Mixtures

To understand mixtures, you will need to understand the intermolecular attractions that cause or allow things to mix. You will also need to understand the process of mixing. You will need to understand the differences between solutions, colloids and suspension and you will need to understand colligative properties. You should also know something about the Tyndall effect. In addition there is some terminology related to mixtures and mixing that you will need to understand.


Mixture Terminology

The following are words that have very specific meaning as they relate to mixtures and mixing


solvent – the thing that something else is dissolved into. In salt-water, the water is the solvent.


Solute – the thing that is dissoved into something else. In salt-water, the salt is the solute


solution – the mixture of the solute and solvent. In salt-water, the salt-water is the solution.


Solvation – the process of dissolving.


miscible – two liquids are miscible if they can be mixed in any proportions. For example, ethanol (ethyl alcohol, C2H5OH) is miscible with water. So, it is possible to have a mixture that is 1% ethanol and 99% water or a mixture that is 99% ethanol and 1% water (or anything in between).


Mixed phases

Foam – a foam is a mixed phase material where a gas is trapped in a liquid. For example, whipped cream is a foam. Styrofoam is a foam because it forms as a liquid and then hardens.


Smoke – a smoke is a mixed phase material where a solid is in a gas.


Mist – a mist is a mixed phase material where a liquid is in a gas. This is what fog, and clouds are.


Gel – a gel is a mixed phase material where a liquid is trapped in a solid. Jello is an example of this type of material. That is why, when you scoop out some jello from a large bowl, water collects in the depression. You can imagine the gel as a sponge, and when you cut it, all of the tiny little (liquid-filled) bubbles at the edges are broken open and the liquid can spill out.


Solvation

Solvation is the scientific name for the process of dissolving. To explain this process we will use the example of sodium chloride (table salt) dissolving in water.

When a crystal of table salt is added to water, the ions on the corners of the salt are vulnerable (since they are only in contact with 3 opposite ions and there is a great deal of open space around the ion where it can come in contact with the solvent.

Image – vulnrble

These corners can be surrounded by water molecules which are attracted by an intermolecular attraction (in this case ion-dipole attractions).

Image – NaCl_H2O

As the ion jostles around (because everything moves a little) water molecules can “sneak” in behind further separating the chloride from the rest of the crystal. Eventually the ion can be pulled entirely aware from the crystal.

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At that point the ion is dissolved. There are are three important things to note about that moment. The first is that the dissolved ion is not alone. Rather it is surrounded by water molecules. The second is that the removal of this ion exposed three more to “attack” by water molecules. The third thing to make sure that you understand is that dissolved sodium chloride is NOT sodium chloride with waters around it, it is comprised of separate ions. In other words, when an ionic solid dissolves it separates into its constituent ions. However this process CANNOT break covalent bonds. That means that when sodium sulfate dissolves, the sodiums separate from the sulfate, but the sulfates do NOT separate into individual atoms. Similarly, table sugar (sucrose, C12H22O11) dissolves, it separates into separate molecules, but not into separate atoms.


Types of mixtures

There are three general types of mixtures which are separated by the size of the particles present.


A solution is a mixture in which the solute is broken down into its smallest constituent parts. In other words, the solute is entirely broken down into individual ions or molecules.

Image – soln

A colloid is a mixture in which the solute is broken down into pieces that are too small to see with the naked eye, but are large enough to interfere with visible light. As a result, colloids are cloudy.

Image – colloid

A suspension is a mixture in which the solute particles are large enough to be seen by the naked eye. In addition, the particles are large enough for gravity to cause them to settle.

Image – susp

So, in simplest terms, the difference between solutions, colloids and suspensions is the size of the solute particles.

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Colligative Properties

Colligative properties are those that exist for solutions, and which are generally measured in comparison to a sample of the pure solvent. Don't worry, I know that doesn't make a lot of sense, but there is no good way to say it without a specific example. So, let's get to it.

There are 4 colligative properties that you should know about. They are:

Decreasing Vapor Pressure – the vapor pressure of the solvent decreases when a solute is added. (In simpler English – the vapor pressure of salt-water is less than that of pure water.)

Boiling Point Elevation – the boiling point of a solution is higher than that of the pure solvent. (In simpler English – the boiling point of salt-water is higher than that of pure water.)

Freezing Point Depression – the freezing point of a solution is lower than that of the pure solvent. (In simpler English – the freezing point of salt-water is lower than that of pure water.)

Osmotic Pressure – The tendency of a solvent to move through a semi-permeable membrane is decreased when a solute is added. (In simple English – water will go through your skin faster than salt water will). This will require the most explanation, but it is worth understanding since this describes more real-world experiences than the others do.


Decrease of Vapor Pressure

Be sure before you read this that you understand what vapor pressure is.

When a solute is added to a solvent several things happen. First since we can assume that there is an attraction between the solvent and the solute that is similar in strength (or stronger) than the solvent's attraction for itself, it should not surprise you that these additional attractions will make it more difficult for molecules of the solvent to break away and evaporate. A decrease in the amount of evaporation will cause a decrease in the vapor pressure (since amount and pressure are inversely related according to the Un-named Gas Law). In addition, the number of particles on the surface (and therefore available to evaporate will be less (since some of those spaces will be occupied by solute particles). This will also decrease the numnber of solvent particles that can evaporate and therefore decrease the vapor pressure.


