chem module 2 textbook: isotopes, atomic mass, and mass spec

1. Isotopes

• Definition:

  • Atoms of the same element.

  • Have the same number of protons.

  • Have different numbers of neutrons.

  • This results in different mass numbers.

• Element Identity:

  • The number of protons (atomic number) uniquely defines an element.

  • Changing the number of neutrons creates an isotope of that element.

• Symbols for Isotopes:

  • The mass number is written as a superscript to the left of the element symbol (e.g., $^{24}\text{Mg}$).

  • The atomic number (number of protons) can be written as a subscript to the left but is often omitted.

  • It's often omitted because the element symbol already indicates the atomic number.

  • A charge (if any) can be added as a superscript to the right.

• Example: Magnesium (Mg):

  • All magnesium atoms always have 12 protons.

  • Its isotopes differ only in their neutron count:

  • $^{24}\text{Mg}$ (magnesium-24): 12 protons, 12 neutrons.

  • $^{25}\text{Mg}$ (magnesium-25): 12 protons, 13 neutrons.

  • $^{26}\text{Mg}$ (magnesium-26): 12 protons, 14 neutrons.

• Common Hydrogen Isotopes:

  • Protium ($1\text{H}$): 1 proton, 0 neutrons (this is the most common form).

  • Deuterium ($2\text{H}$ or $D$): 1 proton, 1 neutron.

  • Tritium ($3\text{H}$ or $T$): 1 proton, 2 neutrons.

• Demonstration: Heavy Water:

  • Regular water: Mostly $^{1}\text{H}_2^{16}\text{O}$, with a molecular weight of 18 amu.

  • "Heavy water": $^{2}\text{H}_2^{16}\text{O}$, with a molecular weight of 20 amu.

  • Observation: Regular ice floats in liquid regular water.

  • This is because solid regular water is less dense than liquid regular water.

  • Key Point: Heavy water ice sinks in liquid regular water.

  • This happens because the increased mass from deuterium makes heavy water ice denser than regular liquid water.

1. Atomic Mass and Natural Abundance

• Atomic Mass Unit (amu):

  • Each proton contributes approximately 1 amu.

  • Each neutron contributes approximately 1 amu.

  • Electrons contribute very little to an atom's mass.

• Average Atomic Mass:

  • The atomic mass listed on the periodic table for most elements is a weighted average.

  • This average accounts for the masses of all its naturally occurring isotopes.

  • Most elements exist as mixtures of two or more isotopes.

  • No single atom (unless the element has only one natural isotope) has a mass exactly equal to the average atomic mass.

• Calculation of Average Atomic Mass:

  • The average mass is found by summing the product of each isotope's mass and its fractional abundance (percentage as a decimal).

  • Formula: $\text{Average mass} = \sum<em>{i} (\text{fractional abundance} \times \text{isotopic mass})</em>{i}$

• Example: Boron:

  • Boron has two isotopes:

  • 19.9% is $^{10}\text{B}$ with a mass of 10.0129 amu.

  • 80.1% is $^{11}\text{B}$ with a mass of 11.0093 amu.

  • Calculation:

  • $\text{Boron average mass} = (0.199 \times 10.0129 \text{ amu}) + (0.801 \times 11.0093 \text{ amu})$

  • $\text{Boron average mass} = 1.99 \text{ amu} + 8.82 \text{ amu}$

  • $\text{Boron average mass} = 10.81 \text{ amu}$

• Example: Neon in Solar Wind:

  • A sample of neon from solar wind consisted of:

  • 91.84% $^{20}\text{Ne}$ (mass 19.9924 amu).

  • 0.47% $^{21}\text{Ne}$ (mass 20.9940 amu).

  • 7.69% $^{22}\text{Ne}$ (mass 21.9914 amu).

  • Calculation:

  • $\text{Neon average mass} = (0.9184 \times 19.9924) + (0.0047 \times 20.9940) + (0.0769 \times 21.9914)$

  • $\text{Neon average mass} = 18.36 \text{ amu} + 0.099 \text{ amu} + 1.69 \text{ amu}$

  • $\text{Neon average mass} = 20.15 \text{ amu}$

  • Note: This average mass differs slightly from terrestrial neon (20.1796 amu), showing origin can affect isotopic abundance.

• Calculation of Percent Abundance (Inverse):

  • Example: Chlorine:

  • Naturally occurring chlorine has $^{35}\text{Cl}$ (34.96885 amu) and $^{37}\text{Cl}$ (36.96590 amu).

  • Its average mass is 35.453 amu.

  • Steps:

  • Let $x$ represent the fractional abundance of $^{35}\text{Cl}$.

  • Then, $(1.00 - x)$ represents the fractional abundance of $^{37}\text{Cl}$.

  • Set up the equation: $35.453 = (x \times 34.96885) + ((1.00 - x) \times 36.96590)$

  • Distribute: $35.453 = 34.96885x + 36.96590 - 36.96590x$

  • Combine $x$ terms: $35.453 - 36.96590 = 34.96885x - 36.96590x$

  • Simplify: $-1.5129 = -1.99705x$

  • Solve for $x$: $x = \frac{1.5129}{1.99705} = 0.7576$

  • Result: Chlorine consists of 75.76% $^{35}\text{Cl}$ and 24.24% $^{37}\text{Cl}$.

1. Mass Spectrometry

• Purpose:

  • A powerful instrument used to experimentally determine:

  • The masses of isotopes in elements.

  • The natural abundance of isotopes.

  • The masses of molecules in compounds.

