Matter: Its Properties and Measurement

Classification of Matter

Matter is anything that has mass and occupies space. It can be classified based on its composition and structure.

• Atom: The fundamental building block of matter; the smallest unit of an element.

• Molecule: Two or more atoms chemically bonded together.

• Element: A substance consisting of identical atoms.

• Compound: A substance composed of different atoms (elements) bonded together.

• Molecules of an element: Two or more atoms of the same element joined together (e.g., O2).

• Molecules of a compound: Two or more atoms of different elements joined together (e.g., H2O).

• Pure substance: Consists of only one type of molecule or atom.

• Mixture: Contains two or more different molecules or atoms physically combined.

Separation and purification techniques are required to separate mixtures into pure substances.

Properties and Changes of Matter

• Physical Properties: Can be observed without changing the substance's identity (e.g., color, melting point, density).

• Chemical Properties: Can only be observed when a substance is transformed into another substance (e.g., flammability, reactivity).

• Physical Changes: Changes that do not alter the chemical composition (e.g., melting, boiling).

• Chemical Changes: Changes that result in the formation of new substances (e.g., combustion, rusting).

Measurement of Matter

Physical quantities in chemistry are measured using the SI system. Common units include:

• Length: meter (m)

• Mass: kilogram (kg)

• Time: second (s)

• Temperature: kelvin (K)

• Amount of substance: mole (mol)

Prefixes (e.g., milli-, centi-, kilo-) are used to indicate multiples or fractions of units. Refer to standard tables for more details.

Mass vs. Weight

• Mass: The amount of matter in an object; does not change with location.

• Weight: The force exerted by gravity on an object; depends on location.

Temperature Conversions

• To convert between Celsius, Fahrenheit, and Kelvin, use the following equations:

Density and Percent Composition

• Density (d): The mass per unit volume of a substance.

• Percent Composition: The percentage by mass of each component in a mixture or compound.

Example: If seawater is 3.5% NaCl by mass, 1.0 kg of seawater contains 35 g NaCl.

Uncertainties in Measurement

• Systematic Errors: Consistent, repeatable errors due to faulty equipment or bias.

• Random Errors: Errors that vary unpredictably from one measurement to another.

• Precision: How close repeated measurements are to each other.

• Accuracy: How close a measurement is to the true value.

Significant Figures

• Significant figures are the digits in a measurement that are known with certainty plus one estimated digit.

• Rules:

  • All nonzero digits are significant.

  • Zeroes between significant digits are significant.

  • Leading zeroes are not significant.

  • Trailing zeroes are significant only if a decimal point is present.

  • In scientific notation, the coefficient determines the number of significant figures.

• Exact numbers (e.g., counting numbers, defined constants) have infinite significant figures.

Calculations:

• For multiplication/division: The result has as many significant figures as the number with the least significant figures used in the calculation.

• For addition/subtraction: The result has as many decimal places as the number with the least decimal places.

Rounding: If the digit to be dropped is greater than 5, increase the last retained digit by one; if less than 5, leave it unchanged.

Atoms & the Atomic Theory

Early Chemical Discoveries and Atomic Theory

• Law of Conservation of Mass (Lavoisier, 1789): Mass is neither created nor destroyed in chemical reactions.

• Law of Constant Composition (Proust, 1794): A given compound always contains the same elements in the same proportion by mass.

• Dalton's Atomic Theory (1803): Atoms are indivisible particles; atoms of the same element are identical; compounds are combinations of different atoms; chemical reactions rearrange atoms.

• Mendeleev (1869): Organized elements into the periodic table based on properties.

Chemical Elements, Isotopes, and Ions

• Atomic Number (Z): Number of protons in the nucleus; defines the element.

• Mass Number (A): Total number of protons and neutrons in the nucleus.

• Isotopes: Atoms of the same element with different numbers of neutrons (e.g., 12C, 13C, 14C).

• Ions: Atoms or molecules that have gained or lost electrons.

  • Cation: Positively charged ion (loss of electrons).

  • Anion: Negatively charged ion (gain of electrons).

Example: For the ion 16O2–: 8 protons, 8 + 2 = 10 electrons, 16 – 8 = 8 neutrons.

Atomic Mass and the Mole Concept

• Average Atomic Mass: Weighted average of the masses of all isotopes of an element.

Example: Chlorine: amu

• Avogadro's Number (NA): particles/mol

• Mole (mol): The amount of substance containing Avogadro's number of particles.

• Molar Mass: Mass of one mole of a substance (g/mol); numerically equal to the formula weight in amu.

Unit Conversions: Use conversion factors to relate moles, mass, and number of particles.

Example: To find the number of Pb atoms in 0.105 cm3 of lead (density = 11.34 g/cm3):

1. Calculate mass: g

2. Calculate moles: mol

3. Calculate atoms: atoms

Chemical Compounds

Types of Chemical Compounds and Their Formulas

• Covalent (Molecular) Compounds: Composed of molecules formed by nonmetals sharing electrons (covalent bonds).

• Ionic Compounds: Composed of cations (usually metals) and anions (usually nonmetals) held together by electrostatic attraction.

Formulas:

• Empirical Formula: Simplest whole-number ratio of elements (e.g., CH2O for glucose).

