Nearly all the solids, liquids, and gases that make up our world are mixtures. If you remember, a mixture occurs when two or more substances are mixed together but do not chemically combine (do not react). Soap is a mixture, glass is a mixture, seawater, soil, trees, and even you are a mixture. The larger the organism, the more complex the mixture. For example, a simple bacterial cell can contain over 5000 different compounds!
Recall that a mixture has two defining characteristics: first, the composition is variable (in contrast to a compound where the composition is fixed), and the mixture also retains some properties of its individual components.
A solution is a homogenous mixture, is uniform throughout, such that the properties are the same, no matter how many samples you take! Some examples of a homogeneous mixture (or solution) include hard alcohol, rubbing alcohol, and sugar water. Sometimes it is very difficult to tell that you have a mixture by simply looking at a solution – it looks like it might contain only one component – but in reality there is more than one component present. A heterogeneous mixture is not uniform throughout.
This means that every time you take a sample, it contains different components or different relative amounts of components. Heterogeneous mixtures are easier to identify as there are multiple phases present. Think vegetable soup! Every spoonful contains different vegetables. You would be waiting a
LONG time to dip your spoon into that soup and come out with the same vegetables and the same amount of liquid soup!
What’s new?
A colloid. A colloid is a heterogeneous mixture in which one component is dispersed as very fine particles in another component. It is very difficult to see that there are distinct phases present. Smoke and milk are colloids.
The difference between a colloid and a solution is one of particle size
In a solution, the particles are individual atoms, ions, or small molecules (e.g. like a sugar molecule)
In a colloid, the particles are either macromolecules or aggregations of small molecules that are not small enough to settle out (form a ppt layer)
We describe solutions in terms of one substance dissolving in another: the solute is dissolved by the solvent. Usually the solvent is the most abundant component in the solution; however, in some cases the substances are miscible, that is, soluble in one another in any proportion and therefore the terms solute and solvent are not meaningful.
The solubility of a substance is defined as the maximum amount of substance (solute) that dissolved in a fixed quantity of solvent at a specified temperature. Different solutes have different solubilities. For example, NaCl has a solubility value of 39.12 grams per 100 mL at 100 o C while AgCl has a solubility value of 0.0021 grams per 100 mL at 100 o C. Obviously NaCl is much more soluble than AgCl is in water.
Solubility has a quantitative meaning (think quantity), while the words dilute and concentrated are
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qualitative terms. When we speak of solutions being dilute and concentrated we are speaking of relative amounts of solute: a dilute solutions contains less solute than does a concentrated solution.
You are all familiar, I am sure, with the fact that some things dissolve in certain solvents and others do not. For example, butter does not dissolve in water. Oil does not dissolve in water, but butter will dissolve in oil. Understanding and applying knowledge of intermolecular forces will help you determine which solutes will dissolve in which solvents!
All intermolecular forces that were discussed previously apply to molecules in a mixture.
Ion-dipole forces are the principle factor in the solubility of ionic compounds. When a salt dissolves, each ion on the crystal’s surface is attracted to the oppositely charged dipole in the water molecule. The attractive forces between the ion and the dipole break down the crystal structure. Spaces start to develop between the ions; water is able to slide in between. This, in essence, shields the ion-ion attractions that hold the ions in the solid lattice. As the water molecules and ions are attracted to one another, the ionic solid “falls apart” otherwise known as dissolves. As each ion separates from the crystal lattice it becomes surrounded by water molecules forming a hydrated shell. For monoatomic ions, the number of water molecules that surround the ion is determined by the ion’s size. Smaller ions are surrounded by fewer water molecules than are larger ions. The formation of a hydrated shell is an ORDERED event. It is not random or jumbled. There is structure to these hydrated cations and anions.
Dipole-dipole forces and the H-bond are both very important in solutions. The H-bond is a primary factor in water’s ability to dissolve numerous oxygen and nitrogen containing compounds (remember that O or N with a lone pair was a necessary component in the ability to form an H bond) such as alcohols, sugars, amines, and amino acids!
