Chemistry Notes: Chemical Symbols, Formulas, Laws of Combination, and Atomic Structure

Chemical Symbols

  • Each chemical element is identified by an internationally recognized symbol.
  • Symbols consist of one or two letters (e.g., C for carbon, He for helium).
  • Capitalization Rule: The first letter of an element's symbol is always capitalized. If there's a second letter, it is always lowercase.
  • Origin of Symbols: Most symbols are abbreviations of the English name, but some derive from older Latin names.
  • Elements with Symbols Based on Non-English Names (Table 2.1):
    • Antimony: Sb (Stibium)
    • Gold: Au (Aurum)
    • Iron: Fe (Ferrum)
    • Lead: Pb (Plumbum)
    • Mercury: Hg (Hydrargyrum)
    • Potassium: K (Kalium)
    • Silver: Ag (Argentum)
    • Sodium: Na (Natrium)
    • Tin: Sn (Stannum)
    • Tungsten: W (Wolfram)
  • A periodic table lists the names and symbols of the 118 known elements.
  • Importance: Proper capitalization and use of symbols are crucial in chemistry.

Chemical Formulas

  • Chemists use chemical symbols in chemical formulas to identify compounds.
  • Chemical formulas indicate the relative number of each type of element present in a compound.
  • Example: CO represents carbon monoxide, a compound made of carbon and oxygen. It is critical not to confuse CO (a compound) with Co (the element cobalt).
  • Subscripts: Indicate the relative proportions of elements.
    • Example: H_2O for water means two hydrogen atoms for every one oxygen atom.
    • A subscript of 1 is never explicitly written in chemical formulas.
  • Parentheses: When present, multiply the number of each atom inside the parentheses by the subscripted number outside.
    • Example: Ca(NO3)2
      • This compound has one calcium atom.
      • For nitrogen: 1 \times 2 = 2 atoms of nitrogen.
      • For oxygen: 3 \times 2 = 6 atoms of oxygen.

The Laws of Chemical Combination

The Law of Conservation of Mass

  • Background: Burning a log. In an open campfire, the ashes have considerably less mass than the log, leading to a misconception that mass is lost.
  • Controlled Experimentation: An open system (like a campfire) allows mass to enter or leave. A closed system is necessary to accurately measure mass changes.
  • Lavoisier's Experiment (Antoine Lavoisier and Marie-Anne Paulze Lavoisier, 1743-1794):
    • Setup: Phosphorus sample on a floating surface in a pan of water, covered by a glass jar. The entire apparatus is placed on a balance.
    • Process: Phosphorus is ignited using sunlight (focused by a magnifying glass) and burns in the air inside the jar.
    • Observations: The total mass of the system does not change (937.4 ext{ g} before and 937.4 ext{ g} after).
    • Detailed Observation: Although the solid product (phosphorus oxide) has more mass than the initial phosphorus, the water level increases, indicating less air (oxygen) in the jar. The mass of oxygen lost from the air exactly equals the mass gained by the phosphorus to form the oxide.
    • Conclusion: Law of Conservation of Mass states that during a chemical reaction, mass is neither gained nor lost. The total mass of reactants equals the total mass of products.
  • Significance: Lavoisier's quantitative measurements laid the groundwork for further quantitative observations and subsequent laws.

The Law of Definite Proportions (Law of Constant Composition)

