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Solutions are homogeneous mixtures of two or more substances. Usually the solution is a liquid, but this is not required. Gaseous and solid solutions do exist.

Normally, a mixture has two components, the solvent and the solute. The solvent has the greater number of moles; the solute has fewer moles. The solute is also normally the substance of interest, whereas the solvent is a convenient vehicle for it. Consequently, solutions are generally labeled with the solute, and the solvent might not even be mentioned. The most common of all solvents is water. Solutions with water as the solvent may be described as aqueous.

Since solutions are a mixture, the ratio of solute to solvent varies. This ratio of solute to solvent (or to the entire solution) is called concentration. Many units can be used for concentration. The two emphasized in this chapter are molarity and molality.

molarity (M) = moles of solute/liters of solution = mmol solute/mL solution (Equation 5.1)

                              >> Explore: Molarity Tutorial

molality (m) = moles of solute/kg of solvent (Equation 5.7)

Molarity is used in problems involving osmotic pressure and stochiometry. Molality is used in problems involving freezing point depression and boiling point elevation. It is important to notice the similarities and differences between the two units. While both look at moles of solute, molarity divides by liters of solution and molality by kilograms of solvent. This means that the method by which solutions of a particular molarity are made is different from that for making solutions of a particular molality. In making a molar solution, the volume of the entire solution, solute and solvent, must be measured. On the other hand, the mass of thesolvent is measured in molality. Solvent and solute must be measured separately. Because the names, symbols, and numeric values for both concentration units are similar, it is easy to confuse these two units. Equations 5.1 and 5.7 are used when working from the pure substance to the mixture or the reverse. If you are diluting, adding solvent to a solution to decrease the concentration, you should use Equation 5.3.

M_iV_i = M_fV_f       (Equation 5.3)

Because of a quirk of the math, you may use any units for volume in this equation, provided that it is the same one for V_i and V_f.

Substances that form ions when dissolved in solution are called electrolytes. Strong electrolytes are solutes that only exist as ions in solutions. For aqueous solutions there are two classes of strong electrolytes, strong acids and soluble salts. Weak electrolytes form some ions but exist primarily in their original form. In aqueous solutions weak electrolytes are moderately soluble salts, weak acids, and weak bases. Nonelectrolytes do not form ions at all. Most molecular compounds other than acids and bases are nonelectrolytes. When doing calculations for colligative properties (osmotic pressure, boiling point elevation, and freezing point depression) of strong electrolytes, the total concentration of ions should be used, unless the calculation is to determine the van't Hoff factor. When doing net ionic equations, only strong electrolytes are written as ions.

Solvent properties affected by the amount of solute and not the identity of the solute are called colligative properties. Three colligative properties are osmotic pressure, boiling point elevation, and freezing point depression. For each of these it is the solvent behavior that is affected. The equation associated with each property can be used to find the magnitude of the change in solvent but not the direction of the change. Consequently, it is important to learn both the equation associated with each property and the direction of the change. To summarize the equations and directions:

•	For osmotic pressure, the solvent moves across the semipermeable membrane into the solution of higher concentration with a force or pressure (P) determined by: = MRT   (Equation 5.5)
•	For boiling point elevation the boiling point of the solvent increases by T which is determined by: T = Kbm   (Equation 5.6)
•	For freezing point depression, the freezing point of the solvent decreases by T, which is determined by: T = Kfm    (Equation 5.8)
	>> Explore	: Osmotic Pressure Tutorial : Boiling and Freezing Points Tutorial

Note that the osmotic pressure equation uses molarity and that the freezing point and boiling point equations use molality. However, both refer to moles of particles, which for strong electrolytes means the total number of ions. The number of moles of particles per mole of solute is the van't Hoff factor. Theoretically, you should be able to determine this from the formula of strong electrolyte. For example, since 1 mole of K₂S dissociates into 2 moles of potassium ion and 1 mole of sulfide ion, its van't Hoff factor should be 3. However, because ions often associate with each other in solution, forming ion pairs, the true van't Hoff factor is often less than its theoretical value. True van't Hoff factors can be calculated from any of the colligative properties, by adding the van't Hoff factor i to the equation. (e.g., T = iKm). If the van't Hoff factor is used in the equation, the concentration refers to the moles of overall solute rather than to moles of particles.

