Isotopes and Their Properties
- You're comparing coins of the same currency.
- Some are slightly heavier than others because they contain more metal, yet they belong to the same denomination and have the same face value.
This is similar to how isotopes work in chemistry.
What Are Isotopes?
- Atoms are defined by their number of protons, known as the atomic number (Z).
- However, atoms of the same element can have different numbers of neutrons, which changes their mass number (A).
- These different versions of the same element are called isotopes.
Definition of Isotopes
Isotopes
Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons.
This means isotopes share:
- The same atomic number (Z), since the number of protons determines the element.
- Different mass numbers (A), because the mass number is the sum of protons and neutrons.
Chlorine isotopes
- Chlorine-35 ($^{35}\text{Cl}$) has 17 protons and 18 neutrons.
- Chlorine-37 ($^{37}\text{Cl}$) has 17 protons and 20 neutrons.
The chemical properties of isotopes are nearly identical because chemical behavior depends on the number of electrons, which remains the same for all isotopes of an element.
Relative Atomic Mass and Isotopic Abundance
- Take a look at the periodic table in the data booklet.
- You’ll notice that atomic masses of elements are rarely whole numbers.
- For instance, chlorine’s relative atomic mass ($A_r$) is 35.45, even though its isotopes have whole-number mass numbers (35 and 37).
- You can ask, why is this?
Relative atomic mass
The relative atomic mass of an element is a weighted average of the masses of its isotopes, based on their natural abundances, compared to 1/12th the mass of a carbon-12 atom. Since it is a ratio, $A_r$ has no units.
Relative abundance
Relative abundance refers to the percentage of a specific isotope of an element present in a naturally occurring sample.
It indicates how common each isotope is compared to the total amount of the element, which is used to calculate the element's average atomic mass.
Calculating Relative Atomic Mass
To calculate the relative atomic mass ($A_r$), use the formula:
$A_r = \frac{\text{(mass of isotope 1 × % abundance of isotope 1)} + \text{(mass of isotope 2 × % abundance of isotope 2)} + \dots}{100}$
Relative atomic mass of chlorine
Chlorine has two isotopes:
- Chlorine-35 ($^{35}\text{Cl}$) with 75.8% abundance.
- Chlorine-37 ($^{37}\text{Cl}$) with 24.2% abundance.
Calculate the relative atomic mass:
$A_r = \frac{(35 \times 75.8) + (37 \times 24.2)}{100}$
Step-by-step:
- Multiply each isotope’s mass by its abundance:
$$35 \times 75.8 = 2653$ and $37 \times 24.2 = 895.4$$ - Add these values together:
$$2653 + 895.4 = 3548.4$$ - Divide by 100 to find the average:
$$A_r = \frac{3548.4}{100} = 35.48$$
Thus, the relative atomic mass of chlorine is approximately 35.45.
Before starting your calculation, double-check that the percentage abundances add up to 100% to avoid errors.
Isotopes and Atomic Mass
Determining Percent Abundances
- To determine percent abundance from the relative atomic mass ($A_r$) and mass numbers of isotopes, use the weighted average formula: $$A_r=(m_1 \times \%_1)+(m_2 \times \%_2)$$ where $m_1$ and $m_2$ are the mass numbers of the isotopes, and $\%_1 + \%_2 = 1$.
- If the percent abundance of one isotope is unknown, let $\%_1 = x$ and solve using: $$A_r = (m_1 \times x) + (m_2 \times (1-x))$$
- Rearrange the equation to solve for $x$, then multiply by 100 to express the abundance as a percentage.
This method can be extended for elements with more than two isotopes.
Physical Properties of Isotopes
- While isotopes of the same element have nearly identical chemical properties, their physical properties can differ.
- These differences arise because isotopes have different masses, which can impact properties like density, melting point, and boiling point.
- The slight difference in mass allows these isotopes to be separated using methods like gas centrifugation.
Hydrogen Isotopes:
- Protium ($^{1}\text{H}$): The most common isotope, with 1 proton and no neutrons.
- Deuterium ($^{2}\text{H}$): A heavier isotope, with 1 proton and 1 neutron.
- Tritium ($^{3}\text{H}$): A radioactive isotope, with 1 proton and 2 neutrons.
Uranium Isotopes:
- Uranium-235 ($^{235}\text{U}$): Used in nuclear reactors and weapons.
- Uranium-238 ($^{238}\text{U}$): More abundant but less useful for nuclear reactions.
- Don’t confuse physical property differences of isotopes with their chemical properties.
- Isotopes react chemically in the same way because they have the same number of electrons.
- What are the key differences between isotopes of the same element?
- Why do isotopes have the same chemical properties but different physical properties?
- Calculate the relative atomic mass of an element with the following isotopes:
- Isotope A: mass = 10, abundance = 20%
- Isotope B: mass = 11, abundance = 80%.
