General Chemistry: Atoms, Molecules, Ions, and Measurement Foundations

Significant Figures and Dimensional Analysis

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one digit that is estimated. They reflect the precision of a measured or calculated quantity.

• Definition: The number of meaningful digits in a value, indicating the precision of the measurement.

• Rules:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros are significant only if there is a decimal point.

• Application: When performing calculations, the result should be reported with the correct number of significant figures based on the operation (addition/subtraction: least decimal places; multiplication/division: least number of sig figs).

Example: 0.00450 has three significant figures (4, 5, and the trailing 0).

Dimensional Analysis

Dimensional analysis is a systematic method used to convert one unit of measurement to another using conversion factors.

• Definition: A technique that uses the units (dimensions) of quantities to guide the calculation and ensure correct results.

• Conversion Factor: A ratio that expresses how many of one unit are equal to another unit (e.g., 1 in. = 2.54 cm).

• General Formula:

$\text{Given unit} \times \frac{\text{desired unit}}{\text{given unit}} = \text{desired unit}$

• Steps:

  1. Identify the starting unit and the desired unit.

  2. Set up the conversion factor so that the given unit cancels, leaving the desired unit.

  3. Multiply through to obtain the answer in the desired unit.

• Example: Convert 8.00 m to inches.

  • Convert meters to centimeters: $1\ \text{m} = 100\ \text{cm}$

  • Convert centimeters to inches: $2.54\ \text{cm} = 1\ \text{in}$

  • Calculation:

  $8.00\ \text{m} \times \frac{100\ \text{cm}}{1\ \text{m}} \times \frac{1\ \text{in}}{2.54\ \text{cm}} = 315\ \text{in}$

Atoms, Molecules, and Ions

Law of Definite Proportions (Proust's Law)

The law of definite proportions states that a chemical compound always contains exactly the same proportion of elements by mass.

• Definition: Different samples of a pure compound always contain the same elements in the same mass ratio.

• Example: In carbon dioxide (CO2), the mass ratio of carbon to oxygen is always the same, regardless of the sample size.

• Sample Calculation:

  • 100 g of CO2: 42.88 g C and 57.12 g O

  • 200 g of CO2: 85.76 g C and 114.24 g O

  • Mass ratio: $\frac{42.88}{57.12} = \frac{85.76}{114.24} = 0.7507$

Law of Multiple Proportions (Dalton's Law)

When two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers.

• Example:

  • CO: C to O ratio is 1:1

  • CO2: C to O ratio is 1:2

  • Na2CO3: C to O ratio is 1:3

Dalton's Atomic Theory

John Dalton's atomic theory laid the foundation for modern chemistry by describing the nature of atoms and their role in chemical reactions.

• All matter is made of indivisible and indestructible atoms.

• All atoms of a given element are identical in mass and properties.

• Compounds are formed by the combination of two or more different kinds of atoms.

• Chemical reactions involve the rearrangement of atoms; atoms are neither created nor destroyed.

Example: The reaction $2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$ shows hydrogen and oxygen atoms combining to form water.

Atomic Structure and Subatomic Particles

Discovery of the Electron

J.J. Thomson's experiments with cathode ray tubes led to the discovery of the electron, a negatively charged subatomic particle.

• Electrons are much lighter than atoms and carry a negative charge.

• Thomson measured the charge-to-mass ratio of the electron: $1.76 \times 10^8$ coulombs/gram.

Millikan Oil Drop Experiment

Robert Millikan determined the charge of the electron using the oil drop experiment.

• Measured the charge on tiny oil droplets suspended in an electric field.

• Found that the charge was always a multiple of a fundamental value: $-1.6022 \times 10^{-19}$ coulombs.

• Combined with Thomson's results, allowed calculation of the electron's mass: $9.10939 \times 10^{-28}$ grams.

Rutherford's Gold Foil Experiment

Ernest Rutherford's gold foil experiment revealed the existence of a small, dense, positively charged nucleus at the center of the atom.

• Most alpha particles passed through the foil, but some were deflected at large angles.

• Concluded that atoms are mostly empty space with a dense nucleus containing protons (and later, neutrons).

Subatomic Particles

Atoms are composed of three main subatomic particles: protons, neutrons, and electrons.

Particle	Mass (g)	Charge (C)	Charge (unit)
Electron (e-)	9.10939 × 10-28	-1.6022 × 10-19	-1
Proton (p+)	1.67262 × 10-24	+1.6022 × 10-19	+1
Neutron (n0)	1.67493 × 10-24	0	0

Additional info: Protons and neutrons are located in the nucleus; electrons are distributed in the space around the nucleus.

The Periodic Table and Classification of Elements

Structure of the Periodic Table

The periodic table organizes elements by increasing atomic number and recurring chemical properties.

• Periods: Horizontal rows (numbered 1–7).

• Groups: Vertical columns (numbered 1–18 or with A/B notation).

• Main Group Elements: Groups 1A–8A (1, 2, 13–18).

• Transition Metals: Groups 3–12 (B groups in older notation).

• Inner Transition Metals: Lanthanides and actinides (bottom two rows).

Classification of Elements

Group Name	Elements
Alkali Metals	Li, Na, K, Rb, Cs, Fr
Alkaline Earth Metals	Be, Mg, Ca, Sr, Ba, Ra
Chalcogens	O, S, Se, Te, Po
Halogens	F, Cl, Br, I, At
Noble Gases	He, Ne, Ar, Kr, Xe, Rn

Additional info: Other groups are sometimes named after the first element in the group (e.g., Group 5A: Nitrides).

Metals, Nonmetals, and Metalloids

• Metals: Majority of elements; good conductors, malleable, ductile, shiny.

• Nonmetals: Upper right of the table; poor conductors, varied states (solids, liquids, gases).

• Metalloids: Elements with properties intermediate between metals and nonmetals (B, Si, Ge, As, Sb, Te).

Diatomic Molecules

Seven elements exist naturally as diatomic molecules (two atoms bonded together): H2, N2, O2, F2, Cl2, Br2, I2.

Isotopes and Ions

Atomic Number and Mass Number

• 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 (same Z) with different numbers of neutrons (different A).

Example: $^{235}_{92}U$ and $^{238}_{92}U$ are isotopes of uranium.

Ions

• Cations: Positively charged ions formed by loss of electrons (usually metals).

• Anions: Negatively charged ions formed by gain of electrons (usually nonmetals).

• Naming: Cations retain the element name; anions take the suffix "-ide" (e.g., chloride for Cl-).

Example: Na loses one electron to form Na+ (cation); Cl gains one electron to form Cl- (anion).

Determining Subatomic Particles in Ions and Isotopes

• Number of protons: Equal to atomic number (Z).

• Number of neutrons: $A - Z$.

• Number of electrons: For neutral atoms, equal to protons; for ions, adjust for charge (cations: fewer electrons, anions: more electrons).

Example: For $^{37}_{17}Cl^-$: 17 protons, 20 neutrons (37-17), 18 electrons (17+1).

Summary Table: Subatomic Particles

Particle	Location	Relative Mass	Charge
Proton	Nucleus	1	+1
Neutron	Nucleus	1	0
Electron	Outside nucleus	~1/1836	-1

Additional info: The structure and classification of atoms, molecules, and ions form the foundation for understanding chemical reactions and properties of matter.