Also although the freezing point and boiling point equations are similar, the constant used (K) is different. For each of the colligative properties, the units on the constant (K_b, K_f, and R) can be used to remind you of what units to use for the other variables in the equation.

Three important skills in working with chemical reactions are to identify the type of reaction, predict products, and write the net ionic equations. This chapter discusses three types of reactions: oxidation–reduction (redox) equations, acid–base (neutralization) equations, and precipitation equations.

Oxidation-reduction equations involve a transfer of electrons that are characterized by a change in oxidation number. Oxidation numbers are used to keep track of the electrons assigned to an element. They are not necessarily based in physical reality. Sometimes a change in oxidation number is obvious (e.g., when a substance appears in its elemental form on one side of the equations and as an ion on the other). At other times the oxidation number of each element can be calculated individually. To determine the oxidation number, the rules discussed in Section 5.5 (in the book) are used. Each element of a given compound has the same oxidation number. It is often convenient to consider each ion of a salt separately (even if it is not a strong electrolyte). In a redox reaction two elements will always change oxidation number. For one of those elements the oxidation number increases (becomes more positive or less negative). This element has lost electrons and is oxidized. The oxidation number of the other element decreases (becomes less positive or more negative). This element gained electrons and was reduced. An oxidation–reduction reaction can be separated into two equations, each called a half-reaction. The half-reactions show the elements changing oxidation state and include electrons. The chemical equation where the electrons are reactants is the reduction half-reaction. The chemical equation where the electrons are products is the oxidation half-reaction. The reactant that provides electrons is called the reducing agent; that reactant contains the element being oxidized in the oxidation half-reaction. The reactant that accepts electrons is the oxidizing agent; it contains the element being reduced in the reduction half-reaction. It is important, and difficult, to keep the oxidation–reduction terminology straight. When the half reactions are combined, the same number of electrons must be lost and gained; the electrons then cancel from the equation.

An acid–base neutralization reaction is the reaction of an acid with a base. Thus an acid and a base must be present as reactants. An acid can be defined as a proton (or H⁺) donor. A base can be defined as a proton (or H⁺) acceptor. Thus an acid–base reaction can also be called a proton transfer. The formulas for acids are commonly written with the hydrogen as the first element. The chapter discusses two types of bases, hydroxides and carbonates. When an acid combines with a hydroxide, one product will be water. When an acid combines with a carbonate (or bicarbonate), the products will include carbon dioxide and water.

When large quantities of ionic compounds, salts, dissolve in water, they are called soluble. If only a small amount (very near zero) dissolves, the salt is considered insoluble. Precipitation reactions produce an insoluble salt, called a precipitate, as a product. Salts are ionic compounds. The general solubility of a salt can be determined from the solubility rules (Table 5.4 in the book).

>> ExploreSaturated Solutions Tutorial

It is possible for a reaction to be both an acid–base reaction and a precipitation reaction. It is possible for a redox reaction to produce a precipitate, but such reactions are generally only classed as redox reactions. Acid–base reactions are never redox reactions, although it is not uncommon for a redox reaction to include either an acid or a base.

Net ionic equations include only the substances that are actually participating in a reaction. Since strong electrolytes exist as ions in solutions, these ions, rather than the compound itself, are used in the net ionic equation. Although weak electrolytes do make some ions in solution, most of the substance exists in its molecular form; thus the molecular form is used in the equation. Not every substance in the reaction solution must participate in the reaction. Some ions are present only to keep the net charge as zero. Ions that do not participate in the reaction are called spectator ions. Spectator ions are not included in net ionic reactions. Any reaction can be written as a net ionic reaction.

Stoichiometry relates quantities of reactants and products in a chemical reaction. Chapter 4 explored these relationships in detail. This chapter adds another way to convert to moles. If the unit is volume of solution, molarity is used to convert moles of solute. Molarity is always used in titrations. A titration is an experiment in which the volume of a solution of one reactant required to react exactly with a specific amount of another reactant is measured. The volume when both reactants have completely reacted, with no excess of either, is called the equivalence point. An indicator is used to determine the equivalence point. A buret is the glassware used to measure the solution volume very precisely. Because reactants are related and each reacts exactly, there is no limiting reactant in titration reactions.