There are two types of IMFs that depend on induced dipole forces. The first is the ion-induced dipole force. Remember that induced dipoles result because the electron cloud of a particle atom or molecule is able to be distorted, which results in the created on a dipole moment. This intermolecular force plays a role in the binding between the Fe +2 ion in hemoglobin and an O
2
molecule in the bloodstream. An ion can also intensify or strengthen a dipole that already exists in a molecule. Thus, this force contributes to the formation of any solution that contains ions. Coulomb’s law states that a greater charge results in a stronger energy of attraction and since ions have complete (and therefore greater charges) than a
2

molecule with a dipole moment (a partial charge), ion-induced dipole forces are stronger than dipoleinduced dipole forces. A dipole-induced dipole forces results when a molecule that has a dipole moment (e.g. a polar molecule) gets close enough to a non-polar molecule or atom such that the partial charge distorts the non-polar molecule’s electron cloud. This distortion creates or induces a dipole moment and the molecules are then attracted to one another. The solubility of O
2
and N
2
nonpolar molecules in water occurs because of this type of IMF.
Finally, do not underestimate the London dispersion forces that all species have. Dispersion forces contribute to the solubility of all solutes in all solvents. Remember they are the principal attractive force in non-polar molecules! For example, petroleum exists as a homogeneous mixture because of dispersion forces.
Remember that a solution can be a solid, liquid, or gas. In most cases, it is the phase of the solvent that determines the phase of the solution.
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From cytoplasm to tree sap, gasoline, iced tea, urine, cleaning fluids . . . solutions in which a liquid is the solvent are commonplace. Water is the most prominent liquid solvent (the “universal solvent”), it is abundant in the environment, and it has the ability to dissolve ionic, polar, and even nonpolar species.
Non-polar substances are substantially less soluble in water, but they are soluble in other non-polar solvents.
This leads to the “rule” that substances with similar types of intermolecular forces dissolve in one another – or like dissolves like.
Liquid-Liquid and Solid-Liquid Solutions
Many salts dissolve in water because the strong ion-dipole forces between the ions and the water molecules are very similar to the strong attractions that the ions have for one another and so they
“substitute” for them. The same salts are insoluble in non-polar solvents (such as hexane) because the ion-induced dipole force is too weak and the attraction is too small. The ions, thus have a stronger attraction to one another than to the hexane molecules and therefore would prefer to stay with the stronger attraction – and thus in the solid phase. Oil does not dissolve in water because the H-bonding that occurs between the water molecules is a much stronger attraction than the dipole-induced dipole attraction that occurs between the water molecules and the oil molecules. Thus, water would prefer to
“stick” to itself. Oil does readily dissolve in a non-polar solvent, such as hexane because the dispersion forces that are present in both individual non-polar species can be substituted for one another between the oil and hexane molecules. Thus, for a solution to form “like dissolves like” means that the forces that will be created between the solute and the solvent molecules must be comparative in strength to the forces in the individual components (the solute alone and the solvent alone). Thus solubility depends on three factors:
Solute-solute interactions (how strongly are the solute molecules attracted to themselves)
Solvent-solvent interactions (how strongly are the solvent molecules attracted to themselves)
Solute-solvent interactions (how strongly are the solute and solvent molecules attracted to each other)
Solubility can also be described in terms of disorder. Disorder is favored in the universe. In fact, the more disorder the better. It is the natural tendency of nature and most systems to become more disordered. Disorder is the lower energy state. Think about it: is it easier or harder to make a mess r or keep your room clean? What about letting the dishes pile up in the sink vs. washing them?
