Key Points

Matter is anything that has mass and occupies space, existing in solid, liquid, or gas states. It is classified into pure substances (elements and compounds) and mixtures (homogeneous and heterogeneous).

In any physical or chemical change, the total mass of the reactants is equal to the total mass of the products. This means matter is neither created nor destroyed.

A given chemical compound always contains its component elements in a fixed ratio by mass, regardless of its source. For example, water ($H_2O$) always contains hydrogen and oxygen in a 1:8 mass ratio.

If two elements form more than one compound, the masses of one element that combine with a fixed mass of the other element are in a ratio of small whole numbers. For example, in $H_2O$ and $H_2O_2$, the mass ratio of oxygen that combines with a fixed mass of hydrogen is 1:2.

At the same temperature and pressure, equal volumes of all gases contain an equal number of molecules. This implies that for a gas reaction like $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$, the volume ratio is also 1:3:2.

This theory states that matter is composed of indivisible atoms, all atoms of a given element are identical, and chemical reactions involve the reorganization of atoms.

Atomic mass is expressed in atomic mass units (u), where 1 u is defined as $\frac{1}{12}$ the mass of a Carbon-12 atom. Molecular mass is the sum of the atomic masses of all atoms present in a molecule.

One mole of any substance contains exactly $6.022 \times 10^{23}$ elementary entities (atoms, molecules, or ions). This value is called the Avogadro constant ($N_A$).

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is numerically equal to the atomic or molecular mass expressed in u.

The mass percentage of an element in a compound is calculated as: Mass % $= \frac{\text{Mass of that element in the compound}}{\text{Molar mass of the compound}} \times 100$.

The empirical formula gives the simplest whole-number ratio of atoms in a compound, while the molecular formula gives the exact number of atoms. Molecular Formula $= n \times (\text{Empirical Formula})$, where $n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$.

Stoichiometry deals with quantitative relationships between reactants and products in a balanced chemical equation. The limiting reagent is the reactant that is completely consumed first and limits the amount of product formed.

Molarity is the number of moles of solute per liter of solution. Its unit is mol/L or M. The formula is Molarity $(M) = \frac{\text{Moles of solute}}{\text{Volume of solution in L}}$.

Molality is the number of moles of solute per kilogram of solvent. Its unit is mol/kg or m. The formula is Molality $(m) = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}$. It does not change with temperature.

Mole fraction is the ratio of the number of moles of a particular component to the total number of moles of the solution. For component A, $X_A = \frac{n_A}{n_A + n_B}$. The sum of mole fractions of all components is always 1.

Significant figures are meaningful digits in a measured or calculated quantity which are known with certainty plus one estimated digit. For example, 0.0025 has two significant figures, and 2.00 has three.