Atomic Structure, Mass Spectrometry, and Percent Composition Study Guide

Fundamental Atomic Structure and Subatomic Particles

• Atomic Architecture:

  • An atom is composed primarily of empty space.
  • Nucleus: A very small, positively charged central core containing protons and neutrons.
  • Electrons: Extremely tiny, negatively charged particles that circulate around the nucleus and occupy the vast majority of the atom's total volume.

• Subatomic Particle Breakdown:

  • Proton:
  • Charge: $+1\,e$
  • Mass: $1\,amu$
  • Location: Resides within the nucleus.
  • Electron:
  • Charge: $-1\,e$
  • Mass: $0.0005\,amu$
  • Location: Circulates around the nucleus in shell orbits.
  • Neutron:
  • Charge: $0\,e$ (neutral)
  • Mass: $1\,amu$
  • Location: Resides within the nucleus.

• Key Principles of Subatomic Particles:

  • Protons and electrons carry equal but opposite electric charges.
  • A neutral atom contains an equal number of protons and electrons.
  • Protons and neutrons have equal masses of $1\,amu$ when measured broadly (their masses are slightly different when measured to several decimal places).
  • The mass of an electron ($0.0005\,amu$) is significantly smaller than the mass of a proton or neutron ($1\,amu$). Because of this vast difference, the mass of electrons is rarely taken into account when determining total atomic mass.

Atomic Number, Mass Number, and Notation

• Atomic Number ($Z$):

  • Represents the number of protons in the nucleus of an atom.
  • In a neutral atom, the atomic number $Z$ also equals the number of electrons.
  • Symbolized by the letter $Z$ (note that $Z$ designates the atomic number, not $A$).

• Mass Number ($A$):

  • Equal to the total number of protons plus the total number of neutrons in an atom's nucleus.
  • Symbolized by the letter $A$.

• Calculating Particle Counts:

  • $\text{Number of Protons} = Z$
  • $\text{Number of Electrons (neutral atom)} = Z$
  • $\text{Number of Neutrons} = A - Z$

• Isotope Symbol Examples:

  • Carbon-12 (${}_{6}^{12}\text{C}$):
  • Mass Number ($A$): $12$
  • Atomic Number ($Z$): $6$
  • Protons: $6$
  • Neutrons: $12 - 6 = 6$
  • Electrons: $6$
  • Carbon-14 (${}_{6}^{14}\text{C}$):
  • Mass Number ($A$): $14$
  • Atomic Number ($Z$): $6$
  • Protons: $6$
  • Neutrons: $14 - 6 = 8$
  • Electrons: $6$

Isotopes and Chemical Reactivity

• Definition of Isotopes:

  • Isotopes are atoms of the same element that have the same number of protons (identical atomic number $Z$) but different numbers of neutrons (differing mass numbers $A$).

• Chemical Behavior of Isotopes:

  • Isotopes of an element exhibit identical chemical behavior because chemical reactivity is governed by proton count and electron arrangement.
  • Both Carbon-12 (${}_{6}^{12}\text{C}$) and Carbon-14 (${}_{6}^{14}\text{C}$) react with oxygen in identical fashion to form carbon dioxide ($\text{CO}_2$).
  • Standard hydrogen (${}_{1}^{1}\text{H}$) and heavy hydrogen/deuterium (${}_{1}^{2}\text{H}$) both bond with oxygen to form water ($\text{H}_2\text{O}$).

• Deuterium and Heavy Water:

  • The hydrogen isotope ${}_{1}^{2}\text{H}$ contains $1$ proton, $1$ neutron, and $1$ electron.
  • It is present in heavy water, which derives its name from the fact that these heavier hydrogen isotopes increase the overall mass of the water molecules.

Relative Atomic Mass Standard and Nuclear Binding Energy

• Carbon-12 Reference Mass:

  • The mass of one Carbon-12 (${}^{12}\text{C}$) atom is defined as exactly $12\,amu$.
  • The masses of all other atoms are measured on a scale relative to the ${}^{12}\text{C}$ standard.
  • Nucleons in all atoms other than Carbon-12 do not weigh exactly $1\,amu$.