  • Discovery: Emerged from careful work by many investigators who broke compounds down into constituent elements and compared their masses.
  • Statement: Any given compound is composed of definite proportions by mass of its elements.
  • Example (Water, H_2O): No matter the source, water always has an 8-to-1 mass ratio of oxygen to hydrogen (8 parts oxygen for every 1 part hydrogen by mass).
  • Challenges in Establishment: Impurities and existence of multiple compounds from the same elements (e.g., nitrogen monoxide, NO, and dinitrogen monoxide, N_2O).
    • NO: Mass of oxygen is 1.14 times the mass of nitrogen (i.e., 1.14 ext{ g} O for every 1 ext{ g} N).
    • N₂O: Mass of oxygen is 0.57 times the mass of nitrogen (i.e., 0.57 ext{ g} O for every 1 ext{ g} N).
    • Mixtures of NO and N₂O would show varying mass ratios between 0.57:1 and 1.14:1. The law applies to pure compounds.
  • Proportion by Mass: Ratio of the mass of an element to the total mass of the compound ( rac{ ext{Mass of Element}}{ ext{Total Mass of Compound}}). This value is always between 0 and 1.
  • Percent by Mass: Proportion by mass multiplied by 100\%. ( rac{ ext{Mass of Element}}{ ext{Total Mass of Compound}} \times 100\% )
  • Example (Sucrose, C{12}H{22}O_{11}): A 342 ext{ g} sample contains 144 ext{ g} C, 22 ext{ g} H, and 176 ext{ g} O.
    • Carbon: Proportion = \frac{144 ext{ g}}{342 ext{ g}} hickapprox 0.421. Percent = 0.421 \times 100\% = 42.1\%.
    • Hydrogen: Proportion = \frac{22 ext{ g}}{342 ext{ g}} hickapprox 0.064. Percent = 0.064 \times 100\% = 6.4\%.
    • Oxygen: Proportion = \frac{176 ext{ g}}{342 ext{ g}} hickapprox 0.515. Percent = 0.515 \times 100\% = 51.5\%.
  • All pure samples of sucrose will have this same percent composition by mass.

The History of the Atom

Dalton's Atomic Theory (John Dalton, 1803-1807)

  • Purpose: Formulated to explain the classical laws of chemical combination.
  • Hypotheses (Key Postulates):
    1. Matter is made up of tiny, indivisible particles called atoms. (Revised by modern theory with subatomic particles and nuclear reactions).
    2. Each atom of a particular element has the same mass, but the mass of an atom of one element is different from the mass of an atom of any other element. (Revised by the discovery of isotopes).
    3. Atoms combine to form molecules in small, whole-number ratios.
    4. Atoms of the same two elements can combine in different small, whole-number ratios to form different compounds (e.g., CO vs. CO_2; this explains the Law of Multiple Proportions).
  • Explanation of Laws of Chemical Combination through Dalton's Theory:
    1. Law of Conservation of Mass: Atoms are merely rearranged (exchange "partners") during a chemical reaction, not created or destroyed. Therefore, their total mass is conserved.
    2. Law of Definite Proportions: All samples of a given chemical compound are composed of the same elements in the same fixed proportion because atoms combine in specific, small, whole-number ratios (e.g., water is always H_2O).
    3. Law of Multiple Proportions: When atoms of two elements form more than one compound, they do so by combining in different small, whole-number ratios. For example, carbon and oxygen can form CO and CO_2.

The Discovery of the Electron

  • Pre-1897 View: Atoms were considered indivisible, the smallest particles of matter.
  • J. J. Thomson (1897):
    • Experiment: Constructed a cathode-ray tube (similar to Figure 2.5), observing cathode rays passing through it.
    • Observations:
      • Cathode rays traveled from the negatively charged electrode (cathode) to the positively charged electrode (anode).
      • They had a negative charge.
      • They traveled in straight lines.
      • Identical cathode rays were produced regardless of the materials used to construct the tube.
      • The beam of cathode rays could be deflected by external electrical or magnetic fields.
    • Key Measurement: By balancing electric and magnetic fields, Thomson measured the charge-to-mass ratio of cathode rays as -1.76 \times 10^8 ext{ C/g}, where C is the coulomb (SI unit of electrical charge).
    • Conclusion: Cathode rays are beams of electrons, which are negatively charged particles much smaller than atoms.
  • Robert Millikan (1909):
    • Experiment: Oil-drop experiment (Figure 2.6).
      • Sprayed small oil drops into an apparatus with oppositely charged electrical plates.
      • X-rays were used to give oil drops extra negative charge.
      • The lower (negatively charged) plate repelled the negatively charged oil drops.
      • Millikan adjusted the electric field strength to slow or stop the falling drops, viewing them through a microscope.
    • Key Measurement: Discovered that the total charge of each drop was always a multiple of a specific number: -1.60 \times 10^{-19} ext{ C}, which is the charge of a single electron.
    • Calculation of Electron Mass: Using his measured electron charge and Thomson's charge-to-mass ratio:
      \text{Mass of an electron} = \text{Charge} \times \frac{\text{Mass}}{\text{Charge}} = (-1.60 \times 10^{-19} \text{ C}) \times \left(\frac{1 \text{ g}}{-1.76 \times 10^8 \text{ C}}\right) = 9.10 \times 10^{-28} \text{ g}
    • Ethical Note: Millikan is a problematic figure due to his association with eugenics; some institutions have removed his name from buildings and awards.
  • Early Atomic Models (Post-Electron Discovery):
    • Dalton's Model (Figure 2.7a): Indivisible sphere.
    • Thomson's Plum-Pudding Model (Figure 2.7b):
      • Proposed after electron discovery, as atoms are neutral but contain negative electrons.
      • Atom consisted of a sphere of diffuse positive charge.
      • Negatively charged electrons were suspended within this positive sphere, like plums in a pudding.
      • The electron's mass was determined to be very small, approximately \frac{1}{1836} the mass of the lightest element, hydrogen.

