Atoms, Elements, and the Foundations of General Chemistry

Atoms & Elements

Law of Conservation of Mass

The Law of Conservation of Mass states that matter is neither created nor destroyed during a chemical reaction. This fundamental principle ensures that the total mass of reactants equals the total mass of products in any chemical process.

• Definition: The mass of substances produced (products) in a chemical reaction is equal to the mass of substances consumed (reactants).

• Example: Decomposition of aluminum oxide ($Al_2O_3$): $2Al_2O_3 \rightarrow 3O_2 + 4Al$ If 150.0 g of $Al_2O_3$ decomposes and 77.115 g of Al is produced, the mass of $O_2$ produced can be calculated by subtracting the mass of Al from the original mass.

• Application: Used to balance chemical equations and solve stoichiometry problems.

Law of Definite Proportions

The Law of Definite Proportions states that a pure substance always contains the same elements in the same proportion by mass, regardless of its source or method of preparation.

• Definition: All samples of a compound have the same elemental composition by mass.

• Example Table: Composition by Number of Atoms

Substance	Composition by Element (Number of Atoms)
Ethanol – C2H6O	2 C, 6 H, 1 O
Glucose – C6H12O6	6 C, 12 H, 6 O
Calcium Phosphate – Ca3(PO4)2	3 Ca, 2 P, 8 O

• Example Table: Composition by Mass and Mass Ratio

Substance	Composition by Mass	Mass Ratio
Ethanol – C2H6O	24.02 g C, 6.06 g H, 16.00 g O (per mole)	24.02:6.06:16.00
Salt – NaCl	22.99 g Na, 35.45 g Cl (per mole)	22.99:35.45
Glucose – C6H12O6	72.06 g C, 12.12 g H, 96.00 g O (per mole)	72.06:12.12:96.00
Calcium Phosphate – Ca3(PO4)2	120.18 g Ca, 61.94 g P, 128.00 g O (per mole)	120.18:61.94:128.00

Additional info: Masses are calculated using atomic masses from the periodic table.

Law of Multiple Proportions

The Law of Multiple Proportions states that 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.

• Definition: If elements A and B form more than one compound, the ratio of the masses of B that combine with a fixed mass of A is a ratio of small whole numbers.

• Example Table: Masses of Elements in Compounds

	Carbon (C)	Hydrogen (H)	Oxygen (O)
Compound #1	52.13 g	13.15 g	34.72 g
Compound #2	54.52 g	9.169 g	36.31 g

• Application: Used to determine empirical formulas and to distinguish between different compounds made from the same elements.

Atomic Structure

Subatomic Particles

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

• Proton (p): Positively charged particle found in the nucleus.

• Neutron (n): Neutral particle found in the nucleus.

• Electron (e): Negatively charged particle found outside the nucleus.

Isotopes

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

• Notation: $^{A}_{Z}X$ where A = mass number (protons + neutrons), Z = atomic number (protons), X = element symbol.

• Example Table: Isotope Composition

Isotope	#p	#e	#n
$^{71}_{31}Ga$	31	31	40
$^{80}_{35}Br$	35	35	45
$^{195}_{78}Pt$	78	78	117
$^{18}_{8}O$	8	8	10
$^{133}_{54}Xe$	54	54	79

Additional info: Number of neutrons = mass number - atomic number.

The Periodic Table

Organization of the Periodic Table

The periodic table arranges elements by increasing atomic number and groups elements with similar chemical properties into columns called groups or families.

• Groups: Vertical columns (numbered 1-18 or IA-VIIIA and IB-VIIIB).

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

• Classification: Elements are classified as metals, nonmetals, or metalloids, and as main group, transition, or inner transition elements.

Groups	Periods	Element	Classification
IIA	6	Ba	Metal, Main Group
VI	2	O	Nonmetal, Main Group
10	6	Pt	Metal, Transition
VIIA	3	Br	Nonmetal, Main Group

Additional info: Group and period numbers help locate elements and predict their properties.

Ions and Chemical Formulas

Formation of Ions

Atoms can gain or lose electrons to form ions. Metals tend to lose electrons to form cations (positively charged ions), while nonmetals tend to gain electrons to form anions (negatively charged ions).

• Cation: Positively charged ion (e.g., Na+).

• Anion: Negatively charged ion (e.g., Cl-).

Chemical Formulas for Ions

The magnitude and charge of an ion are written as a superscript to the right of the element symbol.

Element	Group #	Charge	Symbol
Calcium	2	+2	Ca2+
Cesium	1	+1	Cs+
Gallium	13	+3	Ga3+
Selenium	16	-2	Se2-
Nitrogen	15	-3	N3-
Fluorine	17	-1	F-

Atomic Mass and Isotopes

Atomic Mass

Atomic mass is the weighted average mass of the isotopes of an element based on their natural abundance. It is listed below the element symbol in the periodic table.

• Calculation: $\text{Atomic Mass} = \sum (\text{isotope mass} \times \text{fractional abundance})$

• Example: Magnesium Isotopes

Isotope	Relative Atomic Mass (RAM)	% Abundance
$^{24}$Mg	23.98504 amu	78.99%
$^{25}$Mg	24.98584 amu	10.00%
$^{26}$Mg	25.98259 amu	11.01%

• Example: Chlorine Isotopes

Isotope	Relative Atomic Mass (RAM)
$^{35}$Cl	34.96885 amu
$^{37}$Cl	36.96590 amu

• Dominant Isotope: The isotope with the highest natural abundance.

• Percent Abundance Table (Chlorine):

Approx atomic mass	Cl-35 % Abundance	Cl-37 % Abundance
35.0	75.77%	24.23%
36.0	75.77%	24.23%
37.0	75.77%	24.23%

Additional info: Actual percent abundances for Cl-35 and Cl-37 are approximately 75.77% and 24.23%, respectively.

The Mole and Avogadro's Number

The Mole

The mole is a unit that represents a specific number of particles (atoms, molecules, ions, etc.). One mole contains Avogadro's number of particles.

• Definition: $1 \text{ mole} = 6.022 \times 10^{23}$ particles

• Application: Used as a conversion factor between the number of particles and the amount of substance in moles.

Calculations Using Avogadro's Number

• Number of moles from atoms: $\text{Moles} = \frac{\text{Number of atoms}}{6.022 \times 10^{23}}$

• Number of atoms from moles: $\text{Number of atoms} = \text{Moles} \times 6.022 \times 10^{23}$

• Mass from moles: $\text{Mass (g)} = \text{Moles} \times \text{Molar Mass (g/mol)}$

• Moles from mass: $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$

Example Problems:

• How many moles of carbon are in $2.06 \times 10^{22}$ atoms of carbon?

• What is the mass in grams of 2.91 moles of gold?

• How many moles are in 1.85 g of cesium?

• How many atoms of zinc are in 25.4 mg of zinc?

Combined Conversion Factor Example:

• Chlorine: $35.45 \text{ g/mol} \rightarrow 35.45 \text{ g Cl} / 6.022 \times 10^{23}$ atoms Cl

Additional info: These calculations are fundamental for stoichiometry and quantitative chemical analysis.