Here is an obvious example of disorder: stack piles of nickels, dimes, and quarters heads up in a closed box. This system is very ordered, so it has low entropy (not a lot of disorder). If you pick up the box of coins and shake them, what happens to your nice stacks of coins? When they settle, the coins are going to lie randomly, in piles, alone, heads up and heads down. The disorder of the system has increased, and therefore so has its entropy. Common sense should tell you that if you shook that box for the next ten million years your coins will never land in the stacks that you started with. In fact, to put them back in the stacks, you would have to expend energy sorting and restacking them.
Disorder, otherwise known as entropy, occurs when solvents dissolve in solutes. Even though there are
IMFs occurring between species that dissolve, those IMFs have less order than their solute-solute or solvent-solvent counterparts. The molecules of water and salt, or alcohol molecules and water become intermingled. This mixing is disorder. In contrast, your initially impression might be that mixing a non-
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polar species with a polar species (like oil and water) would make the system more disordered also.
However, experimental evidence has shown that the oil and water do not mix. The introduction of a non-polar species into a polar species – such as water – causes the water to form a more ordered structure which does not favor mixing. So there must be another component that helps to govern solubility that works hand in hand with the entropy components. And it is actually a combination of both factors – enthalpy and entropy that determine if a solute dissolves in a particular solvent (we will discuss the enthalpy factor later). An increase in the entropy that accompanies dissolving favors solution formation; however, a decrease in enthalpy favors solution formation ( H) but an increase in enthalpy hinders dissolving. In many cases, an increase in enthalpy prevents a solute from dissolving, even though dissolution would create a “more” disordered system; the entropy factor is not enough. In some cases, the entropy increase is large enough to overcome the endothermic component: for example, dissolving NH
4
NO
3
is an extremely endothermic process – heat is absorbed by the system but the entropy component of disrupting the organized crystal lattice is large enough to make up for the heat absorbed. We will cover entropy more in depth next term: just know that disorder does play a role in whether or not a substance is soluble in another.
Gas-Liquid Solutions
Gases that are non-polar (such as O
2
and N
2
) have low boiling points because their IMFs are weak. In fact, they are subject really only to dispersion forces. Likewise, they are not readily soluble in water because the solute-solvent forces are weak. For non-polar gases, solubility parallels boiling points. The lower the boiling point, the less soluble the gas. In some cases, the ability of a non-polar gas to dissolve slightly into solution is essential to a process. O
2
dissolving in water – or in your blood for example!
Gas-Gas Solutions
All gases are infinitely soluble in one another!! Air is the classic example of gases that exist as a mixture.
Air consists of about 18 gases in widely different proportions.
Gas-Solid Solutions
When a gas dissolves in a solid it occupies the space in between the closely packed particles. You know that not all atoms are touching in a particular unit cell. We also know that gas molecules tend to be small. Sometimes this solubility is a good thing: for example hydrogen can be purified by passing as impure sample through a solid metal like Palladium. Using high pressure, the H atoms are passed along the Pd crystal structure and emerge as pure H
2
gas. Only H
2
is small enough to fit in the crystal structure. It can be a disadvantage. The ability of O
2
to penetrate copper wire causes the copper to react and form copper (I) oxide which reduces the conductive ability of the wire.
Solid-Solid Solutions
Because solids diffuse so little, their mixtures are usually heterogeneous, such as gravel or sand. Some solid-solid mixtures can be formed by melting the two solids, mixing them, and then allowing them to freeze (solidify) together. Alloys are examples of solid-solid mixtures (e.g. brass, carbon steel). Wax is another type of solid-solid solution.
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For one substance to dissolve in another, three events must occur: (1) solute particles must separate from each other, (2) some solvent particles must separate to make room for the solute particles, and (3) solute and solvent particles must mix together. No matter what the nature of the attractions within the solute and within the solvent, energy MUST be absorbed when particles separate and some energy are released when they mix and attract to one another. As a result of these interactions, the solution process is typically accompanied by a change in enthalpy – or the heat of solution.
Let’s examine this in a step by step manner:
Step 1: solute particles separate from each other: This step involves overcoming the IMF between the solute molecules; therefore we must put energy into the system. If we have to use energy, then this is an endothermic process.
