Atoms and the Periodic Table: Chemical Symbols, Laws, and Atomic History Notes

Chemical Symbols and Elements

• Element Identification: Every chemical element is assigned an internationally recognized symbol consisting of either one or two letters. Examples include the symbol $C$ for carbon and $He$ for helium.

• Capitalization Convention: The first letter of any element's symbol must always be uppercase. If there is a second letter, it must be lowercase. This is critical for distinguishing between elements and compounds (e.g., $Co$ is the element cobalt, while $CO$ is the compound carbon monoxide).

• Etymological Roots of Symbols: Many elements have symbols derived from their original Latin names rather than their English names. These symbols often look unrelated to the English spelling.

• Table 2.1: Latin-Based Chemical Symbols

  • Antimony: Symbol is $Sb$, based on Stibium.

  • Gold: Symbol is $Au$, based on Aurum.

  • Iron: Symbol is $Fe$, based on Ferrum.

  • Lead: Symbol is $Pb$, based on Plumbum.

  • Mercury: Symbol is $Hg$, based on Hydrargyrum.

  • Potassium: Symbol is $K$, based on Kalium.

  • Silver: Symbol is $Ag$, based on Argentum.

  • Sodium: Symbol is $Na$, based on Natrium.

  • Tin: Symbol is $Sn$, based on Stannum.

  • Tungsten: Symbol is $W$, based on Wolfram.

Chemical Formulas and Stoichiometric Ratios

• Chemical Formulas: Compounds are identified by writing chemical symbols together. These formulas convey the relative number of each type of atom present in the compound.

• Interpreting Subscripts: In a formula like $H_2O$, the subscript indicates there are $2$ atoms of hydrogen ($H$) for every $1$ atom of oxygen ($O$).

• Parentheses in Formulas: When a chemical formula contains parentheses, the subscript outside the parentheses applies to every atom inside. For example, in calcium nitrate, $Ca(NO_3)_2$, there is $1$ atom of $Ca$, $2$ atoms of $N$ ($1 \times 2$), and $6$ atoms of $O$ ($3 \times 2$).

• Example 2.1: Identifying Elements from Symbols

  • $C$: carbon

  • $Br$: bromine

  • $Hg$: mercury

  • $Sr$: strontium

• Example 2.2: Determining Relative Numbers of Atoms

  • $CO_2$: Contains two atoms of oxygen ($O$) for every one atom of carbon ($C$).

  • $PCl_3$: Contains three atoms of chlorine ($Cl$) for every one atom of phosphorus ($P$).

  • $Fe(OH)_3$: Contains three atoms of oxygen ($O$) and three atoms of hydrogen ($H$) for every one atom of iron ($Fe$).

The Laws of Chemical Combination

• The Law of Conservation of Mass: Developed by Antoine Lavoisier, this law states that matter is neither lost nor destroyed during a chemical reaction.

  • Lavoisier's Phosphorus Experiment: Lavoisier quantitatively reacted phosphorus with oxygen, initiating the reaction using sunlight focused through a magnifying glass. He proved that the mass of the reactants equaled the mass of the products. This challenged earlier observations, such as wood ash being lighter than the original wood, by accounting for mass lost as gases.

• The Law of Definite Proportions: This law states that any given pure compound is always composed of definite proportions by mass of its elements.

  • Water Example: In all pure samples of water ($H_2O$), the mass ratio of oxygen to hydrogen is consistently $8:1$.

  • Mass Proportion Calculation: The proportion by mass is calculated as: $\text{Proportion of element} = \frac{\text{mass of element}}{\text{total mass of compound}}$.

  • Percent by Mass Calculation: The percent by mass is the proportion multiplied by $100$: $\text{Percent by mass} = \frac{\text{mass of element}}{\text{total mass of compound}} \times 100$.

• Example: Elements in Sucrose ($C_{12}H_{22}O_{11}$)

  • Carbon Proportion: $\frac{144 \text{ g}}{342 \text{ g}} = 0.421$ ($42.1 \text{\%}$)

  • Hydrogen Proportion: $\frac{22 \text{ g}}{342 \text{ g}} = 0.064$ ($6.4 \text{\%}$)

  • Oxygen Proportion: $\frac{176 \text{ g}}{342 \text{ g}} = 0.515$ ($51.5 \text{\%}$)

• The Law of Multiple Proportions: If two or more compounds are composed of the same two elements, for a fixed mass of one element, the masses of the second element will be in a ratio of small whole numbers.

  • Example Calculation (CO vs $CO_2$): In $CO$, there is $1.33 \text{ g}$ of $O$ for every $1 \text{ g}$ of $C$. In $CO_2$, there is $2.66 \text{ g}$ of $O$ for every $1 \text{ g}$ of $C$. Dividing the oxygen masses: $\frac{2.66}{1.33} = \frac{2}{1}$.

Quantitative Exercises on Chemical Laws

• Example 2.3: Invariance of Percent Composition

  • Part A: If a $4.33 \text{ g}$ sample of dinitrogen monoxide ($N_2O$) is $63.65 \text{\%}$ nitrogen and $36.35 \text{\%}$ oxygen, what is the composition of a $14.9 \text{ g}$ sample? Answer: It remains exactly the same ($63.65 \text{\%}$ $N$, $36.35 \text{\%}$ $O$) because the law of definite proportions applies to all pure samples.

  • Part B: In a mixture of $N_2O$ ($63.65 \text{\%}$ $N$) and $NO$ ($46.68 \text{\%}$ $N$), what are the possible nitrogen percentages? Answer: The percentage must fall somewhere between $46.68 \text{\%}$ and $63.65 \text{\%}$.

