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# Solution Representations

When you pour sugar into a hot coffee or tea and swirl it around, it disappears like magic. So why does the sugar disappear? Are we all witches and wizards who can cast very mundane spells? While that would be fun, that isn't the case. The sugar isn't actually "disappearing", it's just been dissolved, so it isn't a (visible) solid anymore. The sugar turns into it's ions and becomes a part of the coffee/tea solution.

In this article, we will be learning how solutions are formed and how we represent solutions.

• First, we will look at the different types of solutions
• Next, we will learn the steps of solution formation and walk through each step
• Next, we will look at how energy changes during solvation
• Lastly, we will learn about the particle model and work on some examples using it.

## Types of solutions

A solution is a mixture where a solute is dissolved in a solvent and is distributed evenly within the solvent.

There are several types of solutions. These types are dependent on the state of the solute and solvent. Here is a table listing the different combinations:

 Solution Solute Solvent Example gas gas gas Air liquid gas liquid Soda (CO2 is dissolved in the water/soda) liquid liquid liquid Alcoholic drink (ethanol in water) liquid solid liquid Salt water solid gas solid H2 dissolved in platinum solid solid liquid (liquid) mercury in gold

## Steps of solution formation

The process of solution formation is simple and is only 3 steps. These are:

1. Solvent expansion
2. Solute expansion
3. Formation of solution

Here is a diagram of these steps:

Steps of the solution process. StudySmarter Original.

While traditionally noted as occurring in three steps, the process can also be though of as just two steps, since the expansion of the solvent and solute happen concurrently.

## Expanding the solvent

During the solvation (solution formation) process, the solvent has to expand, so the solute particles can fit. Energy is used to push the molecules apart, breaking the solvent-solvent interactions.

Below is an example of water expanding:

Water expands to let the solute in. StudySmarter Original.

The dashed lines represent the solvent-solvent interactions. The slightly negative oxygen is attracted to the slightly positive hydrogen. As the solvent expands, these interactions are broken, so new solute-solvent interactions can happen.

It is important to remember that solvation is not a chemical process, it is a physical one. Just as the solvent can be expanded to let the solute in, it can also be compressed to kick the solute out.

### Expanding the solute

Just as the solvent expands, the solute expands too. Below is an example of salt (NaCl) expanding:

Salt expands so it can fit into the solvent. StudySmarter Original.

Like with the solvent, the solute expands to remove the internal interactions (solute-solute) so that solute-solvent interactions can occur. The solute particles also expand, so they can fit inside the solvent.

## Solute solvent interactions

The last step is the formation of the solution. The solute "fits" into the solvent, and new solute-solvent interactions take place. Here is a diagram of these interactions in salt water:

The water solvent "accepts" the salt molecules and new interactions are formed. StudySmarter Original.

The negatively charged chlorine is attracted to the partially positive hydrogen, while the positively charged sodium is attracted to the partially negative oxygen.

These interactions are why we don't see the salt in the water. The salt has been broken down and is now a "part" of the water. Solutions are considered homogeneous since their composition is uniform.

## Solvation processes

Now that we've seen each step in action, let's talk energy.

The expansion step(s) are endothermic, while the formation step is exothermic.

In an endothermic reaction, there is a net gain of heat. In an exothermic reaction, there is a net release of heat.

The net gain/release of heat is dependent on the energy of the individual solute and solvent versus the energy of the combined solution. The formula for this is $$\Delta H_{soln}=\Delta H_1+\Delta H_2+\Delta H_3$$ Where ΔH is the enthalpy (heat energy) of each step.Below is a diagram showing the change in enthalpy for a net endothermic and net exothermic reaction.

Depending on the energy of the solute/solvent and the solution, the solvation reaction is either exothermic or endothermic. StudySmarter Original.

In an exothermic solvation, the enthalpy of the solute and solvent is higher than that of the solution. Since the heat energy is overall decreasing, ΔHsoln< 0.In an endothermic solvation, the enthalpy of the solute and solvent is lower than that of the solution, so ΔHsoln> 0.The magnitude and sign of ΔHsoln is a good indicator of whether a solution will occur (i.e will the solute dissolve?). If ΔHsoln is large and positive, the solution probably won't occur, however a large, negative ΔHsoln means the solution is very likely to occur. A small ΔHsoln of either sign means the solution is likely to occur. A good way to think of the enthalpy change is like pushing a cart up or down a hill. If you push a cart down a hill, it is pretty easy. If you are trying to push it up a hill, the size/steepness of the hill will determine if you can actually push it.

While a large (+) ΔHsoln typically means no solution will occur, there are some instances where that isn't the case. Ammonium nitrate (NH4NO3) has a ΔHsoln of 25.4 kJ/mol, which is why it is used in cold packs. When the packet is squeezed, water and ammonium nitrate come into contact and the ammonium nitrate will dissolve. This reaction pulls in heat from the surroundings, so it feels cold to the touch and can be used to treat injuries.

## Representation of solutions

Now that we've learned all about the solvation process, let's talk about how we represent solutions. We normally use the particulate model, which is what the previous diagrams have been using.

The particulate (particle) model represents species as particles and shows how they behave based on their state, temperature, and attractions.

When we look at solutions in the particle model, there are three things we need to pay attention to: 1. Are the particles in the correct ratios? (Ex: NaCl is 1:1 Na and Cl) 2. Are the particles facing the right way? (Ex: Positive particles will be facing negative ones due to attraction) 3. What is the concentration of the solution? (Ex: Is there 3 mol of NaCl or 4 mol?)
The way we measure concentration is in units of molarity, which is mols/liter. In the particulate model, we consider 1 particle to equal 1 mol. For example, if there are 3 mols of NaCl in 2 liters of water, then the concentration is 1.5 M NaCl.