Solute (IMF) + heat → solute (separated)  H solute
> 0
Step 2: solvent particles separate from each other. This step involves overcoming the IMF between the solvent molecules, therefore we must put energy into the system. If we have to use energy, then this is an endothermic process.
Solvent (IMF) + heat → solvent (separated)  H solvent
> 0
Step 3: solute and solvent molecules mix together. The particles are attracted to one another. New IMFs are formed between the solvent and solute molecules. Energy is given off so this is an exothermic process.
Solute (separate) + solvent (separate) → solution (IMF) + heat  H mix
< 0
The total enthalpy change that occurs when the solute molecules come apart, the solvent molecules come apart, and the solute and solvent particles come together is known as the heat of solution (  H solution
 H solution
is equal to the sum of the individual  H values:
). The
 H solution
=  H solute
+  H solvent
+  H mix
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if the sum of the endothermic processes (solute and solvent) is smaller than the exothermic process
(mix), then  H solution
will be negative. if the sum of the endothermic processes (solute and solvent) is larger than the exothermic process (mix), then  H solution will be positive.
Note: If the endothermic processes are significantly larger than the exothermic process, the substance may not dissolve (it takes too much energy to overcome the solute-solute and solvent-solvent interactions!!)
When ionic species dissolve in water, the process takes into account the ionic crystal breaking up
(termed the lattice energy) and the hydrated cage that forms when the water molecules surround the individual ions (termed hydration). Since hydration actually is a combination of the solvent-solvent particles separating from one another with the solvent-solute particles being attracted to one another,
 H hydration
is really the sum of  H solvent
In water, the equation then becomes:
+  H mix
!
 H solution
=  H solute
+  H hydration
The heat of hydration is a crucial factor in the dissolving of an ionic solid in water. The breaking of some
H-bonds in water is MORE than made up for when the ion-dipole interaction forms. This means that hydration is exothermic – it is a new attraction that forms, which is exothermic, and it will be a larger value than the endothermic process of disrupting the H-bonds in water. The energy required to separate an ionic solute into its ions takes energy, so  H
– which we already determined above. solute
is an endothermic process and therefore (+) in value
Heats of hydration exhibit trends based on the charge density of the ion, or the ratio of the ion’s charge to its volume. In general, the larger the charge density, the more negative the  H hydration value is.
According to Coulomb’s law: the greater the ion’s charge is and the closer an ion can get to another molecule, the stronger the attraction. Therefore:
A +2 ion will be more strongly attracted to a water molecule than a +1 ion of similar size
A small +1 ion attracts H
2
O molecules more strongly than a larger +1 ion
The effect of temperature on gas solubility is rather predictable. When a solid dissolves in solution, the solute particles must separate from one another and that takes energy. In contrast, the particles in the gas phase are already separated from one another! Thus, for gases dissolving in water the equation looks like:
Solute
(g)
+ H
2
O  saturated solution + heat
The double arrow indicates that the reaction can and will go in both directions. It also is another example of equilibrium that can be established. Reading the equation as written shows us that heat is a product in this reaction, which means that heat is “formed” or heat is given off.
Le Chatelier’s Principle tells us that whatever we do to a particular reaction, there will then be a consequence. The system will react to the change and reach equilibrium again. If more water were
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added to the system, then more solute could be dissolved forming a saturated solution. The reaction will shift AWAY from whatever is added – and since the reaction can go either direction, it can be read from right to left or left to right.
If heat is given off, and we raise the temperature of the solution, the reaction will be driven away from the heat and therefore goes back to the reactant side. This means that the gas will come out of solution – thus at higher temperatures, gases are LESS soluble in solution. Gases have weak IMFs and therefore the
IMFs between the gas molecules and the water molecules are also weak. When the temperature rises, the molecules are going to have more kinetic energy – more KE means that the molecules are able to overcome the weak IMFs that they might be experiencing and escape from the liquid phase and turn into a gas.
