Chapter 5

Chapter 5: Solutions

Terminology and Concepts

Solutions are homogeneous mixtures composed of two or more substances. The major component is called the solvent, and the minor component is the solute. When water is the solvent, the solution is termed aqueous.

• Solvent: Major component of the solution

• Solute: Minor component dissolved in the solvent

• Aqueous solution: Solution where water is the solvent

• Concentrated solution: Large amount of solute

• Dilute solution: Small amount of solute

Concentration Unit: Molarity

Molarity (M) is a measure of concentration, defined as moles of solute per liter of solution.

• Formula:

$M = \frac{n}{V}$

• M: Molarity (mol/L)

• n: Moles of solute

• V: Volume of solution (L)

Dilution of Solutions

To dilute a solution, solvent is added to decrease the concentration. The number of moles of solute remains constant before and after dilution.

• Formula:

$M_i V_i = M_f V_f$

• $M_i$: Initial molarity

• $V_i$: Initial volume

• $M_f$: Final molarity

• $V_f$: Final volume

Example: Dilution Calculation

To prepare 0.150 M H2SO4 from 0.100 M H2SO4 using 25.0 mL:

$M_i V_i = M_f V_f$ $0.100 \times 25.0 = 0.150 \times V_f$ $V_f = \frac{0.100 \times 25.0}{0.150} = 16.7$ mL

Steps for BCA (Before-Change-After) Tables

1. Go to moles

2. Find limiting reactant (LR)

3. Use LR to find other quantities

4. Convert to grams if needed

Stoichiometry in Solution Reactions

Limiting Reactant and Stoichiometry

In reactions, the limiting reactant is the substance that is completely consumed first, determining the amount of product formed.

• Convert volumes to moles using molarity

• Use stoichiometric coefficients to relate reactants and products

• Identify limiting reactant by comparing mole ratios

• Calculate quantities of products and excess reactants

Example: Reaction of Li2S with Co(NO3)2

Given: 0.0185 moles Li2S, 0.0185 moles Co(NO3)2

• Stoichiometry: 1 mole Li2S reacts with 1 mole Co(NO3)2

• Both reactants are present in equal moles, so both are completely consumed

Lab Concept: Copper and Aluminum Reaction

Reaction: 2Al(s) + 3CuCl2(aq) → 2AlCl3(aq) + 3Cu(s)

• Calculate moles of Al and CuCl2

• Compare mole ratios to determine limiting reactant

• Calculate excess reactant remaining

Types of Aqueous Solutions & Solubility

Electrolytes and Nonelectrolytes

An electrolyte is a substance that dissolves in water and conducts electricity due to the presence of ions. Electrolytes can be strong or weak.

• Strong electrolytes: 100% dissociation into ions (e.g., ionic compounds, strong acids/bases)

• Weak electrolytes: Partial dissociation (e.g., weak acids/bases)

• Nonelectrolytes: No dissociation, do not conduct electricity (e.g., molecular compounds like sugar)

Examples

• NaCl (ionic compound): strong electrolyte

• H2O, C12H22O11 (sucrose): nonelectrolytes

• Citric acid: weak acid, weak electrolyte

• NaCl: salt, strong electrolyte

Calculating Molarity in Ionic Solutions

To find the molarity of ions in solution, use the formula:

$M = \frac{\text{moles solute}}{\text{volume solution (L)}}$

• Multiply by the number of ions produced per formula unit

Precipitation Reactions

When two soluble solutions are mixed, a solid (precipitate) may form. The reaction is represented as:

$(aq) + (aq) \rightarrow (s) + (aq)$

• Complete ionic and net ionic equations are used to show the species involved

Acid-Base Reactions

Definitions

• Acid: Substance that produces H+ in aqueous solution

• Base: Substance that produces OH- in aqueous solution

• Strong acids/bases: Completely dissociate in solution (strong electrolytes)

• Weak acids/bases: Partially dissociate (weak electrolytes)

Memorize Strong Acids (6)

Strong Acids
HCl
HBr
HI
HNO3
HClO4
H2SO4

Strong Bases

• Group 1 and Group 2 metal hydroxides: NaOH, KOH, Mg(OH)2, Ca(OH)2

Acid-Base Neutralization Reaction

Acid reacts with base to form water and a salt:

$\text{HCl} (aq) + \text{NaOH} (aq) \rightarrow \text{H}_2\text{O} (l) + \text{NaCl} (aq)$

Acid-Base Stoichiometry

Stoichiometry involves calculating the amount of acid or base needed to neutralize the other.

• Titration: Adding a known concentration of acid/base to an unknown concentration

• At equivalence point: moles acid = moles base

Example calculation:

$\text{M}_1 \text{V}_1 = \text{M}_2 \text{V}_2$

Given: 0.118 M KOH, 22.87 mL KOH, 20.00 mL H2SO4

$0.118 \times 0.02287 = 0.09505$ moles KOH $\frac{0.09505}{2} = 0.047525$ moles H2SO4

$M = \frac{0.047525}{0.02000} = 2.38$ M H2SO4

Redox (Oxidation-Reduction) Reactions

Definitions

• Oxidation: Loss of electrons

• Reduction: Gain of electrons

• Redox reaction: Electrons are transferred from one species to another

Assigning Oxidation States

1. Elements in their standard state have oxidation number 0

2. Monatomic ions: oxidation state equals the ion charge

3. Sum of oxidation states in a compound equals the overall charge

4. Common rules:

   • Group 1 metals: +1

   • Group 2 metals: +2

   • Hydrogen: +1 (except in hydrides: -1)

   • Oxygen: -2 (except in peroxides: -1)

   • Halogens: -1 (except when bonded to oxygen or other halogens)

Examples

• Cl2: 0

• FeCl3: Fe = +3, Cl = -1

• Na2O: Na = +1, O = -2

• CH4: C = -4, H = +1

• SO42-: S = +6, O = -2

• ClO4-: Cl = +7, O = -2

Example Redox Reaction

Assign oxidation states and identify what is oxidized and reduced:

$\text{Al}(s) + \text{Ag}^+(aq) \rightarrow \text{Al}^{3+}(aq) + \text{Ag}(s)$

• Al: 0 → +3 (oxidation, loss of electrons)

• Ag: +1 → 0 (reduction, gain of electrons)

Gas Laws (Brief Overview)

Boyle's Law

Describes the inverse relationship between pressure and volume for a fixed amount of gas at constant temperature.

$P_1 V_1 = P_2 V_2$

• As pressure increases, volume decreases, and vice versa

Tables

Stoichiometry Table Example

The following table summarizes the stoichiometry of a reaction involving K2SO4, Pb(CH3CO2)2, KCH3CO2, and PbSO4:

	K2SO4	Pb(CH3CO2)2	2KCH3CO2	PbSO4
Molarity Before	55.0 mL, 0.102 M	3.50 mL, 0.114 M	0	0
Moles Before	0.00561	0.00399	0	0
Charge	+2	+2	+1	+1
Moles After	0.00171	0.00798	0.00399	0.00399
Quantity After	0.019 M	0.87 M	1.21 g	1.21 g

Additional info: Table shows the change in moles and concentrations before and after reaction, useful for stoichiometry and limiting reactant calculations.