Chapter 2: The Components of Matter Flashcards

Classification of Matter

• Matter is classified based on its composition and uniformity:

  • Pure Substance: Composed of only a single type of atom or molecule.

  • Element: A pure substance that cannot be chemically broken down into simpler substances. Example: Helium ($He$).

  • Compound: A pure substance composed of two or more elements in fixed, finite proportions. Example: Pure water ($H_2O$).

  • Mixture: Composed of two or more different types of atoms or molecules.

  • Homogeneous Mixture: A mixture in which the composition is uniform and the same throughout. Example: Tea with sugar.

  • Heterogeneous Mixture: A mixture in which the composition varies from one region to another. Example: Wet sand.

Fundamental Laws of Matter

• Law of Conservation of Mass:

  • Proposed by Antoine Lavoisier in 1789 based on experimental evidence.

  • States that matter is neither created nor destroyed in a chemical reaction.

  • $\text{Total mass of used reactants} = \text{Total mass of products produced}$

  • $\text{Total number of reactant atoms} = \text{Total number of product atoms}$

• Law of Definite Proportions:

  • Proposed by Joseph Proust in 1797.

  • States that all samples of a given compound, regardless of their source or how they are prepared, have the same proportions of their constituent elements.

  • Example: Composition analysis of a $20\text{ g}$ sample of methane yields $15\text{ g}$ of carbon and $5\text{ g}$ of hydrogen.

  • Mass ratio: $5\text{ g hydrogen} : 15\text{ g carbon}$

  • Simplified mass ratio: $1\text{ g hydrogen} : 3\text{ g carbon}$

  • This ratio holds for any sample of methane regardless of its source.

• Law of Multiple Proportions:

  • Published by John Dalton in 1804.

  • States that when two elements (designated A and B) form two different compounds, the masses of element B that combine with $1\text{ g}$ of element A can be expressed as a ratio of small whole numbers.

  • Example: Carbon dioxide vs. Carbon monoxide:

  • Carbon dioxide: $2.67\text{ g}$ of oxygen combines with $1\text{ g}$ of carbon.

  • Carbon monoxide: $1.33\text{ g}$ of oxygen combines with $1\text{ g}$ of carbon.

  • Ratio of oxygen masses: $\frac{2.67}{1.33} = 2.00$

  • Underlying mechanical concept: Dalton suspected molecules were composed of small, indestructible particles. When elements A and B combine to form different compounds, an atom of A combines with 1, 2, 3, etc., atoms of B ($AB$, $AB_2$, $AB_3$, $AB_4$). Consequently, the masses of B reacting with a fixed mass of A always relate as small whole-number ratios.

Dalton's Atomic Theory

• Developed by John Dalton in 1808 to explain the laws of conservation of mass, definite proportions, and multiple proportions.

• The theory incorporates the following key concepts:

  • Elements are composed of tiny, indestructible particles called atoms (derived from Greek atomos, meaning uncuttable).

  • The concept of discrete particles was popularized by the philosopher Democritus around 460 B.C., but lacked experimental evidence until centuries after his death.

  • Atoms of a given element are identical in size, mass, and other properties; atoms of different elements differ in size, mass, and other properties.

  • Atoms cannot be subdivided, created, or destroyed.

  • Atoms combine in simple, whole-number ratios to form compounds.

  • Atoms of one element cannot change into atoms of another element. In a chemical reaction, atoms re-arrange the way they are bound together with other atoms to form new substances.

Discovery of Subatomic Particles and the Electron

• By the late 19th century, experimental observations demonstrated that atoms were composed of smaller, more fundamental subatomic particles.

• Cathode Rays and J. J. Thomson:

  • Late 1800s: J. J. Thomson probed cathode rays using a cathode ray tube—a partially evacuated glass tube fitted with two electrodes connected to a high electric voltage.

  • Cathode rays are emitted by the negatively charged electrode (cathode) and travel to the positively charged electrode (anode).

  • Rays are detected when colliding with a fluorescent coating at the end of the tube.

  • Observed properties of cathode ray particles:

  • Travel in straight lines.

  • Independent of the composition of the source material.

  • Carry a negative electrical charge.

