Lecture on Isotopes and Mass Spectrometry

Introduction to Isotopes

• Isotopes are variants of the same element, having the same number of protons but different numbers of neutrons.

Mass Spectrometer

• Instrument used to identify isotopes by measuring the mass-to-charge ratio of ions.
• Process:
  • Sample is injected and vaporized into a gas phase.
  • Atoms are ionized, usually to a +1 charge.
  • Ions are passed through a magnetic field to separate them by mass-to-charge ratio.
  • Detected ions indicate the isotopes present.
• Example: Carbon-12 and Carbon-13 can be distinguished due to different mass-to-charge ratios.

Atomic Mass

• Atomic mass is a weighted average of the isotope masses, not a simple average.
• Example: Gallium has isotopes with masses 68.9 and 71.9 amu.
  • 60% of gallium atoms have a mass of 68.9 amu.
  • 40% of gallium atoms have a mass of 71.9 amu.
  • Atomic mass (69.7 amu) is closer to 68.9 due to higher abundance.

Estimating Atomic Mass

• Estimate by considering isotopic abundance and mass.
• Silver Example:
  • Two isotopes: Silver-107 and Silver-109.
  • Silver-107 is more abundant, so atomic mass is closer to 107.
  • Estimated atomic mass: 107.9 amu.
  • Actual atomic mass: 107.87 amu.

Atomic Mass Calculations

• Atomic mass is calculated using a weighted average formula.
• Example: Magnesium isotopes and their abundances:
  • Magnesium-24 (78.99%): 23.9850 amu
  • Magnesium-25 (10%): 24.9858 amu
  • Magnesium-26 (11.01%): 25.929 amu
• Formula: Atomic mass = Sum of (Fractional abundance * Isotope mass)
• Calculated magnesium atomic mass: 24.31 amu*

Atomic Weight

• Definitions:
  • Percent: (Part/Whole) * 100
  • Fraction: Part/Whole
  • Weight: Weighted average of isotopic masses*

Example Calculations

• Weighted Average in Grading: Formula used in classes to compute final grades translates to atomic mass calculation.
  • Formula: Sum of (Fractional abundance * Grade)*

Carbon Isotopes Example

• Carbon's atomic weight of 12.01 amu comes from a mix of Carbon-12 and Carbon-13.
• Given:
  • Carbon-12: 12 amu
  • Carbon-13: 13.0035 amu
• Calculate Percent Abundance:
  • Carbon-12 makes up 98.9% of natural carbon.
  • Carbon-13 makes up 1.1%.

Conclusion

• Understanding of isotopes and atomic mass is crucial in chemistry.
• Calculations often involve understanding of fractional abundance and weighted averages to estimate atomic masses.