molecule (having two polar heads-oxygen and hydrogen).

These ion-dipole interactions are responsible for the breakdown of the lattice (weakening the electrostatic attraction between ions in the lattice). They trigger the separation of the solute into its ions.

$XY_{(s)} + aq \rightarrow X^+_{(aq)} + Y^-_{(aq)}$

Let us visualize the ion-dipole interactions below:

Enthalpies of solution can be either endothermic, meaning they take up energy, or exothermic, meaning they release energy. This all depends on the solute and its chemical nature, meaning that the key factor in this is the type of ionic compound being dissolved. Can you see why?

### Enthalpy of Hydration

In this section, we will go over what the enthalpy of hydration is, and you will be able to clearly see how it differs from the enthalpy of solution.

We have defined what enthalpy of solution is, and how it connects to the lattice enthalpy, but what happens to the ions individually? In other words, what happens at the ionic level, so far, we have been looking at this dissolution of compounds at the molecular level.

So what is the enthalpy of hydration?

The standard enthalpy of hydration is the enthalpy change associated with the dissolution of one mole of gaseous ion to its aqueous form.

Let's see an example:

$$X^+(g) + Y^-(g)\rightarrow X^+(aq) + Y^-(aq)$$

The standard enthalpy change is a measure of the energy released by water molecules and the ions that attract and associate with each other.

If the lattice enthalpy describes the energy required to break the ionic bond, and the enthalpy of solution states the enthalpy change of the dissolution of the ionic compound, the enthalpy of hydration can account for the gap between the two values.

Enthalpy of hydration releases energy as it accounts for the formation of ion-dipole interactions. These are the interactions between the ion in question and the dipoles present on water molecules, with the partially positive force on the hydrogens and the partially negative force on the oxygen. Therefore, hydration enthalpies are exothermic

## Enthalpy of Solution and Hydration Equation

In this section, you will see how we can describe the concepts of enthalpy of solution and enthalpy of hydration through thermodynamic equations and cycles.

Firstly, the enthalpy of solution can be stated as the dissolution of an ionic compound. We can look at it in this way:

$XY_{(s)} + aq \rightarrow XY_{(aq)}$

or

$XY_{(s)} + aq \rightarrow X^+_{(aq)} + Y^-_{(aq)}$

In the example above, the X+ is the cation, while the Y- is the anion.

Secondly, the enthalpy of hydration can be described as the following equation:

$X^+_{(g)} + aq \rightarrow X^+_{(aq)}$

You can write the same equation but for the anion too.

Did you know, these two thermodynamic concepts are actually connected? There is another formula you should know that actually link the two. Here it is:

$\Delta H^\circ_{sol} = \Delta H^\circ_{lat} + \Delta H^\circ_{hyd}$

What does the equation trying to communicate?

It establishes the link between the lattice enthalpy (of dissociation in this case), enthalpy of solution and hydration.

To be clear, let us put it this way. You take salt which is in a solid state (obviously) and break it into its individual ions in the gaseous state. The ions are far apart from each other with no forces of attraction left between them in the gaseous state. The enthalpy change for this process is lattice dissociation enthalpy, $$\Delta H^\circ_{lat}$$

When you take the dissociated ions in the gaseous state from the above step and put them in water. The individual gaseous ions are now surrounded by water molecules via ion-dipole interactions. The enthalpy change for this process is the enthalpy of hydration, $$\Delta H^\circ_{hyd}$$ . This is just an indirect route of obtaining ions in aqueous state.

Now, you take some salt again. It is now in a solid state. Instead of dissociating it into ions that exist in the gaseous state, you mix it in water. The salt dissolves completely in water, dissociating into ions. The enthalpy change for this process is the enthalpy of the solution, $$\Delta H^\circ_{sol}$$. This is the direct route of obtaining ions in aqueous state.

What did you observe? How are the 3 processes linked?

The enthalpy of solution is a direct way of dissociating ions and hydrating them. It combines the process of dissociation of salt into ions (lattice enthalpy of dissociation) and then dissolving them in a solvent (Enthalpy of hydration).

Therefore, the sum of the enthalpies of hydration and lattice enthalpy of dissociation gives us the enthalpy of the solution.

## Enthalpy of Solution and Hydration Differences

The enthalpies of solution and hydration are linked, yet they are not the same. Let us now explore some subtle differences between these seemingly alike phenomena.

 Enthalpy of solution $$\Delta H^\circ_{sol}$$ Enthalpy of hydration $$\Delta H^\circ_{hyd}$$ Deals with Ionic compounds as a whole (Eg: NaCl) Deals with gaseous ions [Na+(g)] The process of dissociation into ions(break down of lattice), formation of ion-dipole interactions happen in a swoop simultaneously. The first step is the breakdown of the lattice into gaseous ions. The gaseous ions now dissolve in water to form aqueous ions. It can be exothermic or endothermic It is exothermic A direct route/path to dissolution An indirect path to dissolution The sum of lattice enthalpy and enthalpy of hydration is the enthalpy of solution The difference between the enthalpy of solution and lattice enthalpy is the enthalpy of hydration

## Enthalpy of Solution and Hydration Example

Here we will take a look at some real-life examples at the enthalpies of solution and hydration, and we believe that you will be able to establish the relationship between them while appreciating the subtle differences.