  • Thomson measured the charge-to-mass ratio of cathode ray particles by deflecting them using electric and magnetic fields:     $\text{Mass-to-charge ratio} = -1.76 \times 10^{8}\text{ C/g}$

  • This ratio indicated that cathode ray particles were approximately 2000 times less massive than a hydrogen atom.

  • Thomson had discovered the electron—a low-mass, negatively charged subatomic particle. Practical applications include cathode ray tube televisions.

• Millikan Oil Drop Experiment (1909):

  • Robert Millikan determined the charge of a single electron.

  • Reasoned that electric charge on any oil drop must be an integral multiple of an individual electron's charge.

  • Measured fundamental electric charge per electron: $-1.60 \times 10^{-19}\text{ C}$.

  • Using Thomson's mass-to-charge ratio, the mass of an electron was calculated:     $\text{Mass of electron} = -1.60 \times 10^{-19}\text{ C} \times \frac{1\text{ g}}{-1.76 \times 10^{8}\text{ C}} = 9.10 \times 10^{-28}\text{ g}$

Atomic Structure and the Nuclear Model

• Plum-Pudding Model:

  • Most popular atomic model around 1900.

  • Pictured electrons distributed inside a uniform sphere of positive charge.

• Rutherford's Gold Foil Experiment (1909):

  • Ernest Rutherford, alongside J. J. Thomson, directed positively charged $\text{α}$ (alpha) particles emitted by radioactive materials at an ultrathin gold foil surrounded by a detector.

  • Expected outcome under the plum-pudding model: All $\text{α}$ particles would pass through undeflected due to mass and charge being evenly spread.

  • Experimental outcome: Most $\text{α}$ particles passed straight through with little or no deflection, but a small fraction were deflected through large angles.

  • Rutherford described his shock: "about as credible as if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

• Rutherford's Nuclear Theory of the Atom (Planetary Model):

  • Most of the atom's mass and all of its positive charge are concentrated in a tiny core called the nucleus.

  • Most of the volume of an atom is empty space, throughout which small, negatively charged electrons are dispersed.

  • An atom is electrically neutral because the number of negatively charged electrons outside the nucleus equals the number of positively charged particles (protons) inside the nucleus.

• Discovery of Neutrons:

  • Discrepancy observed: A hydrogen atom has 1 proton and a helium atom has 2 protons. If protons were the only massive particles, the helium-to-hydrogen mass ratio should be $2:1$. However, the actual mass ratio is $4:1$.

  • Rutherford later demonstrated that the unaccounted mass was due to neutrons—neutral subatomic particles located in the nucleus with mass equal to protons.

Properties of Subatomic Particles

• Proton: Positively charged; located in the nucleus; mass = $1.67262 \times 10^{-27}\text{ kg}$ ($≈ 1\text{ amu}$); charge = $+1.60 \times 10^{-19}\text{ C}$ ($+1$ relative atomic charge unit).

• Neutron: Neutral charge; located in the nucleus; mass = $1.67493 \times 10^{-27}\text{ kg}$ ($≈ 1\text{ amu}$); charge = $0\text{ C}$ ($0$ relative atomic charge unit).

• Electron: Negatively charged; located in orbitals outside the nucleus; mass = $9.1 \times 10^{-31}\text{ kg}$ ($0.00055\text{ amu}$); charge = $-1.60 \times 10^{-19}\text{ C}$ ($-1$ relative atomic charge unit).

• Atomic Mass Unit (amu): Defined as exactly $\frac{1}{12}$ the mass of a carbon atom containing 6 protons and 6 neutrons.

• Distribution: The nucleus contains almost all of the mass in a tiny volume. Orbital electrons account for virtually all of the spatial volume, despite having negligible mass.

Elements, Isotopes, and Atomic Mass

• Atomic Number ($Z$): The number of protons in an atom's nucleus. Determines elemental identity.

• Chemical Symbols: One- or two-letter abbreviations.

  • Based on English names: Carbon ($C$), Chlorine ($Cl$).

  • Based on Latin names: Sodium ($Na$, Natrium), Gold ($Au$, Aurum).

  • Based on German names: Tungsten ($W$, Wolfram).

  • Derived from properties: Argon ($Ar$, from Greek argos, meaning inactive).