The Nuclear Model of the Atom

  • Discovery of Radioactivity (Henri Becquerel, 1896; Marie Curie, early 1900s):
    • Uranium emitted high-energy radiation, termed radioactivity.
    • Three types of particles: alpha (\alpha), beta (\beta), and gamma (\gamma).
    • Alpha particles have a positive charge; beta particles have a negative charge.
  • Rutherford's Gold Foil Experiment (Ernest Rutherford, 1909, with Hans Geiger and Ernest Marsden):
    • Purpose: To test Thomson's plum-pudding model.
    • Setup: A radioactive source emitted positively charged alpha particles towards a thin piece of gold foil, surrounded by a fluorescent screen.
    • Prediction (based on plum-pudding model): Alpha particles (positive charge) should pass through the diffuse positive charge of the gold atoms with minimal deflection.
    • Observations (Figure 2.8):
      • Most alpha particles passed straight through the foil with little or no deflection.
      • A substantial number of particles were deflected at large angles.
      • A few particles were deflected directly backward (towards the source).
    • Conclusions: Thomson's model was incorrect. The atom must contain a highly concentrated, small region of positive charge and mass.
  • Rutherford's Nuclear Model of the Atom (Post-1909):
    1. The atom's positive charge and the majority of its mass are located in a very small, dense central region called the nucleus.
    2. The majority of the atom is empty space.
    3. Small, negatively charged electrons are spread throughout this empty space, orbiting the nucleus.
    4. The number of negatively charged electrons equals the number of positively charged particles (later called protons) inside the nucleus, making the atom electrically neutral.
      • The charge of a proton is +1 (equal in magnitude but opposite in sign to an electron's -1 charge).
  • Discovery of the Neutron (James Chadwick, 1932):
    • Rutherford hypothesized another particle in the nucleus to explain mass discrepancies (e.g., helium having four times the mass of hydrogen but only one more proton).
    • Chadwick demonstrated the existence of neutral particles (neutrons) in the nucleus.
    • Neutrons have approximately the same mass as protons.
    • Example: A helium atom (2 protons, 2 neutrons) is four times heavier than a hydrogen atom (1 proton, 0 neutrons).
  • Modern Atomic Structure (Figure 2.9):
    • Protons and neutrons reside in the small, dense, positively charged nucleus.
    • Electrons exist in the mostly empty space (electron cloud) surrounding the nucleus.
    • Rutherford's model, though refined by Bohr and others, is largely consistent with the currently recognized structure.

