Chemistry is the branch of science that deals with the composition, structure, properties, and transformation of matter. Everything around us — air, water, food, medicines — is made of chemicals. This chapter lays the quantitative foundation that makes all of chemistry precise and measurable.
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Key Concepts
Matter and Its Classification
Matter is anything that has mass and occupies space. It is classified as pure substances (elements and compounds) and mixtures (homogeneous and heterogeneous).
- Laws of Chemical Combination
- Law of Conservation of Mass (Lavoisier): In any chemical reaction, the total mass of reactants equals the total mass of products. Mass is neither created nor destroyed.
- Law of Definite Proportions (Proust): A pure chemical compound always contains the same elements in the same fixed mass ratio.
- Law of Multiple Proportions (Dalton): When two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other are in a simple whole-number ratio.
- Gay-Lussac's Law of Gaseous Volumes: When gases react together, the volumes of reactants and products (at the same temperature and pressure) are in simple whole-number ratios.
- Avogadro's Law: Equal volumes of all gases, under the same conditions of temperature and pressure, contain equal numbers of molecules.
- Atomic and Molecular Mass
- Atomic mass unit (amu or u): 1 u = 1/12 the mass of one carbon-12 atom = 1.66056 x 10-27 kg.
- Atomic mass of an element is the average relative mass of its atoms compared to 1/12 the mass of a C-12 atom.
- Molecular mass is the sum of atomic masses of all atoms in a molecule.
- Formula mass is used for ionic compounds (which do not have discrete molecules).
Mole Concept and Molar Mass
The mole is the SI unit for amount of substance. One mole contains exactly 6.022 x 1023 entities (Avogadro's number, NA). The molar mass of a substance (in g/mol) is numerically equal to its atomic or molecular mass in u.
- Key relations:
- Number of moles (n) = given mass (m) / molar mass (M)
- Number of entities = n x NA
- At STP (0 degree C, 1 atm): 1 mole of any gas occupies 22.4 L (molar volume).
- Percentage Composition and Empirical/Molecular Formula
- % by mass of element = (mass of element in 1 mole of compound / molar mass of compound) x 100
- Empirical formula gives the simplest whole-number ratio of atoms.
- Molecular formula = n x Empirical formula, where n = Molar mass / Empirical formula mass.
Stoichiometry and Limiting Reagent
A balanced chemical equation is essential for stoichiometric calculations. The limiting reagent is the reactant that is completely consumed first and determines the maximum yield of product. Percent yield = (actual yield / theoretical yield) x 100.
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Worked Examples
Calculate the molar mass of H2SO4.
H2SO4 contains 2 H, 1 S, and 4 O.
Molar mass = 2(1) + 32 + 4(16) = 2 + 32 + 64 = 98 g/mol
How many moles are present in 9 g of water (H2O)?
Molar mass of H2O = 2(1) + 16 = 18 g/mol
n = 9/18 = 0.5 mol
Calculate the number of molecules in 44 g of CO2 (molar mass = 44 g/mol).
n = 44/44 = 1 mol
Number of molecules = 1 x 6.022 x 1023 = 6.022 x 1023 molecules
A compound contains 40% C, 6.67% H, and 53.33% O by mass. Find its empirical formula.
Mole ratio: C = 40/12 = 3.33, H = 6.67/1 = 6.67, O = 53.33/16 = 3.33
Divide by smallest (3.33): C = 1, H = 2, O = 1
Empirical formula = CH2O
If the molecular mass of the compound above is 180 g/mol, find its molecular formula.
Empirical formula mass of CH2O = 12 + 2 + 16 = 30 g/mol
n = 180/30 = 6
Molecular formula = C6H12O6 (glucose)
In the reaction N2 + 3H2 → 2NH3, if 28 g of N2 reacts with 9 g of H2, identify the limiting reagent.
Moles of N2 = 28/28 = 1 mol; Moles of H2 = 9/2 = 4.5 mol
N2 needs 3 x 1 = 3 mol H2 but only 4.5 mol available. Check H2: 4.5 mol H2 needs 4.5/3 = 1.5 mol N2 but only 1 mol available. So N2 is the limiting reagent.
Calculate the volume (at STP) occupied by 4 g of oxygen gas (O2).
Molar mass of O2 = 32 g/mol; n = 4/32 = 0.125 mol
Volume = 0.125 x 22.4 = 2.8 L
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Common mistakes
Students often confuse atomic mass (relative, in u) with molar mass (absolute, in g/mol) — numerically they are equal but the units differ. Another frequent error is forgetting that Avogadro's number applies to any entity (atoms, molecules, ions, electrons), not just molecules.
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Summary
This chapter establishes that all chemical calculations rest on the mole concept, balanced equations, and the laws of chemical combination. Master the conversions: mass <→ moles <→ number of particles <→ volume at STP. These skills underpin every quantitative problem in chemistry.