General Chemistry 115: Exam 1B Study Notes

General Chemistry Fundamentals

Unit Conversions and Useful Constants

Understanding unit conversions and key constants is essential for solving a variety of problems in general chemistry, including calculations involving mass, volume, and concentration.

• Density (D): The ratio of mass to volume. Formula: $D = \frac{\text{mass}}{\text{volume}}$

• Volume of a Sphere: Formula: $V = \frac{4}{3} \pi r^3$, where $\pi = 3.141592$

• Common Conversion Factors:

  • 1 mile = 5280 feet

  • 1 foot = 12 inches

  • 1 inch = 2.54 cm

  • 1 liter = 1.05669 quarts

  • 1 mile = 1.60934 km

  • 1000 mg = 1 g

  • 1 mL = 1 cm3

Chemical Nomenclature and Formulas

Elements, Ions, and Compounds: Naming and Symbolism

Chemists use systematic rules to name elements, ions, and compounds. Mastery of nomenclature is crucial for communication and problem-solving in chemistry.

• Element Symbols: Each element is represented by a one- or two-letter symbol (e.g., Na for sodium, Fe for iron).

• Common Polyatomic Ions:

  • Hydrogen phosphite: $\text{HPO}_3^{2-}$

  • Acetate: $\text{C}_2\text{H}_3\text{O}_2^-$ or $\text{CH}_3\text{COO}^-$

  • Copper(II) perchlorate: $\text{Cu(ClO}_4)_2$

  • Strontium oxide: $\text{SrO}$

  • Calcium nitrite: $\text{Ca(NO}_2)_2$

• Writing Formulas: The chemical formula shows the types and numbers of atoms in a compound. For ionic compounds, the total positive and negative charges must balance.

• Naming Compounds:

  • Ionic Compounds: Name the cation first, then the anion. Use Roman numerals for transition metals with variable charge.

  • Molecular Compounds: Use prefixes (mono-, di-, tri-, etc.) to indicate the number of each atom.

• Examples:

  • Na2SO4: Sodium sulfate

  • HCO3-: Hydrogen carbonate (bicarbonate)

  • HBr(aq): Hydrobromic acid

Significant Figures

Counting Significant Figures

Significant figures (sig figs) reflect the precision of a measured or calculated quantity. Correctly identifying the number of significant figures is essential for reporting scientific data.

• Rules for Significant Figures:

  1. All nonzero digits are significant.

  2. Zeros between nonzero digits are significant.

  3. Leading zeros are not significant.

  4. Trailing zeros after a decimal point are significant.

  5. Trailing zeros in a whole number with no decimal shown are ambiguous.

• Examples:

  • 1.057 × 104 has 4 significant figures.

  • 0.00230122 has 6 significant figures.

  • 13.3 × 102 has 3 significant figures.

  • 0.00048 has 2 significant figures.

  • 499.100 has 6 significant figures.

Writing and Interpreting Chemical Formulas

Formulas for Compounds

Writing correct chemical formulas requires knowledge of the names and charges of ions, as well as the rules for combining them.

• Tetraphosphorous decoxide: $\text{P}_4\text{O}_{10}$

• Potassium sulfate: $\text{K}_2\text{SO}_4$

• Barium chlorate: $\text{Ba(ClO}_3)_2$

• Sulfur dioxide: $\text{SO}_2$

• Magnesium chloride: $\text{MgCl}_2$

Solution Concentration: Molarity

Calculating Molarity

Molarity (M) is a measure of concentration, defined as moles of solute per liter of solution. It is a fundamental concept in solution chemistry.

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

• Steps to Calculate Molarity:

  1. Convert mass of solute to moles using molar mass.

  2. Convert volume of solution to liters.

  3. Divide moles of solute by liters of solution.

• Example: To find the molarity of a solution with 26.0 g of BaCl2 (molar mass = 208.2 g/mol) in 450.0 mL:

  • Moles of BaCl2: $\frac{26.0\ \text{g}}{208.2\ \text{g/mol}} = 0.125\ \text{mol}$

  • Volume in liters: $450.0\ \text{mL} = 0.4500\ \text{L}$

  • Molarity: $M = \frac{0.125}{0.4500} = 0.278\ \text{M}$