• Nuclear Binding Energy:

  • When subatomic particles bind together to form a nucleus, a portion of mass is converted directly into energy.
  • This mass-energy conversion occurs in accordance with the formula:     $E = mc^2$
  • This mass defect accounts for why individual nucleons in bound nuclei weigh slightly different amounts than expected.

Mass Spectroscopy and Average Atomic Mass

• Constancy of Average Atomic Mass:

  • The atomic mass reported on the periodic table is a weighted average of all naturally occurring isotopes of an element.
  • The ratio of naturally occurring isotopes for a given element is constant; therefore, the average mass of any large collection of atoms of that element is always identical.

• Calculation Procedure:

  • To calculate average atomic mass, multiply the exact atomic mass of each isotope by its percent abundance expressed in decimal form, then sum the resulting values:     $\text{Average Atomic Mass} = \sum (\text{Isotope Mass} \times \text{Fractional Abundance})$

• Specific Isotope Reference Values:

  • The actual measured mass of Silver-107 (${}^{107}\text{Ag}$) is $106.90509\,amu$

• Sample Problem: Identifying an Element from Mass Spectrum Data:

  • Given Spectrum Data:
  • Isotope 1: Mass number = $35$, Exact mass = $34.969\,amu$, Relative abundance = $75.78\%$ ($0.7578$
  • Isotope 2: Mass number = $37$, Exact mass = $36.966\,amu$, Relative abundance = $24.22\%$ ($0.2422$
  • Calculation:     $\text{Average Atomic Mass} = (34.969\,amu \times 0.7578) + (36.966\,amu \times 0.2422)$$\text{Average Atomic Mass} = 26.4995\,amu + 8.9532\,amu = 35.45\,amu$
  • Element Identification:
  • Locating the average mass of $35.45\,amu$ on the periodic table identifies the element as Chlorine (symbol $\text{Cl}$).

Mass Percent Composition in Pure Compounds

• Pure Sample Analysis of Ilmenite ($\text{FeTiO}_3$):

  • Background & Applications:
  • Ilmenite ($\text{FeTiO}_3$) is a mineral found in rocks that serves as a primary natural source of titanium in Canada, the United States of America (USA), and Australia.
  • Determining percentage composition by mass is vital when extracting iron and titanium from ilmenite.
  • In pop culture, Lieutenant Dan's "magic legs" in the movie Forrest Gump were made of titanium alloy.

• Atomic Masses for Calculation:

  • Iron ($\text{Fe}$): $55.85\,amu$
  • Titanium ($\text{Ti}$): $47.88\,amu$
  • Oxygen ($\text{O}$): $16.00\,amu$

• Total Formula Mass of Ilmenite ($\text{FeTiO}_3$):   $\text{Formula Mass} = (1 \times 55.85\,amu) + (1 \times 47.88\,amu) + (3 \times 16.00\,amu)$$\text{Formula Mass} = 55.85\,amu + 47.88\,amu + 48.00\,amu = 151.73\,amu$

• Mass Percent Calculations:

  • Mass Percent of Iron ($\text{Fe}$):     $\text{Mass \% Fe} = \frac{(1\text{ Fe atom}) \times (55.85\,amu/\text{Fe atom})}{151.73\,amu} \times 100$$\text{Mass \% Fe} = \frac{55.85}{151.73} \times 100 = 36.81\%$
  • Mass Percent of Titanium ($\text{Ti}$):     $\text{Mass \% Ti} = \frac{(1\text{ Ti atom}) \times (47.88\,amu/\text{Ti atom})}{151.73\,amu} \times 100$$\text{Mass \% Ti} = \frac{47.88}{151.73} \times 100 = 31.56\%$
  • Mass Percent of Oxygen ($\text{O}$):     $\text{Mass \% O} = \frac{(3\text{ O atoms}) \times (16.00\,amu/\text{O atom})}{151.73\,amu} \times 100$$\text{Mass \% O} = \frac{48.00}{151.73} \times 100 = 31.64\%$

• Verification Check:   $\text{Sum of Mass Percents} = 36.81\% + 31.56\% + 31.64\% = 100.01\%$

  • A total sum of $100.01\%$ is acceptable as it reflects minor round-off error.