• General Working Principle (Hard-Ionization Mass Spectrometer):

  1. Ionization: The sample is vaporized and then exposed to a high-energy plasma.

  • This process breaks chemical bonds (if it's a molecule).

  • It causes atoms or molecules to become electrically charged (typically positive ions by losing electrons).

  1. Acceleration/Deflection: These ions then pass through an electric or magnetic field.

  • The field deflects their path based on their mass-to-charge ratio ($m/Z$).

  • Lighter ions (or ions with a higher positive charge) are deflected more significantly.

  • Heavier ions (or ions with a lower positive charge) are deflected less.

  1. Detection: The deflected ions hit a detector.

  • The detector records their $m/Z$ ratio.

  • It also measures their relative abundance.

  • This data is plotted as a mass spectrum (relative number of ions vs. $m/Z$).

    • Resolution: Mass spectrometers can measure masses with very high resolution (e.g., 0.0001 amu).

    • This allows them to readily detect even slight mass differences, like those between isotopes.

3.1. Mass Spectra of Elements (Hard-Ionization)

• Interpretation:

  • For elements, a hard-ionization mass spectrum shows distinct peaks.

  • Each peak corresponds to a different isotope present in the sample.

  • The x-axis ($m/Z$) indicates the mass of each isotope (assuming a +1 charge, so $Z=1$).

  • The height of each peak (y-axis) is directly proportional to the relative abundance (percentage) of that isotope.

• Example: Magnesium (Mg):

  • A hard-ionization mass spectrum of Mg shows three peaks at $m/Z$ ratios of 24, 25, and 26 amu.

  • These peaks directly indicate the presence of three isotopes: $^{24}\text{Mg}$, $^{25}\text{Mg}$, and $^{26}\text{Mg}$.

  • The relative heights of these peaks show their natural abundances:

  • Approximately 79% for $^{24}\text{Mg}$.

  • Approximately 10% for $^{25}\text{Mg}$.

  • Approximately 11% for $^{26}\text{Mg}$.

3.2. Mass Spectrometry of Molecular Elements

• Main Difference for Molecules: Hard vs. Soft Ionization MS:

  • Hard-Ionization MS:

  • Process: Uses high-energy methods that break all covalent bonds within molecules.

  • Result: Produces atomic ions from the individual constituent atoms.

  • Information: Provides the mass and relative abundance of the individual atoms/isotopes present in the original molecule.

  • Soft-Ionization MS:

  • Process: Uses gentler methods that do not break covalent bonds; the molecule remains intact.

  • Result: Forms molecular ions ($\text{M}^+$), which are the entire molecules with a charge.

  • Information: Provides the molecular weight of the intact compound and its relative abundance.

• Example: Bromine (Br₂ Molecule):

  • Bromine has two stable isotopes:

  • $^{79}\text{Br}$ (mass 78.9183 amu, 50.65% abundance).

  • $^{81}\text{Br}$ (mass 80.9163 amu, 49.35% abundance).

  • Elemental bromine exists as a diatomic molecule, $Br_2$.

• Hard-Ionization Mass Spectrum of Br₂:

  • Process: The covalent bond connecting the two Br atoms breaks.

  • Result: Only atomic ions ($^{79}\text{Br}^+$ and $^{81}\text{Br}^+$) are detected.

  • Peaks: Peaks would appear at $m/Z \approx 79$ and $m/Z \approx 81$. (No peak at the average atomic mass of 79.90 amu because no single atom has this mass).

  • Conclusion: Hard ionization provides information about the composition of individual atoms in the sample.

• Soft-Ionization Mass Spectrum of Br₂:

  • Process: The covalent bond connecting the two bromine atoms remains intact.

  • Result: $Br_2^+$ molecular ions (intact molecules with a charge) are detected.

  • Peaks: There are three possible molecular ions that can form from the bromine isotopes, leading to three peaks:

  • 1. $^{79}\text{Br-}^{79}\text{Br}^+$:

    • Mass: $78.918 \text{ amu} + 78.918 \text{ amu} = 157.836 \text{ amu}$.

    • Abundance: $0.5065 \times 0.5065 = 0.2565$ (or 25.65%).

  • 2. $^{79}\text{Br-}^{81}\text{Br}^+$ (and $^{81}\text{Br-}^{79}\text{Br}^+$):

    • Mass: $78.918 \text{ amu} + 80.916 \text{ amu} = 159.834 \text{ amu}$.

    • Abundance: $(0.5065 \times 0.4935) + (0.4935 \times 0.5065) = 0.2500 + 0.2500 = 0.5000$ (or 50.00%).

  • 3. $^{81}\text{Br-}^{81}\text{Br}^+$:

    • Mass: $80.916 \text{ amu} + 80.916 \text{ amu} = 161.832 \text{ amu}$.

    • Abundance: $0.4935 \times 0.4935 = 0.2435$ (or 24.35%).

  • Conclusion: Soft ionization provides information about the molecular mass of the entire compound.

• Average Molecular Mass of Br₂:

  • Can be calculated from the molecular ion masses and their abundances:

  • $(0.2565 \times 157.836 \text{ amu}) + (0.5000 \times 159.834 \text{ amu}) + (0.2435 \times 161.832 \text{ amu}) \approx 159.8 \text{ amu}$.

  • Alternatively, it's simply the sum of the average atomic masses of the constituent atoms:

  • $79.90 \text{ amu} (\text{for Br}) + 79.90 \text{ amu} (\text{for Br}) = 159.8 \text{ amu}$.