Increasing temperature of a solvent can have disastrous effects on the environment. Hot water can hold less dissolved O
2
. Fish and marine life need O
2
to survive. Less O
2
means less fish and marine life.
Solids are a little more erratic when it comes to temperature effects on solubility but in general, they follow the trend that the higher the temperature, the more soluble the solute. In this case, dissolving a salt in solution has the following equation:
Solute + solvent + heat  saturated solution
Now the heat is a reactant. If the reaction will shift AWAY from whatever is added, then increasing the heat will cause the reaction to shift towards saturation – or the dissolving of the solute. There are limits to this though! Raising the temperature does not suddenly make solutes infinitely soluble!
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Because solids and liquids are virtually incompressible, pressure has little effect on their solubility.
Gases, however, we know, are compressible. In fact, we know that gases have LOTS of space between their molecules.
At a given pressure, the same number of gas molecules enter and leave solution per unit time (the system is at equilibrium).
Gas + solvent  saturated solution
If the pressure is increased, the gas molecules will be compressed towards the liquid. More gas molecules will be in contact with the surface of the liquid. If the gas is interacting with the surface of the liquid more then there is a greater chance and an increase in the attraction between the gas molecules and the liquid. This attraction will solubilize the gas molecules – thus more gas is able to enter into the liquid phase. The gas will continue dissolving until the system reaches equilibrium again where gas molecules will enter and leave the liquid at the same rate.
This effect has long been used in the beverage industry where carbonated beverages are bottled under
CO
2
pressures of up to 4 atm. It is also used in oxygen therapy for CO poisoning and for certain infections such as gangrene. The use of high-pressure oxygen chambers are used to treat these conditions based on the fact that there will be increased solubility of O
2 pressures.
in the blood at elevated oxygen
A medically significant effect of increased gas solubility under pressure is the painful condition known as decompression illness which can be caused by the sudden reduction of pressure (atmospheric or under water!) on the body. Nitrogen gas, under normal atmospheric pressure is not really all that soluble in water or blood. However, under pressure, nitrogen gas can become soluble and enter the bloodstream of an individual. Nitrogen gas in the air (or in the tank) is dissolved in body fluids and as a person returns to normal atmospheric pressure, the nitrogen is less soluble. Returning to normal pressures too quickly can cause the nitrogen gas bubbles to come out of solution which get into the tissues, bloodstream, and lung capillaries. These bubbles exert pressure and clog small blood vessels.
Gradual decompression allows for the dissolved N
2
to exit the bodily fluids slowly with no bubble formation.
Henry’s Law: the solubility of a gas (S solution: gas
) is directly proportional to the partial pressure (P gas
) above the
S gas
= k
H
x P gas
Where k
H
is Henry’s Law constant and is specific for a given gas-solvent combination at a given temperature
S gas
units are in mol/L k
H
P gas
units are in atm
units are in mol/Latm
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Concept Test:
The partial pressure of carbon dioxide gas inside a bottle of cola is 4.0 atm at 25 o C. What is the solubility of CO
2
? Henry’s law constant for CO
2
at 25 o C = 3.3 x 10 -2 mol/Latm
We have already discussed some terms of concentration and some of these will be new. Concentration is an intensive property – meaning it does not depend on the quantity of the mixture – thus 1000 mL of 1.0
M NaCl will have the same concentration as 1 mL of 1.0 M NaCl. Concentration is most often expressed as the ratio of the quantity of solute to the quantity of solvent but sometimes it can be expressed as the ratio of solute to solvent.
Here are the common forms of concentration that we will work with:
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Molarity = M = moles of solute
L of solution
However, volumes are affected by temperature. Heating a solution causes its volume to expand slightly, so a unit of volume will actually contain less solute than the same volume of cold solution. Mixing certain liquids together can result in volume changes. This makes Molarity difficult to work with when doing precise work.
