Masses of Atoms and Atomic Structure

Masses of Atoms

Introduction

The study of atomic masses is fundamental to understanding the structure and properties of matter. Atoms are the basic units of elements, and their masses are essential for calculations in chemistry, such as determining the number of atoms in a sample or converting between mass and moles.

Elements and Nuclear Symbols

Atomic Structure and Identity

• Element Identity: Each element is defined by its number of protons (atomic number, Z).

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

• Ions: Atoms with variable numbers of electrons. Ions can be positively charged (cations) or negatively charged (anions).

The nuclear symbol for an atom is written as:

$^A_ZX$

• X: Chemical symbol of the element

• Z: Atomic number (number of protons)

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

Subatomic Particles

Properties of Subatomic Particles

Atoms are composed of three main subatomic particles: electrons, neutrons, and protons. Their properties are summarized in the table below.

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

Atomic Masses

Definition and Calculation

• Atomic Mass Unit (amu): Defined as 1/12 the mass of a single 12C atom (exact).

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

• Conversion: $1\ \text{amu} = 1.66054 \times 10^{-24}\ \text{g}$

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

Sample Calculation: Number of Atoms in a Sample

• To find the number of atoms in a given mass of an element, use the formula:

$\text{Number of atoms} = \frac{\text{mass of sample (g)}}{\text{mass of one atom (g)}}$

Example: How many silver atoms are in a coin weighing 31.1034768 g? (Mass of one Ag atom = $1.79 \times 10^{-22}$ g)

$\text{Number of Ag atoms} = \frac{31.1034768\ \text{g}}{1.79 \times 10^{-22}\ \text{g/atom}} = 1.74 \times 10^{23}\ \text{atoms}$

Avogadro's Number

Definition and Significance

• Avogadro's Number ($N_A$): The number of atoms, molecules, or particles in one mole of a substance.

• Value: $N_A = 6.022 \times 10^{23}\ \text{mol}^{-1}$

• This large number allows chemists to relate macroscopic amounts of material to the number of atoms or molecules present.

Examples of Scale:

• Thickness of a dime: 1.35 mm

• Average distance to the moon: $3.84 \times 10^8$ m

• Average distance to the sun: $1.50 \times 10^{11}$ m

*Additional info: These comparisons help illustrate the magnitude of Avogadro's number.*

Isotopes and Average Atomic Mass

Isotopes

• Isotopes: Atoms of the same element with different numbers of neutrons, resulting in different mass numbers.

• Notation: Isotopes are denoted as AX, where A is the mass number.

• Example: Magnesium has three naturally occurring isotopes: 24Mg, 25Mg, and 26Mg.

Average Atomic Mass Calculation

• The average atomic mass is calculated using the relative abundances and masses of each isotope:

$\text{Average atomic mass} = \sum (\text{fractional abundance} \times \text{isotopic mass})$

Example Table: Magnesium Isotopes

Isotope	Abundance (%)	Isotopic Mass (amu)
24Mg	78.99	23.9850
25Mg	10.00	24.9858
26Mg	11.01	25.9826

*Additional info: The average atomic mass of magnesium is calculated as follows:*

$\text{Average atomic mass} = (0.7899 \times 23.9850) + (0.1000 \times 24.9858) + (0.1101 \times 25.9826) = 24.305$

Practice Problems and Applications

Sample Questions

• How many (average) iron atoms are in 55.85 g Fe?

• How many (average) tellurium atoms are in 127.6 g Te?

• If the mass of one atom of an element is $9.3 \times 10^{-23}$ g, which element is it?

To solve these, use the relationships between atomic mass, Avogadro's number, and the mass of a sample.

General Steps for Calculations

1. Find the molar mass (g/mol) of the element from the periodic table.

2. Calculate the number of moles in the sample: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

3. Calculate the number of atoms: $\text{atoms} = \text{moles} \times N_A$

Example: How many atoms are in 20.04 g Ca?

• Molar mass of Ca = 40.08 g/mol

• Moles of Ca = $\frac{20.04}{40.08} = 0.500$ mol

• Atoms of Ca = $0.500 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$ atoms

Summary Table: Subatomic Particles

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

Key Terms

• Atomic Number (Z): Number of protons in the nucleus of an atom.

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

• Isotope: Atoms of the same element with different numbers of neutrons.

• Ion: Atom or molecule with a net electric charge due to the loss or gain of electrons.

• Atomic Mass Unit (amu): A unit of mass used to express atomic and molecular weights.

• Avogadro's Number: The number of particles in one mole of a substance ($6.022 \times 10^{23}$).