Some Basic Concepts of Chemistry — Notes

A measurement is a number with a unit. The SI base units used in chemistry are metre, kilogram, second, kelvin and mole; $1\ \text{L} = 1\ \text{dm}^3$. Scientific notation writes $N \times 10^{n}$ with $1 \le N < 10$.

Precision is the agreement between repeated readings; accuracy is the agreement with the true value.

Significant figures: non-zero digits and zeros between them count; leading zeros do not; trailing zeros count after a decimal point. In addition or subtraction keep the fewest decimal places; in multiplication or division keep the fewest significant figures. Exact numbers (counts, definitions) have unlimited significant figures.

• Conservation of mass (Lavoisier): mass of reactants equals mass of products.
• Constant proportions (Proust): a pure compound has a fixed mass ratio of elements.
• Multiple proportions (Dalton): for a fixed mass of one element, the masses of another that combine with it in different compounds are in a simple whole-number ratio.
• Gay-Lussac’s law: gaseous reactants and products are in simple whole-number volume ratios at the same temperature and pressure.
• Avogadro’s law: equal volumes of gases at the same temperature and pressure hold equal numbers of molecules.

Dalton’s theory: matter is made of atoms; atoms of an element are alike; compounds form by combination of atoms in simple whole-number ratios; atoms are rearranged, not created or destroyed in reactions.

1 u $= \tfrac{1}{12}$ of the mass of a carbon-12 atom $\approx 1.66 \times 10^{-27}$ kg. Average atomic mass $= \sum (\text{fractional abundance} \times \text{isotopic mass})$. Molecular mass is the sum of atomic masses in the molecule; formula mass is used for ionic compounds.

Mole: the amount of substance containing $6.022 \times 10^{23}$ elementary entities (the Avogadro constant $N_\text{A}$). Molar mass $M$ (g mol⁻¹) is numerically equal to the atomic or molecular mass in u. At 273.15 K and 1 atm one mole of an ideal gas occupies about 22.4 L.

Mass percent of an element $= \dfrac{\text{mass of the element in one mole}}{\text{molar mass of compound}} \times 100$.

Empirical formula: (1) take mass of each element (use percentages as grams in 100 g); (2) divide by atomic mass to get moles; (3) divide by the smallest; (4) multiply by 2, 3 … if any ratio is near a fraction such as 1.5 or 1.33.

Molecular formula $= (\text{empirical formula})_n$ with $n = M / M_\text{empirical}$. Several compounds can share an empirical formula (for example ethyne and benzene, both CH).

A balanced equation gives mole ratios. Plan: mass $\to$ moles ($\div M$) $\to$ moles of wanted substance (coefficient ratio) $\to$ mass ($\times M$).

Limiting reagent: the reactant consumed first. Divide each amount in moles by its coefficient; the smallest quotient identifies it. The yield is calculated from the limiting reagent only; the other is in excess and the leftover is found by subtraction.

Percentage yield $= \dfrac{\text{actual yield}}{\text{theoretical yield}} \times 100$.

Mass percent $= \dfrac{m_\text{solute}}{m_\text{solution}} \times 100$; ppm $= \dfrac{m_\text{solute}}{m_\text{solution}} \times 10^{6}$; mole fraction $x_\text{A} = \dfrac{n_\text{A}}{\sum n}$ (sum of all mole fractions is 1); molarity $c = n / V(\text{L})$; molality $m = n / m_\text{solvent}(\text{kg})$.

Molarity changes with temperature (volume changes); molality and mole fraction do not. Dilution: $c_1 V_1 = c_2 V_2$. From a label: $c = \dfrac{10\, w\, \rho}{M}$ with $w$ in mass percent and $\rho$ in g mL⁻¹.