A concentration term that does not contain volume in its formula is molality (m), which is the number of moles of solute that are dissolved in 1000 grams (1 kg) of solvent: molality = m = moles of solute mass (kg) of solvent
Note that molality is expressed in terms of the quantity of solvent – NOT the total solution. Mass is not going to change with temperature, so neither will molality. However, since the density of water is approximately 1 gram/mL, 1L of water will have a mass of 1 kg, therefore molality and Molarity are nearly the same for dilute solutions.
Concept Test:
What is the molality of a solution that is prepared by dissolving
32.0 grams of CaCl
2
in 271 grams of H
2
O?
Other types of concentrations are based on the number of solute or solvent parts present per number of solution parts present. This results in a ratio so the numbers are “unitless” so to speak – but since there are several different ways of taking this ratio – you should indicate which method was used.
Parts of Solute by Parts of Solution: the ratios
The most common parts by mass is the mass percent. Mass percent of solute means the mass of solute dissolved per total mass of the solute plus the solution:
Mass % = mass of solute mass of solute
 mass of solvent x 100
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The units are often written as % (w/w) meaning the % weight to weight (more accurately it should say mass to mass . . .) note: you have probably seen parts per billion and parts per million on bottles before instead of multiplying by 100 you would either multiply by 10 9 (billion) or by 10 6 (million) to get your concentration
Another concentration ratio is volume percent.
Volume % = volume of solute x 100 volume of solution
The units are % (v/v)
Another concentration ratio is the mass to volume percent. This is very common in medical labs and combines a mass component (solute) per volume component (solution). m/v% = mass of solute x 100 volume of solution
Thus for a solution that is 1.5% m/v NaCl that means that there are 1.5 grams of NaCl per
100 mL of solution
We have previously discussed the mole fraction as being the number of moles of substance divided by the total number of moles present. The same formula applies here except you must remember that the total number of moles will also include the moles of solvent!
Mole Fraction = X
A
= moles of moles solute of solute
A
 moles
A of solvent and the Mole percent would be to take the mole fraction value x 100
Mole Percent = X
A
x 100
One might expect that the presence of solute particles might make the physical properties of a solution different from those of the pure solvent, however, what you might not expect is that, in the case of four important solution properties, it is the number of solute particles and NOT the identity of the solute that makes a difference. These properties, colligative or “collective” properties are vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.
The focus for colligative properties will be on solutes that do not dissolve into ions and have negligible vapor pressure even at the boiling point of the solvent. Such solutes are called non-volatile
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nonelectrolytes. Remember that an electrolyte is a species that conducts electricity or a current when it dissolves while a non-electrolyte did not. A non-volatile sample is one that does not readily turn into a gas. Sugar is an example of a non-volatile nonelectrolyte.
Vapor Pressure Lowering
The vapor pressure of a solution of a nonvolatile non electrolyte is always lower than the vapor pressure of the pure solvent. Remember that vapor pressure measures how readily a sample will turn into a gas and how much gas will be formed. The more the sample is converted from the liquid into the gas phase, the higher the vapor pressure. Vapor pressure lowering can be explained by entropy – or disorder. A mixture of solute and solvent has more disorder than the pure solvent. Since all systems want to achieve as much disorder as possible, a pure solvent solution “needs” to send more of its molecules into the gas phase to achieve disorder. Since a mixture already begins with disorder, fewer molecules need to go into the gas phase, thus a lower vapor pressure.
Raoult’s Law” the vapor pressure of solvent above the solution (P solvent
) equals the mole fraction of solvent in the solution (X solvent
) times the vapor pressure of the pure solvent (P osolvent ).
P solvent
= X solvent
x P osolvent
In a solution the mole fraction will always be less than 1, so P solvent
will always be less than P osolvent . An ideal solution is one that follows Raoult’s law at any concentration. However, just like gases deviate from the ideal gas law, solutions do not always behave ideally. In reality, Raoult’s law works best for dilute solutions.
