Isotopes and Relative Atomic Mass: Study Notes

Isotopes

Definition and Properties

Isotopes are different forms of the same chemical element that have the same number of protons but differ in the number of neutrons. This results in isotopes having identical chemical properties but varying physical properties.

• Isotopes of an element have the same atomic number (number of protons) but different mass numbers (total number of protons and neutrons).

• Chemical properties (such as reactivity) are determined by the number of protons and electrons, so isotopes behave similarly in chemical reactions.

• Physical properties (such as mass, density, and volume) differ due to the variation in neutron number.

• Example: Lithium-6 and Lithium-7 are isotopes of lithium. Both have 3 protons, but Lithium-6 has 3 neutrons and Lithium-7 has 4 neutrons.

Relative Atomic Mass

Concept and Calculation

Measuring the mass of a single atom is challenging due to its extremely small size. To address this, chemists use the concept of relative atomic mass ($A_r$), which compares the mass of an atom to a standard reference.

• Relative atomic mass ($A_r$): The mass of an atom compared to one-twelfth (1/12) the mass of a carbon-12 atom.

• Unified atomic mass unit (u): Defined as 1/12 the mass of a carbon-12 atom. This is approximately the mass of a single proton or neutron.

• Example: Three helium atoms have the same mass as one carbon atom. Thus, the relative atomic mass of helium is $\frac{1}{3} \times 12 = 4$.

• One titanium atom has the same mass as four carbon atoms, so its relative atomic mass is $4 \times 12 = 48$.

Calculation of Relative Atomic Mass for Elements with Isotopes

The relative atomic mass of an element that has multiple isotopes is calculated by taking into account the abundance of each isotope in a natural sample.

• Abundance (%): The percentage of each isotope present in a natural sample of the element.

• Formula:

$A_r = \frac{(%a \times A_{a}) + (%b \times A_{b})}{100}$

• $%a$ = percentage abundance of isotope a

• $A_{a}$ = relative atomic mass of isotope a

• $%b$ = percentage abundance of isotope b

• $A_{b}$ = relative atomic mass of isotope b

Examples and Practice Problems

Worked Example

• Thallium: A natural sample consists of two isotopes. One has $A_r = 203.0$ and makes up 29.50% of the atoms. The other has $A_r = 205.0$ and makes up 70.50% of the atoms.

• Calculation:

$A_r = \frac{(29.50 \times 203.0) + (70.50 \times 205.0)}{100}$

Practice Problems

• Copper: Copper has two isotopes: copper-63 (69.17% abundance) and copper-65 (30.83% abundance). Calculate the relative atomic mass of copper.

• Vanadium: Vanadium has two naturally occurring isotopes, vanadium-50 and vanadium-51. The mass number on the periodic table for vanadium is 50.94. Predict which isotope is more abundant and explain your reasoning.

Summary Table: Isotope Properties

Isotope	Protons	Neutrons	Chemical Properties	Physical Properties
Lithium-6	3	3	Same as Lithium-7	Lower mass
Lithium-7	3	4	Same as Lithium-6	Higher mass

Homework

• Pearson: 2.3 review page 35

• Essential Chemistry: Set 2 Question 1-13

Additional info: The concept of isotopes and relative atomic mass is foundational in general chemistry and is relevant for understanding molecular representations and analytical techniques in organic chemistry.