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# Mixtures and Solutions

## DEFINITIONS

A mixture exists when two or more substances are combined so that each of the substances retains its chemical identity. Some mixtures are heterogenous, in that their components can be easily identified. These mixtures can exist in multiple phases and are non-uniform. For example, a suspension is an undissolved solid in a liquid, like juice with pulp in it. An emulsion is the combination of two liquids that don’t mix, such as oil and water.

Other mixtures are homogenous--they are uniform and exist in a single phase, like brass, which is a solid homogenous mixture of zinc and copper. A colloid is a homogenous mixture that remains unsettled unless it is mixed, i.e. mayonnaise or milk. But the most important type of homogenous mixture is a solution. A solution is a homogenous mixture of two or more substances than exist in any phase. We are most concerned with solutions in liquid phase. In a liquid solution, the substance being dissolved is the solute and the substance dissolving the solute is called the solvent.

## CONCENTRATION

When considering solutions, we want to express how much solute is present. This is called the concentration of a solution. Concentration can be measured in several different ways:

• The molarity of a solution is the moles of solute per liter of solution.
• The molality of a solution is the moles of solute per kilogram of solvent.
• The mass percent of a solution is the percent by mass of solute in the solution.
• The mole fraction is the ratio of moles of solute to the total moles of solution.

We can change the concentration of a solution via dilution, meaning we manipulate the amount of solvent. For example, if commercial nitric acid is available at 16.0 M, and we want to create a 500 mL nitric acid solution that is 4.0 M, we use the following equation:

M1V1 = M2V2

If Solution 1 is the commercial nitric acid, and Solution 2 is what we are trying to produce, then we plug in the numbers as follows:

(16.0 M)V1 = (4.0 M)(.5 L)

Solving for Volume 1, we get .125 L, or 125 mL. Given that we want a 500 mL solution, we simply combine 125 mL of the commercial nitric acid with 500 - 125 = 375 mL of water to form our new solution.

## ENERGETICS OF SOLUTION FORMATION

The dissolution of a solute to form a solution can be an exergonic or endergonic process, meaning it may or may not be energetically favorable. Let’s say the solute particles are the blue circles and the solvent particles are the black circles.

When a solute is introduced into a solution, the molecules are pulled apart, which requires energy. Then the solute interacts with the solvent particles. If the solute-solute (blue-blue) attraction is stronger than the solute-solvent (blue-black) attraction, then it is not energetically favorable to form a solution. However, if the solute-solvent attraction is stronger, then solution formation is favored. In all solutions, the entropy of solution formation is positive because the solution state is more disorderly that the solid state, favoring solution formation.

Here are some general rules for solubility in solutions -- these conditions will encourage solution formation. (You can find more specific rules in the solubility rules section of this page.)

1. Like dissolves like. Polar solutes will dissolve in polar solvents, like NaCl in water, and nonpolar solutes will dissolve in nonpolar solvents, like oil in benzene.
2. Solids are more soluble at higher temperatures, while gases are more soluble at lower temperatures and higher pressures. Pressure doesn’t affect solid solubility.

## COLLIGATIVE PROPERTIES

Some properties of a solution vary based on the amount of solute present. These are called colligative properties.

One example of a colligative property is vapor pressure. The presence of solute in a solution means that there are fewer solvent molecules at the surface of the solution, so there is less solvent trying to escape. This lowers the vapor pressure. We can relate vapor pressure to the amount of solute/solvent via Raoult’s Law, as follows:

Pi = XiPio
Pi = the vapor pressure of the solution
Xi = the mole fraction of the solvent
Pio = the vapor pressure of pure solvent

According to Raoult’s Law, more moles of solute, and consequently a lower mole fraction of solvent, results in a greater reduction in vapor pressure.

Boiling point is another colligative property. The addition of a nonvolatile solute to a solute will result in boiling point elevation by the following equation:

ΔTb = iKbm
ΔTb = change in boiling point
i = van't Hoff factor, which is the number of solute particles in the solution
Kb = molal boiling constant of the solvent (K * kg/mol)
m = molality of the solute (mol/kg)

Nonvolatile solutes in a solution will also result in freezing point depression.

ΔTb = iKfm
Kf = the molal freezing constant of the solvent

Osmotic pressure is the fourth important colligative property. Osmosis is the flow of liquids across a selectively permeable membrane. Osmotic pressure is the pressure that is applied to stop osmosis. An increase in solute concentration will raise the osmotic pressure of a solution, as demonstrated by the following equation:

π = iMRT
π = osmotic pressure
M = molarity of the solution
R = the gas constant (0.0821 L*atm/mol*K)
T = temperature (in Kelvins)

We often consider solutes in terms of electrolytes and non-electrolytes. Electrolytes are compounds that dissolve in water and produce ions, like salts and acids/bases. Non-electrolytes are compounds, namely organic compounds, that do not dissolve in water and do not produce ions.

## Mixtures and Solutions Practice Quiz

True or False? Molarity is moles of solution per kg of solvent.

A. True
B. False
The correct answer here would be B.
Molarity is moles of solution per L of solvent. Molality is moles of solution per kg of solvent.

48.5 g of NaCl is added to 500 mL of water. What is the molarity of the solution?

A. .2 M
B. .5 M
C. 2.0 M
D. 0.02 M
The correct answer here would be C.
The molar mass of NaCl is appr. 48.5 g/mol, so there is 1 mol of NaCl. 1/0.5 L = 2.0 M.

Gases are more soluble in liquids at _______ temperatures and _______ pressures.

A. low, high
B. low, low
C. high, low
D. high, high
The correct answer here would be A.

Which of these is not a colligative property? Vapor pressure, osmotic pressure, boiling point depression, freezing point depression.

A. vapor pressure
B. osmotic pressure
C. boiling point depression
D. freezing point depression
The correct answer here would be C.
The presence of solutes leads to boiling point elevation, not depression.

### References

Lower, Stephen. "Solutions: Their Chemistry and Physical Properties." Chem1 Virtual Textbook. Web. http://www.chem1.com/acad/webtext/virtualtextbook.html.