How does the AMOUNT of solute that is dissolved in solution affect the magnitude of the vapor pressure lowering – or  P?
 P = X solute
x P osolvent
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Concept Test:
Calculate the vapor pressure lowering,  P, when 10.0 mL of glycerol (C
3
H
8
O
3
) is added to 5.00 x 10 2 mL of water at 50 o C. At this temperature the vapor pressure of pure water is 92.5 torr and its density is 0.988 g/mL. The density of glycerol is 1.26 g/mL.
Boiling Point Elevation
A solution will boil at a higher temperature than the pure solvent. The boiling point of a liquid is the temperature at which the vapor pressure equals the external temperature. The vapor pressure of a solution is lower than the external pressure at the solvent’s boiling point because the vapor pressure of a solution is lower than that of the pure solvent. This means that the mixture of solutions needs a higher temperature in order to boil. It is believed that one reason the boiling point is elevated is because of competition for space on the surface of the solution. When a solution boils, molecules on the surface leave and internal molecules also make their way through the solution to the surface. Solute molecules take up space at the surface and within the solution and “get in the way of” the solvent molecules attempting to leave the solution. So more energy must be put into the system to give the molecules the energy to overcome any IMFs the solvent molecules might be having with the solute and also to get out and past the solute molecules.
The magnitude of the boiling point elevation is proportional to the concentration of solute particles:
 T b
= K b mi where m is the solution molality, K and  T b b
is the molal boiling point elevation constant.
is the boiling point elevation i = the number of particles the solute makes in solution
Molality is used as the unit for concentration because it is directly related to mole fraction and thus to particles of solute. It also involves mass rather than volume (like Molarity) so it will not be affected by temperature changes. The K b
has the units of o C/m and is specific for given solvents.
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Freezing Point Depression
Only the solvent molecules vaporize from the solution, and the same applies for when the solution freezes. It is not the solute molecules that freeze, it is the solvent. The non-volatile solute molecules are left behind. Because the vapor pressure of the solution is lower than that of the solvent at any temperature, the solution will freeze at a lower temperature than the solvent.
 T f
= K f mi
K f
is the freezing point depression constant which has units of o C/m
Concept Test:
You add 1.00 kg of ethylene glycol antifreeze (C
2
H
6
O
2
) to your car radiator, which contains
4450 grams of water. What are the boiling and freezing points of the solution?
K b
= 0.512 o C/m
K f
= 1.86
o C/m
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Osmotic Pressure
The fourth colligative property applies only to aqueous solutions. It arises when two solutions are separated by a semi-permeable membrane. A semi-permeable membrane will allow water molecules but not solute molecules to pass through. The holes in the membrane are of a certain size that only the solvent molecules are small enough to pass through. Solute molecules are left behind and unable to make it because of their size. This process is called osmosis. Many parts of organisms have semipermeable membranes that regulate internal concentrations by osmosis.
The pure solvent is the high water concentration while the solute and solvent mixture contains the lower concentration of solvent. So solvent will move from the pure side, to the mixture side. When this movement happens, more total molecules will be on the solution side, the solution will become diluted, and the volume will be larger. The height of the solution will rise and the height of the pure solvent will decrease. Eventually the weight of the solution will be affected by gravity and some of the solvent molecules will be pushed back across the membrane to the pure solvent side. Remember that ONLY solvent molecules are moving. Equilibrium will be reached when the rate of solvent molecules pushed out of the solution equals the number of solvent molecules that enter the solution. Osmotic pressure is defined as the pressure that needs to be applied to prevent the solution from rising in volume, thus to prevent the net movement of water/solvent molecules into the solution.
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Osmotic pressure is going to be related to the number or amount of solute particles that are present in solution. The more solvent particles, the lower the concentration of solvent and the MORE the pure solvent will want to transverse the membrane. Thus, the higher the osmotic pressure.