• Example 2.4: Calculating Mass from Percentage

  • Problem: Find the mass of nitrogen in a $4.75 \text{ g}$ sample of nitrogen monoxide ($NO$) with $46.68 \text{\%}$ nitrogen.

  • Solution Strategy: $\text{mass of N} = \frac{\text{Percent by mass}}{100 \text{\%}} \times \text{mass of sample}$.

  • Calculation: $\frac{46.68 \text{\%}}{100 \text{\%}} \times 4.75 \text{ g} = 2.22 \text{ g N}$.

• Example 2.5: Verifying Law of Multiple Proportions

  • Problem: $NO$ has $14.01 \text{ g N}$ and $16.00 \text{ g O}$. $NO_2$ has $14.01 \text{ g N}$ and $32.00 \text{ g O}$.

  • Step 1 ($N:O$ Ratio for $NO$): $\frac{14.01 \text{ g}}{16.00 \text{ g}} = 0.8756$.

  • Step 2 ($N:O$ Ratio for $NO_2$): $\frac{14.01 \text{ g}}{32.00 \text{ g}} = 0.4378$.

  • Step 3 (Comparing Ratios): $\frac{0.8756}{0.4378} = 2.000$. This whole number verifies the Law of Multiple Proportions.

Dalton's Atomic Theory

• Fundamental Postulates (John Dalton):

  1. Matter is composed of extremely tiny, indivisible particles called atoms.

  2. All atoms of a specific element are identical in mass, and this mass differs from atoms of other elements.

  3. Atoms combine in small, whole-number ratios to form what are now known as molecules.

  4. Atoms of the same pair of elements can combine in different ratios to form different compounds.

• Explanatory Power of Dalton's Theory:

  • Conservation of Mass: Atoms do not break down or arise from nothing; they simply exchange partners during reactions. Since the atoms themselves are preserved, total mass is conserved.

  • Definite Proportions: Because compounds consist of specific atoms in specific fixed ratios, the proportion of mass contributed by each element must be constant.

  • Multiple Proportions: Since atoms combine in whole-number increments (e.g., $1:1$ or $1:2$), the mass ratios between different compounds formed by the same elements must involve simple whole numbers.

• Modern Revisions:

  • Atoms are not indivisible (subatomic particles exist).

  • Nuclear reactions can divide or build atoms.

  • The discovery of isotopes disproved the idea that all atoms of a single element have identical masses.

The Discovery of Subatomic Particles

• J. J. Thomson and the Electron (1897):

  • Thomson used a cathode-ray tube where high voltage caused rays to be emitted from a negative electrode (cathode) toward a positive electrode (anode).

  • These rays were deflected by magnetic fields and consisted of negatively charged particles, later named electrons.

  • Regardless of the substance used, the rays were identical, proving electrons were universal components of all atoms.

  • Charge-to-Mass Ratio: Thomson determined the ratio to be $-1.76 \times 10^8 \text{ C/g}$ (Coulombs per gram).

• Robert Millikan and the Oil-Drop Experiment (1909):

  • Millikan sprayed charged oil drops into a chamber between two plates.

  • By adjusting the electric field to suspend drops against gravity, he calculated the charge on individual drops.

  • He determined the fundamental charge units were multiples of $-1.60 \times 10^{-19} \text{ C}$, the charge of a single electron.

• Mass Calculation of the Electron:

  • Using Thomson's ratio and Millikan's charge:

  • $\text{mass} = (-1.60 \times 10^{-19} \text{ C}) \times \frac{1 \text{ g}}{-1.76 \times 10^8 \text{ C}} = 9.10 \times 10^{-28} \text{ g}$.

• Early Atomic Models:

  • Dalton's Model: A simple, indivisible sphere.

  • Thomson's Plum-Pudding Model: Negatively charged electrons (plums) suspended within a larger sphere of uniform positive charge (the pudding).

The Nuclear Model of the Atom

• Detection of Radioactivity: Discovered by Henri Becquerel (1896) and Marie Curie, radioactivity involved three types of particles/rays:

  1. Alpha ($\alpha$) particles: Positively charged.

  2. Beta ($\beta$) particles: Negatively charged.

  3. Gamma ($\gamma$) particles: Neutral.

• Rutherford’s Gold Foil Experiment:

  • Ernest Rutherford, with Geiger and Marsden, fired alpha particles at a thin sheet of gold foil.

  • Initial Hypothesis: Alpha particles would pass straight through the "plum pudding" atoms because there was no concentrated mass or charge to deflect them.

  • Actual Observations: Most particles passed through, but some were deflected at large angles, and a few bounced directly back.

• Rutherford’s Conclusions:

  1. The positive charge and almost all of the mass of the atom are concentrated in a tiny central region called the nucleus.

  2. The rest of the atom is primarily empty space.

  3. Small, negatively charged electrons are distributed throughout this empty space.

  4. An atom is electrically neutral because the number of protons in the nucleus equals the number of electrons outside it.

• The Neutron: James Chadwick (1932) demonstrated the existence of neutral particles in the nucleus to account for mass discrepancies (e.g., helium having four times the mass of hydrogen despite only having twice the protons).

• Example 2.6: Thomson's Insight: Beyond Dalton’s conclusion that matter is composed of atoms, Thomson’s experiments revealed that atoms are not the smallest unit of matter; they contain internal, negatively charged particles (subatomic particles).