## Representation of solution example questions

Let's move on to some example questions.

For the diagram below, is this an accurate model for CaCl2 in water?

CaCl2 solution. StudySmarter Original.

Since we aren't asked about concentration, we need to focus on our first two questions: Is the ratio correct and are the particles facing the correct way?

To check our ratio, we need to count how many particles of Ca and Cl there are. There are 3 of each, so there is a 1:1 ratio of Ca to Cl. This means the ratio is incorrect, since the ratio should be 1:2 based on the chemical formula (CaCl2).

Next, we need to make sure that the particles are facing the correct way. Hydrogen (in green) has a partial positive charge and should be facing the negatively charged chlorine, while the partially negative oxygen (in blue), should be facing the positively charged calcium. Based on our diagram, this is the case, so the orientations are correct.

While the orientations are correct, the ratio isn't, so this is not an accurate model of a CaCl2 solution.

Now let's look at an example that focuses on concentration.

Based on the diagram below, rank the solutions from least to most concentrated.

The concentration is based on number of particles and total volume. StudySmarter Original.

Let's start by calculating the concentration of solution A and then we will move from left to right.

Solution A has 6 mols of particles and has a volume of 2 liters, so it has a concentration of 3 M.

Solution B has 4 mols of particles and has a volume of 1 liter, so it has a concentration of 4 M.

Solution C has 5 mols of particles and has a volume of 2 liters, so it has a concentration of 2.5 M.

Lastly, solution D has 9 mols of particles and has a volume of 3 liters, so it has a concentration of 3 M.

Ranking these from least to most concentrated, we get:

Solution B < Solution A = Solution D < Solution B

Let's so one last example, shall we?

Draw a solution of AlBr3 with a concentration of 2 moles. If there is 3 L of water in the solution, what is its concentration?

Our first step is to count how many particles of each we need. There is a 1:3 ratio of Al to Br, so since we want a 2 mol concentration, we need 2 mols of Al and 6 mols of Br.

Next, we need to know what direction the water molecules should face. Aluminum has a +3 charge, so oxygen will be drawn to it. Bromine has a -1 charge, so hydrogen will be drawn to it.

Now we can draw our solution, which would look something like this:

Balanced solution diagram of AlBr3. StudySmarter Original

For the last portion of the question, all we need to do is divide the number of moles by the volume. Since we have 2 moles per 3 liters, the concentration is 0.67 M

## Solution Representations - Key takeaways

• A solution is a mixture where a solute is dissolved in a solvent and is distributed evenly within the solvent.
• The 3 steps of solvation are:
1. Solvent expansion
2. Solute expansion
3. Formation of solution
• In an endothermic reaction, there is a net gain of heat. In an exothermic reaction, there is a net release of heat.
• The expansion step(s) are endothermic, while the formation step is exothermic.
• The particulate (particle) model represents species as particles and shows how they behave based on their state, temperature, and attractions.
• When looking at particle models we focus on:
• Ratio of particles
• Orientation of particles
• Concentration of particles

The three steps are:

1) Solvent expansion

2) Solute expansion

3) Formation of solution

We draw the ions of each dissolved solute, making sure they are in the correct ratio (Ex: AlBr3 would have 3 Br- ions for every 1 Al3+ ion). Then you add the solvent particles, making sure the ions are facing the correct way. (Ex: the hydrogen in water are partially positive, so they will face anions).

Solvation can be either endothermic or exothermic, depending on the energy of the individual solute and solvent versus the energy of the solution. However, the expansion of the solute/solvent is endothermic, and the formation of the solution is exothermic.

Some examples of different solutions are:

• Air (gas solute + gas solvent)
• Soda (gas solute + liquid solvent)
• Salt water (solid solute + liquid solvent)

The solute and solvent expand for two reasons:

1) To break the solute-solute and solvent-solvent interactions so solute-solvent interactions can be formed

2) So they each have space to fit into each other (solvent needs "room" for the solute. The solute needs to be far apart enough to fit in these gaps).

## Final Solution Representations Quiz

Question

What is a solution?

A solution is a mixture where a solute is dissolved in a solvent and is distributed evenly within the solvent.

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Question

Which of the following is NOT a possible combination to form a solution?

A liquid solute and solid solvent

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Question

In soda, which is the solute, and which is the solvent?

CO2 is the solute and water/soda is the solvent

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Question

What are the three steps in solution formation?

1. Solvent expansion
2. Solute expansion
3. Formation of solution

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Question

Which of the following are reasons why the solvent expands? (Select all that apply)

To open up space for the solute

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Question

True or False: Expansion of the solute and solvent are exothermic processes

False

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Question

What is the formula for $$\Delta H_{soln}$$?

$$\Delta H_{soln}=\Delta H_1+\Delta H_2+\Delta H_3$$

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Question

Fill in the blanks: When the solute/solvent are higher in energy than the solution, solvation is a ___ process. When they are lower in energy, it is a ___ process

Exothermic, Endothermic

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Question

In which of these cases is a solution NOT likely to occur?

$$\Delta H_{soln}>0\,\text{and is large}$$

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Question

What is the particulate/particle model?

The particulate (particle) model represents species as particles and shows how they behave based on their state, temperature, and attractions.

Show question

Question

When looking at particle models, what factors do we focus on?

• Ratio of particles
• Orientation of particles
• Concentration of particles

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