General Chemistry Study Notes: Matter, Measurement, Atomic Structure, and Subatomic Particles

Matter, Measurement & Problem Solving

Significant Figures in Calculations

Significant figures (sig figs) are crucial for expressing the precision of measurements and calculations in chemistry.

• Multiplication/Division: Keep the smallest number of significant figures from the numbers used.

• Addition/Subtraction: Keep the fewest decimals from the numbers used.

• Rounding: Round 5s down if after 0-4, up if after 5-9. Always round at the end, not at each step.

• Example: $\frac{131 - 86.7}{53.09}$ should be rounded according to the rules above.

Scientific Notation and Significant Figures

Scientific notation is used to express very large or small numbers efficiently and to clarify significant figures.

• Count decimals outside of scientific notation.

• Example: $2.32 \times 10^{-3}$ has 3 significant figures.

• Numbers like 0.00232 have 3 significant figures (the zeros are not significant).

Order-of-Magnitude Estimations

Order-of-magnitude calculations provide quick, approximate answers by rounding to the nearest power of ten.

• Put numbers in scientific notation.

• Round to the nearest power of 10 for estimation.

• Example: $\frac{m_p}{m_e} = \frac{1.67492728 \times 10^{-27}\,\text{kg}}{9.10938262 \times 10^{-31}\,\text{kg}} \approx 10^3$

• A proton is roughly 1,000 times more massive than an electron.

Unit Conversions and Dimensional Analysis

Unit conversions and dimensional analysis are essential for solving chemical problems and ensuring correct units in answers.

• Sort: Take inventory of given information, with units.

• Strategize: Identify steps and ensure units cancel to the desired unit.

• Solve: Plug numbers into your steps with units.

• Check: Ensure the answer makes sense (e.g., no negative mass).

• Example: Converting 173,231 L of jet fuel (density 0.768 g/cm3) to kilograms: $173,231\,L \times \frac{1000\,mL}{1\,L} \times \frac{1\,cm^3}{1\,mL} \times \frac{0.768\,g}{1\,cm^3} \times \frac{1\,kg}{1000\,g} = 1.33 \times 10^5\,kg$

Problems Involving Equations

Solving problems often involves using equations and ensuring units are consistent throughout.

• Density Equation: $d = \frac{m}{V}$

• Volume of a Cylinder: $V = \pi r^2 l$

• Example: For a cylinder with $m = 8.3\,g$, $l = 1.94\,cm$, $r = 0.55\,cm$: $d = \frac{8.3\,g}{\pi (0.55\,cm)^2 (1.94\,cm)} = 4.5\,g/cm^3$

Atoms & Elements

The Law of Conservation of Mass

In a chemical reaction, matter is neither created nor destroyed. The total mass of reactants equals the total mass of products.

• Example Reaction: $\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}$

• If 52g of methane and oxygen react, the mass of products will also be 52g.

The Law of Definite Proportions

All samples of a given compound have the same proportions of their constituent elements, regardless of source or preparation.

• Example: Water always has a mass ratio of 8:1 for oxygen to hydrogen.

• Application: Sugar from different sources is chemically identical.

The Law of Multiple Proportions

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: Carbon dioxide (CO2) and carbon monoxide (CO): CO2: 2.67g O per 1g C; CO: 1.33g O per 1g C; $\frac{2.67}{1.33} = 2$

• Application: For nitrogen oxides, use mass ratios to deduce formulas.

Dalton’s Atomic Theory

Dalton's theory laid the foundation for modern atomic theory.

• Each element is composed of tiny, indestructible particles called atoms.

• All atoms of a given element have the same mass and properties.

• Atoms combine in simple, whole-number ratios to form compounds.

• Atoms of one element cannot change into atoms of another element in chemical reactions.

Subatomic Particles

Structure of an Atom

Atoms consist of a nucleus (protons and neutrons) surrounded by a cloud of electrons.

• Electrons occupy most of the volume of the atom.

• Atoms are not mostly empty space; electrons form a cloud.

Protons, Neutrons, and Electrons

Atoms are made up of three main subatomic particles, each with distinct properties.

Particle	Charge (au)	Mass (amu)	Mass of Atom	Volume of Atom
Electron	-1	0.00055	<0.001%	99%
Proton	+1	1.00727	>99.9%	<1%
Neutron	0	1.00866	>99.9%	<1%

• Protons: Define the element (atomic number Z).

• Neutrons: With protons, define isotopes (same element, different mass).

• Electrons: With protons, determine charge and define ions.

Isotope Notation

Isotopes are atoms of the same element with different numbers of neutrons.

• Mass number (A): Number of protons + neutrons.

• Atomic number (Z): Number of protons.

• Isotope notation: $^A_ZX$

• Number of neutrons (N): $N = A - Z$

Electrons and Ions

Atoms can gain or lose electrons to form ions.

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

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

• Example: $\text{Na} \rightarrow \text{Na}^+ + e^-$ (cation), $\text{Cl} + e^- \rightarrow \text{Cl}^-$ (anion)

Summary of Particle Roles in Atoms

Particle	Charge (au)	Mass (amu)	Changing number affects atom by
Electron	-1	0.00055	Changes charge (ion)
Proton	+1	1.00727	Changes element (Z)
Neutron	0	1.00866	Changes mass (isotope)

Atoms & Elements: Periodic Table

Memorizing Element Names and Symbols

Students are often required to memorize the names and symbols of key elements, especially those highlighted in green on the periodic table.

• Elements such as H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, etc.

• Knowing these is essential for chemical nomenclature and formula writing.

Additional info:

• Some slides reference worksheet problems and group work, which are typical in active learning chemistry courses.

• Practice with dimensional analysis and significant figures is foundational for all subsequent chemistry topics.