 = MRTi where  is osmotic pressure
M = Molarity
R = 8.206 x 10 -2 Latm/molK
T = temperature in Kelvin i = number of solute particles creates in solution
The similarity of this equation to the gas law equation should make sense as both relate the pressure of a system to its concentration and temperature.
COMMON THEMES
A common thread runs through and connects all the colligative properties of all solutions containing nonvolatile solutes. Each property rests on the inability of the solute to change phases. In each case, only the solvent is involved in the phase change. It is the presence of the solute however, that affects the solvent’s ability to undergo the phase change. The solute will not enter the gas phase: which leads to vapor pressure lowering and boiling point elevation. The solute will not enter the solid phase: which leads to freezing point depression. They also cannot cross a semi-permeable membrane which leads to osmotic pressure.
When considering colligative properties for electrolyte solutions, the molecular formula will tell you the number of particles. For example, NaCl tells you that there are two particles – a Na +1 ion and a Cl -1 that result from NaCl dissolving in solution. Unlike sugar, when the molecule dissolves but does not
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dissociate – which results in only 1 molecule being present per 1 molecule being dissolved. When
Mg(NO
3
)
2
dissolves, there are 3 species present: an Mg +2 ion and two NO
3-1
ions. Thus colligative properties will be affected since they depend on the number of solute particles present! The equations for all the colligative properties will be mathematically affected by using a multiplying factor (i). This is known as the van’t Hoff factor named after the Dutch chemist. All van’t Hoff factors approach a whole number – since there will be a whole number multiple of extra solute particles present, but a whole number is rarely achieved. However, that would be if every electrolytic solution behaved ideally – which they do not. Ions in solution do not act independently – they are attracted to one another. This attraction and interaction causes deviations. The ions get “tied up” with one another – even when dissociated in solution so its concentration seems lower than it really is. The van’t Hoff factor is determined by taking the ratio of the measure value for the colligative property in the electrolytic solution to the expected value in a nonelectrolytic solution.
For vapor pressure lowering:  P = i(X solute
) x P osolvent
The I value is deceptive here. Remember that it applies to the moles of solute – so consider that when calculating the mole fraction – if the solute breaks into particles, it has more moles of particles!
For boiling point elevation:  T b
For freezing point depression:  T
= i(K f b m)
= i(K
For osmotic pressure:  = i(MRT) f m)
If you stir a handful of sand into water the sand particles are suspended for a shirt amount of time but then gradually sink to the bottom. Sand in water is an example of a suspension: a heterogeneous mixture which contains particles that are large enough to be seen with the naked eye and are clearly distinct from the surrounding fluid. In contrast, when you stir sugar into water the sugar molecules disappear from view (they dissolve!), and form a solution, or a homogeneous mixture in which the solute is made up of particles that are individual molecules that are evenly distributed throughout the solution and are not visible to the naked eye.
Between the two extremes of suspensions and solutions are colloids. In a colloid there is a solute like substance that is distributed throughout a solvent-like substance. Colloidal particles are larger than simple molecules but are small enough to remain “suspended” in the solution and not settle out. They have a range of diameters from 1-1000 nm. A colloidal particle can be a single molecule, or it can a group of atoms, molecules, or ions. Many common substances are colloids. For example, whipped cream is a foam, which is a gas dispersed in a liquid – which is a colloid. Marshmallows are colloids where a gas is dispersed into a solid substance. Milk is a colloid.
Most colloids are cloudy or opaque – turbid. Some are transparent to the naked eye. When light is passed through a colloidal substance, it scatters and does not stay as a “beam”. The light is being scattered by the particles in solution. This is known as the Tyndall effect. Dust in the air displays this effect as does mist when your headlights shine into it at night.
Under low magnification you can watch the solute particles as they are affected by Brownian motion.
The Brownian motion results because the colloids are being pushed this way and that by the solvent molecules. The movement is the primary reason t hat keeps the colloidal particles from settling out like a precipitate.
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