The example we will be using for the equations above is the dissolution of sodium chloride (NaCl) in water. Firstly, the enthalpy of solution can be constructed into the following equation:

$NaCl_{(s)} + (aq) \rightarrow Na^+_{(aq)} + Cl^-_{(aq)} \qquad \Delta H^\circ_{sol} = +1 \space kJmol^{-1}$

Now below are the equations for the enthalpies of hydration of each of the ions.

$Na^+_{(g)} + (aq) \rightarrow Na^+_{(aq)} \qquad \Delta H^\circ_{hyd(cation)} = -406 \space kJmol^{-1}$

$Cl^-_{(g)} + (aq) \rightarrow Cl^-_{(aq)} \qquad \Delta H^\circ_{hyd(anion)} = -364 \space kJmol^{-1}$

Can you see how the values for the enthalpies of solution and hydration of ions are so different?

This is because each one is involved in a different process and shows the energy values for a completely different phenomenon. As you can see the enthalpies of hydration are exothermic, meaning that they give off a lot of energy, while the enthalpy of solution is very low. When you mix a tablespoon of salt into water, do you get a vigorous reaction? Not usually, and that is supported by the enthalpy of solution being a low value. In fact, if the enthalpy of solution is just a bit more positive, the compound will not dissolve. That explains why some salts are soluble while the others are not.

You can, calculate the lattice enthalpy if you know the values of the enthalpy of solution and hydration. Take a look at the example below:

We can use this formula to find the lattice enthalpy: $$\Delta H^\circ_{sol} = \Delta H^\circ_{lat} + \Delta H^\circ_{hyd}$$

the values are:

Enthalpy of solution = +1 kJ per mole.

Enthalpy of hydration of Na+ = -406 kJ per mole

Enthalpy of hydration of Cl- = -364 kJ per mole

thus plugging in the numbers:

$$+1 = \Delta H^\circ_{lat} + [(-406) + (-364)]$$

rearranging the equation:

$$\Delta H^\circ_{lat} = +1 - [(-406)+(-364)]$$

finally solving the equation:

$$\Delta H^\circ_{lat} = +771 \space kJmol^{-1}$$

You can calculate any of the three enthalpy constants if you know the other two! In the next section we will take a look of how this relationship can be viewed diagrammatically.

## Enthalpy of Solution and Hydration Relation

In this section we will take a look at the relationship between these two closely related thermodynamic concepts. Did you know you can actually create energy cycles from these two concepts and link them through the lattice enthalpy? Take a look at the figure below, which explains how you can connect these two concepts together, and more importantly how you can calculate any of these values if you know two of them.

Energy diagram, Enthalpy of solution and hydration

In this article, you should have gained a strong grasp on the topics of the enthalpy of solution and the enthalpy of hydration, and more importantly their differences! Knowing these thermodynamic concepts will also help you in all types of different chemical topics and concepts.

## Enthalpy of Solution and Hydration - Key takeaways

• The enthalpy of solution is the enthalpy associated with the energy released when one mole of an ionic solution is dissolved in water.
• The enthalpy of hydration is the enthalpy associated with the energy released when one mole of gaseous ion is dissolved in water.
• You can calculate these thermodynamic concepts with the following equations:
• enthalpy of solution: $$XY_{(s)} + aq \rightarrow X^+_{(aq)} + Y^-_{(aq)}$$
• enthalpy of hydration: $$X^+_{(g)} + aq \rightarrow X^+_{(aq)}$$
• These two concepts can be linked by the lattice enthalpy, as described by the equation: $$\Delta H^\circ_{sol} = \Delta H^\circ_{lat} + \Delta H^\circ_{hyd}$$

#### Flashcards in Enthalpy of Solution and Hydration 15

###### Learn with 15 Enthalpy of Solution and Hydration flashcards in the free StudySmarter app

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What is hydration enthalpy?

Hydration enthalpy is the energy associated with the dissolution of one mole of a gaseous ion to its aqueous state.

What is the difference between enthalpy of solution and enthalpy of hydration?

The enthalpy of solution concerns whole ionic compounds, while the enthalpy of hydration only the dissolution of sole ions.

How does enthalpy of hydration affect solubility?

If the enthalpy of hydration is large, then the compound is soluble.

What is the formula for enthalpy of hydration?

X+(s) + aq --> X+(aq)

## Test your knowledge with multiple choice flashcards

Is the enthalpy of hydration always exothermic or endothermic?

Which of the following enthalpies applies in this situation: dissolving a tablespoon of salt in water.

What is the following equation describing:Mg+(g) + aq = Mg+(aq)

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