Solutions

	Types of Solutions
	Molarity
	Molality
	Mole Fraction
	Kf and Kb

You may be asking yourself why solutions are necessary. Well, they serve a lot of practical purposes. For instance, most chemical reactions are run in solution. Solutions also usually have a lower melting and freezing point than just a substance by itself.

Let's say that we have a handful of salt crystals, NaCl. When this salt dissolves in water, there is a uniform dispersion of ions in this water. What we have just formed is called a solution. A solution is defined as a homogeneous mixture of two or more substances, consisting of ions or molecules. A solution can be a solid, liquid, or gas. A solution results from the combination of a solute and a solvent. A solute is, in the case of a gas or solid dissolved in liquid, the gas or solid, but in other cases it is the part that has the smaller amount. A solvent is, in the case of a gas or solid dissolved in liquid, the liquid, but in other cases it is the part that has the larger amount. In the example concerning the salt, the solvent would be water and the salt would be the solute.

So that we can understand the concept of solubility, let's consider the process of dissolving sodium chloride in water. We know that NaCl is an ionic compound, and that it dissolves in water as Na⁺ and Cl^- ions. When we mix 50 grams of salt in 100 mL of water we find something cool going on. The sodium and chlorine ions leave the surface of the crystal and enter into the solution. These ions then move about at random in the solution and occasionally bump into another crystal and stick, returning to their crystalline state. As time passes, more sodium chloride continues to dissolve into the solution, which means that the ion concentration increases. This means that eventually more ions are going to bump into each other and return to their crystalline state. Over time, a dynamic equilibrium will be reached in which the rate at which ions leave the crystals is equivalent to the rate at which ions collide to form a crystal.

At this equilibrium, no more salt appears to dissolve. We have reached what we call a saturated solution. A saturated solution is a solution that is in equilibrium with respect to a given dissolved substance. An unsaturated solution is a solution that is not in equilibrium with respect to given dissolved substance, leaving room for more substance to dissolve. The solubility of a substance is the amount that dissolves in a given quantity of water at a given temperature to give a saturated solution. Sometimes, through special circumstances we can obtain a supersaturated solution. A supersaturated solution is a solution that contains more dissolved solute than is normally possible at that temperature.

Molar Concentration or Molarity is defined as the moles of solute dissolved in one liter of solution.

Molarity =	moles of solute
	liter of solution

Example:

.0678 g of NaCl is placed in a 25.0 ml flask full of water. When the NaCl dissolves, what is the molarity of the solution?

.0464 M NaCl

The molality of a solution is the moles of solute per kilogram of solvent.

molality =	moles of solute
	kilogram of solvent

Example:

.20 mol of ethylene glycol / 2.0 Kg of solvent = .10 m ethylene glycol

Mole fraction is the number of moles of a substance divided by the total number of moles in the solution.

Mole Fraction =	moles of substance A
	Total Moles of solution

Example:

If there is 4.0 moles of HCl in 12 moles of solution then the mole fraction of HCl would be 1/3. When all mole fractions are added together the total is always 1.

K_f and K_b are the freezing point depression constant and boiling point elevation constant. When a solute is added to a solvent, the boiling point of the solution is always greater than the boiling point o the pure solvent. Adding a solute also lowers the freezing point.

Solvent	Formula	Melting Point (oC)	Boiling Point(oC)	Kf(oC/m)	Kb(oC/m)
Benzene	C6H6	5.455	80.2	5.065	2.61
Ethanol	C2H5OH	--	78.3	--	1.07
Water	H20	0.000	100.000	1.858	0.521

To determine the amount of change in boiling point you will need this equation:

T_b = K_b * m

	Tb change in boiling point
	Kb boiling point elevation constant
	m molality of solution

Then T_b is added to the normal boiling point of the pure solvent. Note that the identity of the solute is not important, just its concentration (expressed in molality). Therefore, boiling point elevation is a colligative property.

To determine the freezing point of a solution, you need to calculate the decrease in freezing point caused by the addition of a solute to the solvent. Use the equation:

T_f = K_f * m

	Tf change in freezing point
	Kf freezing point depression constant
	m molality of solution

Then the T_f is subtracted from the normal freezing point of the pure solvent. Freezing point depression is also a colligative property.

Example:

Calculate the boiling point and freezing point of a solution of .30 g of glycerol (C₃H₈O₃) in 20.0 g of water.

moles glycerol = (.30 g) (1 mole / 92 g) = .0033 moles molality of solution = .0033 moles / .020 kg = .16 m

T_b = (.521 ^oC/m)(.16 m) = .083 ^oC

Boiling point = 100.00 + .083 = 100.083 ^oC

T_f = (1.858 ^oC/m)(.16m) = .30 ^oC

Freezing point = 0.00 ^oC - .30 ^oC = -.30 ^oC

In an ionic solution, the total concentration of ions is important. Therefore, another factor (i) is included in the equations.

T_b = K_b * m * i

T_f = K_f * m * i

"i" is the number of ions from each formula unit. In the previous example, if NaCl had been the solute your change in boiling point and freezing point would have needed to be multiplied by 2. (i=2 because NaCl consists of a Na⁺ ion and a Cl^- ion