Vapor Pressure

Vapor pressure is a measure of the tendency of something to evaporate. Understanding how it is measured may help to make sense of this idea.

Image a container that is truly empty (vacuum, not filled with air). The pressure inside such a box would be zero.

image – box

Now imagine that we could magically insert a small amount of a liquid into the space.

Image – box_n_liq

Within the liquid we know that there will me some molecules moving faster and some more slowly (Boltzmann). The fastest ones will break free from their neighbors and evaporate. As a result, there will now be pressure as these particles bounce against the walls of the container.

Image – box_evap

It might be tempting to think that the pressure in the box will continue to rise as more and more of the liquid evaporates. You may even expect that all of the liquid will evaporate, but Boltzmann comes back to haunt us here. As soon as there are particles in the gas phase, we can look at the distribution of speeds for those molecules. Some of them will be fast, but some of them will be very slow. These slow molecules, if they bump into each other, or the surface of the liquid will condense. So, while the liquid is evaporating, the gas is condensing.

Image - box_ev_cond

Initially the rate of condensation is very slow (there isn't much gas there) but as more and more of the liquid evaporates, the rate of condensation will increase until it is EQUAL to the rate of evaporation. At that point the amount of particles in the gas phase will stop changing, and so will the pressure.

That pressure (when the rate of evaporation and condensation are equal) is called the vapor pressure.

Image – box_vp

One thing that you should know is that vapor pressure is dependent on temperature. At higher temperatures, more molecules are moving quickly and therefore more will evaporate. In the hotter gas, fewer of the molecules will be going slowly enough to condense, so more will need to evaporate before the two rates can be the same. With more material in the gas phase, the pressure of that vapor will be higher. Of course the opposite is true when the temperature is decreased. This temperature dependence means that you can look up the vapor pressure of water (and some other liquids) on a table that will tell you the expected vapor pressure at various temperatures.

The last point you should understand is that since (as Dalton's Law of Partial Pressures tells us) gases ignore each other, the box (in the example above) does NOT have to be empty to work. The change in the pressure that results from the evaporating liquid will be the same whether the pressure starts at zero (a vacuum) or at some other value.


Boiling Point Elevation

Boiling point elevation is based on the decrease in vapor pressure in a solution, so you will need to understand that first.

One of the definitions of boiling point is the temperature at which the vapor pressure is equal to the atmospheric pressure. Normally then, the vapor pressure of water at 100oC is 1 atmosphere. However, since a solution has a lower vapor pressure, then the vapor pressure of salt-water (for example) at 100oC will be lower than the atmospheric pressure. This means that you will need to heat the solution to a higher temperature before the vapor pressure is the same as the atmosphere.

There is also some math that can be done related to this idea. The formula used is:

image – fpd_form

where the ΔT is the increase in the boiling point compared to the pure solvent, kb is the boiling point elevation constant (which depends on the identity of the solvent), m is the molality of the solution, and i is the vant Hoff factor.

Here is a sample problem:

What is the boiling point of a solution made by dissolving 12.7 g of NaI into 578 g of water if the kb for water is 0.51oC/molal?

Setting up the equation

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it becomes clear that we need to calculate the molality of the solution

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substituting in, we find ΔT = &&&&&. Since the normal boiling point of water is 100oC, the boiling point of this solution will be *****oC.

We can also do some useful algebra on this formula. We start by remembering that molality is mols of solute per kg of solvent.

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then we remember that moles of solute is equal to grams of solute divided by the molar mass of the solute.

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Lastly we can rearrange this formula to solve for the molar mass.

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This allows us to solve a problem like this:

If 1.3 g of a non-ionic solid dissolved in 10.67 g of benzene cause the boiling point to rise from 76.8oC to 81.5oC what is the molar mass of the solute?



Vant Hoff Factor

The vant Hoff factor is equal to the number of particles that a substance breaks into when it dissolves in the solvent. It's easier to see with an example:

NaCl breaks into Na+ and Cl- so i = 2

Na2S breaks into 2 Na+ ions and 1 S-2 ion so i = 3

Na3PO4 breaks into 3 Na+1 ions and 1 PO4-3 ion (remember that dissolving does NOT break the covalent bonds inside the phospahte ion, so i = 4

C12H22O11 is non-ionic, so it doesn't break up at all. Therefore i = 1


Units of Concentration

There are several units of concentration that you will need to be familiar with in order to do the math associated with colligative properties. They are:

Molarity (M) – molarity is the mols of solute over the liters of solution

Molality (m) – molality is the moles of solute over the kilograms of solvent

Mole Fraction (Χ, this is a chi from the Greek alphabet not an x) – mole fraction is the moles of solute over the total moles in the mixture (solute + solvent). However, it is important to note that the mole fraction can also be found for the solvent (instead of the solute) in which case it is the moles of solvent over total moles.