  • Named after mythology: Mercury ($Hg$, Roman god of commerce and communication).

  • Named after places: Erbium ($Er$), Terbium ($Tb$), Ytterbium ($Yb$), Yttrium ($Y$) after Ytterby, Sweden; Polonium ($Po$) after Poland (birthplace of Marie Curie).

  • Named after scientists: Einsteinium ($Es$) after Albert Einstein; Bohrium ($Bh$) after Niels Bohr.

• Isotopes:

  • Atoms of the same element with identical numbers of protons ($Z$), but different numbers of neutrons.

  • Disproves Dalton's assertion that all atoms of an element have identical mass.

  • Example: Carbon always has 6 protons, but can have 6, 7, or 8 neutrons.

  • Natural Abundance: The relative percentage of a specific isotope in a naturally occurring sample of an element. Example: Natural bromine consists of $50.7\text{ }$ $^{79}_{35}\text{Br}$ (44 neutrons) and $49.3\text{ }$ $^{81}_{35}\text{Br}$ (46 neutrons).

  • Mass Number ($A$): The total sum of protons and neutrons in an atom:     $A = \text{number of protons} + \text{number of neutrons}$

• Atomic Mass:

  • The weighted average mass of all naturally occurring isotopes of an element based on natural abundance.

  • Example 1 (Calculating Average Atomic Mass):

  • Iron ($Fe$) isotopes:

    • $5.85\text{ }$ of $^{54}\text{Fe}$ ($53.94\text{ amu}$) $\rightarrow 0.0585 \times 53.94\text{ amu} = 3.15549\text{ amu}$

    • $91.75\text{ }$ of $^{56}\text{Fe}$ ($55.93\text{ amu}$) $\rightarrow 0.9175 \times 55.93\text{ amu} = 51.315775\text{ amu}$

    • $2.12\text{ }$ of $^{57}\text{Fe}$ ($56.94\text{ amu}$) $\rightarrow 0.0212 \times 56.94\text{ amu} = 1.207128\text{ amu}$

    • $0.28\text{ }$ of $^{58}\text{Fe}$ ($57.93\text{ amu}$) $\rightarrow 0.00028 \times 57.93\text{ amu} = 0.162204\text{ amu}$

  • Sum of contributions: $3.15549 + 51.315775 + 1.207128 + 0.162204 = 55.84\text{ amu}$.

  • Example 2 (Calculating Isotopic Abundance):

  • Boron ($B$) isotopes: $^{10}\text{B}$ ($10.01\text{ amu}$) and $^{11}\text{B}$ ($11.01\text{ amu}$); average atomic mass = $10.81\text{ amu}$.

  • Let $x$ equal natural abundance of $^{10}\text{B}$:       $x(10.01\text{ amu}) + (1 - x)(11.01\text{ amu}) = 10.81\text{ amu}$       $10.01x + 11.01 - 11.01x = 10.81$       -1x = -0.2 −−−> x = 0.2

  • Abundance percentages: $^{10}\text{B} = 20\text{ }$, $^{11}\text{B} = 80\text{ }$.

Ions and the Periodic Table

• Ions:

  • Formed when neutral atoms gain or lose electrons during chemical changes.

  • Cation: Positively charged ion resulting from electron loss. Example: Sodium ($Na$) loses 1 electron to form $Na^+$ (11 protons, 10 electrons).

  • Anion: Negatively charged ion resulting from electron gain. Example: Bromine ($Br$) gains 1 electron to form $Br^-$ (35 protons, 36 electrons).

• Development of the Periodic Table:

  • In 1869, Russian chemistry professor Dmitri Mendeleev organized 65 known elements in order of increasing mass.

  • Periodic Law: When elements are arranged in order of increasing mass, certain properties recur periodically.

  • Mendeleev left gaps for undiscovered elements and successfully predicted their existence and properties.

  • Modern periodic tables organize elements by increasing atomic number ($Z$) rather than atomic mass.

• Classification Regions of the Periodic Table:

  • Metals: Located on the lower left side and middle. Conduct heat and electricity well, malleable, ductile, shiny, tend to lose electrons during chemical changes.

  • Nonmetals: Located on the upper right side. Poor conductors of heat and electricity, tend to gain electrons during chemical changes.

