Masses of Atoms and Atomic Structure: Study Notes

Masses of Atoms

Introduction

The mass of atoms is a foundational concept in general chemistry, essential for understanding atomic structure, chemical reactions, and the mole concept. Atomic masses are measured in atomic mass units (amu), and the relationships between mass, number of atoms, and moles are central to quantitative chemical analysis.

Elements and Nuclear Symbols

Element Identity and Atomic Structure

• Element Identity: Defined by the number of protons in the nucleus. Each element has a unique number of protons, known as its atomic number (Z).

• Isotopes: Atoms of the same element with different numbers of neutrons. Isotopes have the same atomic number but different mass numbers (A).

• Ions: Atoms with variable numbers of electrons. Ions are charged species formed by the loss or gain of electrons.

The nuclear symbol for an atom is written as:

$^{A}_{Z}X$

• X: Chemical symbol of the element

• Z: Atomic number (number of protons)

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

Example: $^{12}_{6}C$ represents carbon-12, with 6 protons and 6 neutrons.

Subatomic Particles

Properties of Electrons, Protons, and Neutrons

Atoms are composed of three fundamental subatomic particles: electrons, protons, and neutrons. Their properties are summarized below:

Particle	Symbol	Relative Mass (amu)	Relative Charge
Electron	e-	0.0005	1−
Neutron	n	1	0
Proton	p+	1	1+

Example: The mass of a proton is approximately equal to that of a neutron, while the electron is much lighter.

Atomic Masses

Definition and Calculation

• Atomic Mass Unit (amu): Defined as 1/12 the mass of a single carbon-12 ($^{12}C$) atom.

• Average Atomic Mass: The weighted average mass of all naturally occurring isotopes of an element.

Example: The average atomic mass of iron (Fe) is 55.85 amu/atom, which equals $9.274 \times 10^{-23}$ g/atom.

Calculation Example: To find the number of iron atoms in 55.85 g Fe:

• Number of atoms = $\frac{\text{mass of sample}}{\text{mass of one atom}}$

• $\frac{55.85\ \text{g}}{9.274 \times 10^{-23}\ \text{g/atom}}$

Atomic Masses and the Mole Concept

Relating Mass to Number of Atoms

• Avogadro's Number: $6.022 \times 10^{23}$ atoms/mol. This is the number of atoms in one mole of any element.

• Conversion: $1\ \text{g} = 6.022 \times 10^{23}\ \text{amu}$

Example: To find the number of tellurium atoms in 127.6 g Te:

• Atomic mass of Te = 127.6 amu/atom

• Number of atoms = $\frac{127.6\ \text{g}}{2.12 \times 10^{-22}\ \text{g/atom}}$

• Alternatively, use Avogadro's number for mole calculations.

Avogadro’s Number and Scale

Understanding Large Numbers in Chemistry

• Avogadro’s Number ($N_A$): $6.022 \times 10^{23}$ is used to relate atomic scale to macroscopic quantities.

• Physical Comparisons: The thickness of a coin (1.35 mm), the average distance to the moon ($3.84 \times 10^8$ m), and the sun ($1.50 \times 10^{11}$ m) are used to illustrate the magnitude of Avogadro’s number.

Example: If you stacked $6.022 \times 10^{23}$ coins, the stack would reach far beyond the moon or sun.

Sample Calculations

Finding Number of Atoms and Moles

• Given: Mass of one atom of an element is $9.3 \times 10^{-23}$ g. To identify the element, divide by the atomic mass unit in grams.

• Number of Atoms in a Sample: $\text{Number of atoms} = \frac{\text{mass of sample}}{\text{mass of one atom}}$

• Number of Moles: $\text{Number of moles} = \frac{\text{mass of sample}}{\text{molar mass}}$

Example: How many silver atoms are in a coin weighing 31.1034768 g?

• Mass of one Ag atom = $1.79 \times 10^{-22}$ g

• Number of atoms = $\frac{31.1034768\ \text{g}}{1.79 \times 10^{-22}\ \text{g/atom}}$

Periodic Table and Atomic Masses

Using the Periodic Table

• The periodic table lists the atomic number and average atomic mass for each element.

• Atomic mass values are used for mole and atom calculations.

Example: The atomic mass of iron (Fe) is 55.85 amu, and of tellurium (Te) is 127.6 amu.

Summary Table: Subatomic Particles

Main Properties

Particle	Symbol	Relative Mass (amu)	Relative Charge
Electron	e-	0.0005	1−
Neutron	n	1	0
Proton	p+	1	1+

Key Equations

• Atomic Mass Unit: $1\ \text{amu} = \frac{1}{12}\ \text{mass of a } ^{12}C \text{ atom}$

• Number of Atoms: $\text{Number of atoms} = \frac{\text{mass of sample}}{\text{mass of one atom}}$

• Number of Moles: $\text{Number of moles} = \frac{\text{mass of sample}}{\text{molar mass}}$

• Avogadro’s Number: $N_A = 6.022 \times 10^{23}\ \text{atoms/mol}$

Applications and Examples

Practical Use in Chemistry

• Calculating the number of atoms in a given mass of an element.

• Relating atomic mass to macroscopic quantities using Avogadro’s number.

• Understanding the scale of atomic particles compared to everyday objects.

Example: Determining the number of silver atoms in a coin, or the number of iron atoms in a sample.

Additional info: These notes expand on the brief points in the original slides, providing full academic context and formulas for calculations. The periodic table images referenced are used to illustrate atomic numbers and masses for elements.