General Chemistry Unit 2: Key Concepts and Calculations

Empirical and Molecular Formulas

Empirical Formulas

The empirical formula of a compound represents the simplest whole-number ratio of the elements present. It is determined from experimental data, such as percent composition or mass of each element.

• Definition: The simplest ratio of atoms in a compound.

• Calculation Steps:

  1. Convert mass or percent composition to moles for each element.

  2. Divide each mole value by the smallest number of moles calculated.

  3. If necessary, multiply all ratios by a whole number to eliminate fractions.

• Example: A compound contains 40% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. Find the empirical formula.

  • Convert to moles: C: 40 g / 12.01 g/mol = 3.33 mol; H: 6.7 g / 1.008 g/mol = 6.65 mol; O: 53.3 g / 16.00 g/mol = 3.33 mol.

  • Divide by smallest: C: 1, H: 2, O: 1.

  • Empirical formula: CH2O

Molecular Formulas

The molecular formula shows the actual number of atoms of each element in a molecule. It is a whole-number multiple of the empirical formula.

• Definition: The actual number of atoms of each element in a molecule.

• Calculation: $\text{Molecular Formula} = n \times \text{Empirical Formula}$, where $n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$

• Example: If the empirical formula is CH2O (mass = 30 g/mol) and the molar mass is 180 g/mol, then $n = 180/30 = 6$. Molecular formula: C6H12O6

Empirical Formula of a Hydrate

A hydrate is a compound that contains water molecules within its crystal structure. The empirical formula of a hydrate includes both the salt and water.

• Calculation:

  1. Find moles of anhydrous salt and water lost upon heating.

  2. Express as a ratio: $\text{Salt} \cdot n\text{H}_2\text{O}$

• Example: If 1 mole of salt is associated with 5 moles of water, formula is Salt·5H2O.

Percent Composition and Proportions

Percent Composition

Percent composition refers to the percentage by mass of each element in a compound.

• Formula: $\%\,\text{Element} = \frac{\text{Mass of Element in 1 mol}}{\text{Molar Mass of Compound}} \times 100$

• Application: Used to determine empirical formulas and analyze chemical purity.

Proportions

Proportions are used to relate quantities in chemical reactions, such as reactants and products.

• Example: If 2 moles of H2 react with 1 mole of O2 to produce 2 moles of H2O, the proportion is 2:1:2.

Dimensional Analysis with Moles

Dimensional analysis is a method for converting between units using conversion factors. In chemistry, it is often used to convert between mass, moles, and number of particles.

• Key Conversion Factors:

  • 1 mole = molar mass (g)

  • 1 mole = $6.022 \times 10^{23}$ particles (Avogadro's number)

• Example: Convert 10 g of NaCl to moles: $10 \text{ g} \times \frac{1 \text{ mol}}{58.44 \text{ g}} = 0.171 \text{ mol}$

Beer’s Law Lab

Beer’s Law relates the absorbance of a solution to its concentration.

• Equation: $A = \varepsilon l c$ Where:

  • $A$ = absorbance

  • $\varepsilon$ = molar absorptivity (L·mol−1·cm−1)

  • $l$ = path length (cm)

  • $c$ = concentration (mol/L)

• Application: Used to determine unknown concentrations by measuring absorbance.

Molarity Calculations

Molarity

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

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

• Example: 0.5 moles of NaCl dissolved in 1.0 L of water: $M = 0.5/1.0 = 0.5$ M

Molarity Calculations #1, #2, #3

• Calculate moles from given mass using molar mass.

• Convert moles to molarity using volume of solution.

• Use dilution equation for mixing solutions: $M_1V_1 = M_2V_2$

Solubility

Solubility describes how much solute can dissolve in a solvent at a given temperature.

• Factors Affecting Solubility: Temperature, pressure, nature of solute and solvent.

• Solubility Rules: General guidelines for predicting whether an ionic compound will dissolve in water.

• Example Table:

Compound Type	Solubility in Water
Group 1 salts (e.g., Na+, K+)	Soluble
Nitrates (NO3−)	Soluble
Chlorides (Cl−)	Usually soluble (except Ag+, Pb2+, Hg22+)
Sulfates (SO42−)	Usually soluble (except Ba2+, Pb2+, Ca2+)
Carbonates (CO32−)	Insoluble (except Group 1 and NH4+)

Solution Vocabulary

Key terms related to solutions:

• Solute: Substance dissolved in a solution.

• Solvent: Substance that dissolves the solute (often water).

• Concentration: Amount of solute per unit volume of solution.

• Saturated Solution: Contains maximum amount of solute at given conditions.

• Unsaturated Solution: Can dissolve more solute.

• Supersaturated Solution: Contains more solute than is normally possible at given conditions.

Electrolytes

Electrolytes are substances that conduct electricity when dissolved in water due to the presence of ions.

• Strong Electrolytes: Completely dissociate into ions (e.g., NaCl, HCl).

• Weak Electrolytes: Partially dissociate (e.g., acetic acid).

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

Acids and pH

Acids are substances that donate protons (H+) in solution. pH is a measure of the hydrogen ion concentration.

• pH Formula: $\text{pH} = -\log[\text{H}^+]$

• Acidic Solution: pH < 7

• Neutral Solution: pH = 7

• Basic Solution: pH > 7

• Example: If $[\text{H}^+] = 1 \times 10^{-3}$ M, $\text{pH} = 3$

Additional info: Some content and examples have been inferred and expanded for completeness and academic clarity.