• Molecular Formula: Actual number of atoms of each element (e.g., C6H12O6 for glucose).

• Structural Formula: Shows the arrangement of atoms and bonds.

• Condensed, Line-Angle, Ball-and-Stick, and Space-Filling Models: Various ways to represent molecular structure, especially for organic compounds.

Ionic Compounds

• Formed when atoms transfer electrons to achieve noble gas configurations.

• Cations: Positively charged, usually metals (e.g., Na+).

• Anions: Negatively charged, usually nonmetals (e.g., Cl–).

• Formula units represent the simplest ratio of ions (e.g., NaCl).

• Ionic compounds are typically hard, crystalline solids with high melting points.

The Mole Concept and Chemical Compounds

• 1 mole of a compound contains Avogadro's number of molecules or formula units.

• Formula Mass: Mass of one formula unit (ionic compounds).

• Molecular Mass: Mass of one molecule (covalent compounds).

Example: To find grams of MgCl2 needed to extract Cl– ions:

• 1 mol MgCl2 contains 2 mol Cl–

• Calculate moles of MgCl2 needed, then mass using molar mass.

Composition of Chemical Compounds

• Mass Percent Composition:

• Empirical Formula: Determined from mass percent composition by converting masses to moles and finding the simplest ratio.

Example: Sorbitol (molecular mass 182 u, 39.56% C, 7.74% H, 52.70% O):

1. Assume 100 g sample: 39.56 g C, 7.74 g H, 52.70 g O

2. Convert to moles: , ,

3. Divide by smallest to get ratio, then write empirical formula.

Combustion Analysis: Used to determine C and H content by measuring CO2 and H2O produced; O is found by difference.

Chemical Reactions

Chemical Reactions and Chemical Equations

• Chemical Equation: Symbolic representation of a chemical reaction.

• Reactants are written on the left, products on the right (e.g., ).

• Balancing Equations: Adjust coefficients to ensure the same number of each atom on both sides; do not change subscripts.

• State symbols: (s) solid, (l) liquid, (g) gas, (aq) aqueous.

Chemical Equations and Stoichiometry

• Coefficients in a balanced equation indicate the mole ratio of reactants and products.

• Use molar mass to convert between grams and moles.

Example: To produce 1.00 kg methanol () from , calculate moles and then grams of H2 needed.

Chemical Reactions in Solution

• Molarity (M):

• Percent by mass and density can be used to convert to molarity.

Example: Commercial H2SO4 is 98% by mass, density 1.84 g/mL. Calculate molarity using mass, volume, and molar mass.

• Dilution: (concentration and volume before and after dilution)

Limiting Reactant and Percent Yield

• Limiting Reactant: The reactant that is completely consumed first, limiting the amount of product formed.

• Excess Reactant: The reactant that remains after the reaction is complete.

• Convert all reactant amounts to moles and compare using stoichiometric ratios.

Percent Yield:

Consecutive and Simultaneous Reactions: Some syntheses require multiple steps (consecutive reactions) or involve multiple reactions occurring at once (simultaneous reactions). Stoichiometric calculations must account for these complexities.

Introduction to Reactions in Aqueous Solutions

The Nature of Aqueous Solutions

• Electrolyte: Substance that dissolves in water to produce ions and conducts electricity.

• Nonelectrolyte: Dissolves in water but does not produce ions; does not conduct electricity.

• Strong Electrolyte: Completely dissociates into ions in water (e.g., NaCl).

• Weak Electrolyte: Partially dissociates into ions (e.g., acetic acid).

Example: Seawater contains 0.438 M NaCl and 0.0512 M MgCl2; total anion concentration is the sum of Cl– from both sources.

Precipitation Reactions

• When two solutions are mixed and an insoluble compound forms, a precipitate is produced.

• Solubility rules help predict whether a precipitate will form.

• Ionic Equation: Shows all strong electrolytes as ions.

• Net Ionic Equation: Shows only the species that actually change during the reaction; spectator ions are omitted.

Example: Full ionic: Net ionic:

Acid-Base Reactions

• Arrhenius Definition: Acids produce H+ in water; bases produce OH–.

• Brønsted-Lowry Definition: Acids are proton donors; bases are proton acceptors.

• Amphiprotic: Species that can act as either acid or base (e.g., H2O).

• Strong Acids: Completely ionize in water (e.g., HCl, HNO3, H2SO4).

• Weak Acids: Partially ionize (e.g., acetic acid).

• Strong Bases: Soluble hydroxides of alkali and heavy alkaline earth metals (e.g., NaOH, Ca(OH)2).

• Weak Bases: Ammonia (NH3), poorly soluble metal hydroxides.

• Neutralization: Acid + base → salt + water (for most reactions).

Example: Net ionic:

Stoichiometry of Reactions in Aqueous Solutions: Titrations

• Titration: Gradual addition of one solution to another to determine concentration, ending at the equivalence point.

• At equivalence point: moles of H+ = moles of OH–

• Use balanced equations for calculations.

Example: 15.2 mL of 0.100 M NaOH required to titrate 10.0 mL HNO3. Calculate initial concentration of acid:

• mol

• Since 1:1 ratio, mol

• M