Subatomic Particles, Isotopes, and Ions

Subatomic Particles

  • The fundamental particles that make up an atom are protons (p), neutrons (n), and electrons (e).
  • Nucleus: Where protons and neutrons reside. It is incredibly small, with a radius about \frac{1}{10\text{,}000} the size of the atom's radius.
    • The nucleus comprises almost all the mass of an atom.
    • The space occupied by electrons makes up almost all the volume of an atom.
  • Everyday Analogy:
    • Mass: If an electron had the mass of a marble, a proton or neutron would have the mass of a bowling ball. The mass of electrons is negligible compared to the nucleus.
    • Size: If the nucleus were the size of a marble, the atom would be the size of a stadium.
  • Properties of Subatomic Particles (Table 2.2):
    • Proton (p):
      • Charge: +1 (relative charge, equivalent to +1.60 \times 10^{-19} ext{ C})
      • Mass: 1.0073 ext{ u} (atomic mass units)
      • Location: In the nucleus
    • Neutron (n):
      • Charge: 0
      • Mass: 1.0087 ext{ u}
      • Location: In the nucleus
    • Electron (e):
      • Charge: -1 (relative charge, equivalent to -1.60 \times 10^{-19} ext{ C})
      • Mass: 0.000549 ext{ u}
      • Location: Outside the nucleus (electron cloud)
  • Neutral Atom: The number of positively charged protons (p) equals the number of negatively charged electrons (e).
    • Number of protons = Number of electrons (for a neutral atom).
    • Neutrons do not affect the atom's charge as they are electrically neutral.

Atomic Number and Element Identity

  • Atomic Number (Z): The number of protons (p) in an atom's nucleus. (Z = p)
  • Identity: All atoms with the same number of protons (same Z) are atoms of the same element.
    • Example: All atoms with Z=1 are hydrogen; all atoms with Z=8 are oxygen.
  • In the periodic table, the atomic number (Z) is the whole number shown above the element symbol.
  • The atomic number uniquely determines an element's identity.

Isotopes

  • Definition: If two atoms have the same number of protons (same atomic number, Z) but different numbers of neutrons (n), they are called isotopes of one another.
  • Characteristics: Isotopes are still atoms of the same element but have different masses due to the varying number of neutrons.
  • Origin of Term: "Isotopes" (coined by Margaret Todd M.D. in 1913) is Greek for "at the same place," referring to occupying the same position in the periodic table despite different masses.
  • Mass Number (A): The sum of the number of protons and the number of neutrons in an atom (A = p + n).
    • Since Z = p, the mass number can also be written as A = Z + n.
  • Calculating Neutrons: The number of neutrons (n) is the difference between the mass number (A) and the atomic number (Z).
    • n = A - Z
  • Isotopic Symbol: Individual isotopes are identified by their symbol and mass number.
    • Notation: ^A_Z\text{X} or ext{X}-A
    • Example (Hydrogen):
      • Hydrogen-1 (^1_1\text{H} or H-1): 1 proton, 1 mass number \rightarrow 0 neutrons.
      • Hydrogen-2 ($^2_1\text{H} or H-2): 1 proton, 2 mass number \rightarrow 1 neutron. This is also called deuterium.
    • The atomic number (Z) as a subscript (e.g., _1\text{H}) is often omitted because the element symbol already implies the atomic number (it's redundant).
  • Example 2.7 (Determining Subatomic Particles in Neutral Atoms):
    • a. S-32:
      • Sulfur (S) has atomic number Z = 16, so 16 protons (p).
      • Neutral atom \rightarrow 16 electrons (e).
      • Mass number A = 32. Neutrons n = A - Z = 32 - 16 = 16.
      • Result: 16 protons, 16 neutrons, 16 electrons.
    • b. ^{19}\text{F}:
      • Fluorine (F) has atomic number Z = 9, so 9 protons (p).
      • Neutral atom \rightarrow 9 electrons (e).
      • Mass number A = 19. Neutrons n = A - Z = 19 - 9 = 10.
      • Result: 9 protons, 10 neutrons, 9 electrons.
    • c. Neon atom with equal numbers of protons and neutrons:
      • Neon (Ne) has atomic number Z = 10, so 10 protons (p).
      • Neutral atom \rightarrow 10 electrons (e).
      • If neutrons = protons \rightarrow 10 neutrons (n).
      • Result: 10 protons, 10 neutrons, 10 electrons.
    • d. ^{238}_{92}\text{U}:
      • Uranium (U) has atomic number Z = 92 (indicated by subscript), so 92 protons (p).
      • Neutral atom \rightarrow 92 electrons (e).
      • Mass number A = 238. Neutrons n = A - Z = 238 - 92 = 146.
      • Result: 92 protons, 146 neutrons, 92 electrons.

