Unit 2: The Mole and Solutions – General Chemistry Study Notes

Unit 2: The Mole and Solutions

Overview

This unit covers foundational concepts in General Chemistry, focusing on the mole as a counting unit, molar mass calculations, empirical and molecular formulas, solution composition, solubility, and acid-base chemistry. Mastery of these topics is essential for understanding chemical reactions, stoichiometry, and laboratory solution preparation.

The Mole – The SI Unit of Chemistry

Definition and Importance

• The mole is the SI base unit for amount of substance, used to count atoms, molecules, ions, etc.

• One mole contains Avogadro’s number ($6.022 \times 10^{23}$) of elementary entities (atoms, molecules, etc.).

• Allows chemists to relate macroscopic measurements (grams) to microscopic particles (atoms/molecules).

Example: 1 mole of carbon atoms = $6.022 \times 10^{23}$ atoms = 12.01 g

Molar Mass Calculations

Definition and Calculation

• Molar mass is the mass of one mole of an element or compound, expressed in grams per mole (g/mol).

• For elements, use the atomic mass from the periodic table.

• For compounds, sum the atomic masses of all atoms in the formula.

Examples:

• Carbon (C): 12.01 g/mol

• Aluminum (Al): 26.98 g/mol

• Water (H2O): $2 \times 1.01 + 16.00 = 18.02$ g/mol

• Calcium phosphate (Ca3(PO4)2): $3 \times 40.08 + 2 \times (30.97 + 4 \times 16.00) = 310.18$ g/mol

Mole-Mass Conversions

• Use the molar mass to convert between mass (g) and moles (mol):

$\text{Moles (mol)} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$

$\text{Mass (g)} = \text{Moles (mol)} \times \text{Molar Mass (g/mol)}$

Example: How many moles of carbon are in 26 g of carbon? $\text{Moles} = \frac{26\ \text{g}}{12.01\ \text{g/mol}} = 2.16\ \text{mol}$

Percent Composition and Empirical Formulas

Percent Composition

• Percent composition is the percentage by mass of each element in a compound.

• Calculated as: $\text{Percent by mass of element} = \frac{\text{Mass of element in 1 mol of compound}}{\text{Molar mass of compound}} \times 100\%$

Example: Find the percent composition of copper in Cu2S.

Empirical and Molecular Formulas

• Empirical formula: Simplest whole-number ratio of atoms in a compound.

• Molecular formula: Actual number of atoms of each element in a molecule.

• Steps to determine empirical formula from percent composition:

  1. Assume 100 g sample; convert percentages to grams.

  2. Convert grams to moles for each element.

  3. Divide by the smallest number of moles to get ratios.

  4. Multiply to get whole numbers if necessary.

• To find molecular formula:

  1. Find empirical formula and its mass.

  2. Divide the given molecular mass by the empirical mass.

  3. Multiply subscripts in empirical formula by this ratio.

Example: A compound is 25.9% nitrogen and 74.1% oxygen. Find the empirical formula.

Solution Composition

Solute and Solvent

• Solute: Substance being dissolved.

• Solvent: Substance doing the dissolving (in aqueous solutions, this is water).

Table: Common Solutes and Solvents

Example	Solute State	Solvent State
Air, natural gas	Gas	Gas
Sugar water	Solid	Liquid
Salt water	Solid	Liquid
Carbonated water	Gas	Liquid
Brass	Solid	Solid

Electrolytes

• Electrolyte: Substance that produces ions in solution, allowing it to conduct electricity.

• Strong electrolytes: Completely ionize in water (e.g., NaCl).

• Weak electrolytes: Partially ionize (e.g., acetic acid).

• Nonelectrolytes: Do not produce ions (e.g., sugar).

Factors Affecting Solubility

Polarity and Solubility

• Polarity affects solubility: "Like dissolves like" (polar solvents dissolve polar/ionic solutes).

• Hydrophilic: Water-loving, polar substances.

• Hydrophobic: Water-fearing, non-polar substances.

Pressure Effects – Henry’s Law

• Applies to gases dissolved in liquids.

• Henry’s Law: $C = kP$

  • $C$ = concentration of dissolved gas

  • $k$ = constant

  • $P$ = partial pressure of gas above solution

Temperature Effects

• Solubility of most solids increases with temperature.

• Solubility of gases decreases with increasing temperature.

• The steeper the solubility curve, the more temperature affects solubility.

Solubility Vocabulary

• Unsaturated solution: Contains less solute than can be dissolved at a given temperature.

• Saturated solution: Contains the maximum amount of solute that can dissolve.

• Supersaturated solution: Contains more solute than normally possible; unstable.

Solution Concentration: Molarity and Dilution

Molarity (M)

• Molarity is the number of moles of solute per liter of solution.

$M = \frac{\text{moles of solute}}{\text{liters of solution}}$

Example: What is the molarity if 0.500 g of potassium phosphate is dissolved in enough water to make 1.50 L of solution?

Dilution

• To dilute a solution, add solvent to decrease concentration.

• Use the formula: $M_1V_1 = M_2V_2$ where $M_1$ and $V_1$ are the initial molarity and volume, $M_2$ and $V_2$ are the final molarity and volume.

Example: How much of a 2.00 M NaOH stock solution is needed to prepare 150.0 mL of 0.800 M NaOH?

Acids, Bases, and pH

Acids in Solution

• An acid is a substance that produces hydronium ions (H3O+) in water.

• Binary acids contain hydrogen and one other element (e.g., HCl, H2S).

pH Calculations

• pH is defined as the negative base-10 logarithm of the hydronium ion concentration:

$pH = -\log [H_3O^+]$

Example: Calculate the pH if $[H_3O^+] = 3.4 \times 10^{-3}$ M.

Decimal places in given molarity = sig figs in answer

Summary Table: Key Concepts and Formulas

Concept	Formula/Definition
Mole	1 mol = $6.022 \times 10^{23}$ entities
Molar Mass	Sum of atomic masses (g/mol)
Percent Composition	$\frac{\text{mass of element}}{\text{molar mass of compound}} \times 100\%$
Molarity	$M = \frac{\text{moles}}{\text{liters}}$
Dilution	$M_1V_1 = M_2V_2$
pH	$pH = -\log [H_3O^+]$
Henry's Law	$C = kP$

Additional info:

• These notes are aligned with common General Chemistry textbooks and cover all major learning objectives for Unit 2: The Mole and Solutions.

• Practice problems and lab activities (e.g., Hydrate Lab, Beer's Law Lab) reinforce these concepts.