Atomic Masses

  • Challenge: Individual atoms are too tiny to be weighed directly until the 20th century.
  • Solution: A relative atomic mass scale was developed.
  • Historic Standard: The naturally occurring mixture of oxygen isotopes was initially assigned an atomic mass of exactly 16 atomic mass units (u or amu).
  • Modern Standard (since 1961): Based on the ^{12}\text{C} isotope.
    • The mass of a single ^{12}\text{C} atom is defined as exactly 12 ext{ u}.
  • Atomic Mass Unit (u or amu):
    • A very tiny unit of mass.
    • Conversion: 6.022 \times 10^{23} ext{ u} = 1.00 ext{ g}.
    • Atoms typically have masses between 1 and 250 ext{ u}.
  • Atomic Mass of an Element (as seen on the Periodic Table):
    • This is the weighted average of the actual masses of its naturally occurring isotopes on Earth.
    • It considers the relative abundance of each isotope.
    • Example: The atomic mass of carbon is 12.011 ext{ u}, not exactly 12 ext{ u}, because carbon exists as a mixture of isotopes ($^{12}\text{C} and $^{13}\text{C} predominantly).
  • Weighted Average Example (Example 2.12 - Student Grades):
    • Exams: 50\%, Quizzes: 25\%, Homework: 20\%, Participation: 5\%.
    • Scores: Exams 80.2\%, Quizzes 77.3\%, Homework 87.8\%, Participation 100.0\%.
    • Calculation:
      \text{Grade} = 0.50(80.2\%) + 0.25(77.3\%) + 0.20(87.8\%) + 0.05(100\%)
      \text{Grade} = 40.10\% + 19.33\% + 17.56\% + 5.00\%
      \text{Grade} = 82.0\%

The Periodic Table

Development of the Periodic Table

  • For over 140 years, chemists have arranged elements into groups with similar chemical characteristics.
  • The modern periodic table is the result of continuous refinement.
  • Organization:
    • Elements are numbered sequentially by increasing atomic number (Z) from left to right, top to bottom.
    • Elements are grouped vertically into columns (groups) based on similar chemical properties.
    • Horizontal rows are called periods.
  • Pioneering Work: Dmitri Mendeleev (Figure 2.15) and Lothar Meyer (1830-1895) independently developed the periodic table.
  • Mendeleev's Contributions: Often given sole credit because he used his periodic table to predict the existence and properties of undiscovered elements.
    • Mendeleev's Method (1860s): Arranged known elements in ascending order of their atomic masses (atomic numbers had not yet been defined).
    • Observation: Noticed that properties were generally similar for every seventh known element.
    • Arrangement: Placed elements with similar properties in the same group.
    • Predictions (Figure 2.16): When an element's atomic mass placed it in a position inconsistent with its chemical properties, Mendeleev hypothesized an undiscovered element for that spot.
      • Example: Between zinc (Zn) and arsenic (As), he predicted two elements whose properties would be intermediate between elements above and below them. These were later discovered as gallium (Ga) and germanium (Ge).
    • Discrepancies: Mendeleev encountered cases where elements seemed "out of order" by atomic mass.
      • Example: Iodine (126.9 ext{ u}) before Tellurium (127.6 ext{ u}) by mass, but chemical properties suggested the opposite order.
      • Mendeleev's Insight: He concluded that the atomic masses must have been determined incorrectly (or that properties mattered more) and placed elements consistent with their chemical properties.
  • Modern Understanding: The periodic properties of elements are based on their atomic numbers (Z), not atomic masses. This explains Mendeleev's challenges with elements like Iodine and Tellurium.
  • Example 2.16 (Elements Out of Order by Atomic Mass in Modern Table):
    • Argon (Ar, Z=18; 39.95 ext{ u}) and Potassium (K, Z=19; 39.10 ext{ u}): Argon has a higher atomic mass but comes before Potassium by atomic number.
    • Cobalt (Co, Z=27; 58.93 ext{ u}) and Nickel (Ni, Z=28; 58.69 ext{ u}$$): Cobalt has a higher atomic mass but comes before Nickel by atomic number.
    • These examples highlight Mendeleev's brilliance in prioritizing chemical properties when atomic numbers were unknown.