  • Metalloids: Lie along the zigzag diagonal line separating metals and nonmetals. Exhibit mixed metallic and nonmetallic properties.

• Divisions and Groups:

  • Main-Group Elements: Properties are predictable based on position.

  • Group 1A: Alkali metals (extremely reactive).

  • Group 2A: Alkaline earth metals (fairly reactive).

  • Group 7A: Halogens (extremely reactive nonmetals).

  • Group 8A: Noble gases (rarely form compounds).

  • Transition Metals: Properties are less predictable based on position.

  • Lanthanides and Actinides: Inner transition elements.

• Ion Charge Predictions:

  • Main-group metals lose electrons to form cations with the electron configuration of the nearest noble gas (e.g., $Li^+$, $Na^+$, $K^+$, $Rb^+$, $Mg^{2+}$, $Ca^{2+}$, $Sr^{2+}$, $Ba^{2+}$, $Al^{3+}$).

  • Main-group nonmetals gain electrons to form anions with the electron configuration of the nearest noble gas (e.g., $N^{3-}$, $O^{2-}$, $S^{2-}$, $Se^{2-}$, $Te^{2-}$, $F^-$, $Cl^-$, $Br^-$, $I^-$).

Chemical Bonds and Compounds

• Chemical Bonds: Hold atoms together in compounds.

  • Ionic Bonds: Form between metals and nonmetals. Electrons are transferred from metal to nonmetal, forming cations and anions held together by electrostatic forces in a crystalline lattice.

  • Covalent Bonds: Form between two or more nonmetals. Electrons are shared between bonding atoms and interact with both nuclei.

• Chemical Formulas and Representations:

  • Empirical Formula: Gives the relative whole-number ratio of atoms of each element in a compound (experimentally determined).

  • Molecular Formula: Gives the actual number of atoms of each element in a molecule. Example: Hydrogen peroxide empirical formula = $HO$; molecular formula = $H_2O_2$

  • Structural Formula: Represents how atoms in a molecule are physically connected or bonded.

  • Molecular Models: Ball-and-stick models represent atoms as spheres and bonds as rods; space-filling models represent atoms filling spatial volume.

• Molecular vs. Atomic Forms:

  • Atomic Elements: Exist in nature as single individual atoms (e.g., $He$, $Ar$, $Ne$).

  • Molecular Elements: Exist as diatomic molecules (e.g., $O_2$, $N_2$) or polyatomic molecules (e.g., $S_8$).

  • Molecular Compounds: Composed of two or more covalently bonded nonmetals.

  • Ionic Compounds: Composed of alternating cations and anions bonded in non-directional ionic lattices.

  • Formula Unit: The smallest electrically neutral collection of ions representing an ionic compound.

  • Charge balance rule: Sum of positive charges must equal sum of negative charges ($\text{Net charge} = 0$).

Chemical Nomenclature

• Naming Binary Ionic Compounds:

  • For metals with invariant charges: [Name of Metal] [Base name of Nonmetal + -ide]

  • Example: $CaF_2$ = Calcium fluoride.

  • For metals with variable charges (Transition Metals): [Name of Metal](Roman Numeral of Charge) [Base name of Nonmetal + -ide]

  • Examples: $FeCl_2$ = Iron(II) chloride; $FeCl_3$ = Iron(III) chloride.

• Common Metals forming Variable Cations:

  • Chromium: $Cr^{2+}$ (Chromium(II) / Chromous), $Cr^{3+}$ (Chromium(III) / Chromic)

  • Iron: $Fe^{2+}$ (Iron(II) / Ferrous), $Fe^{3+}$ (Iron(III) / Ferric)

  • Cobalt: $Co^{2+}$ (Cobalt(II) / Cobaltous), $Co^{3+}$ (Cobalt(III) / Cobaltic)

  • Copper: $Cu^+$ (Copper(I) / Cuprous), $Cu^{2+}$ (Copper(II) / Cupric)

  • Tin: $Sn^{2+}$ (Tin(II) / Stannous), $Sn^{4+}$ (Tin(IV) / Stannic)

  • Mercury: $Hg_2^{2+}$ (Mercury(I) / Mercurous), $Hg^{2+}$ (Mercury(II) / Mercuric)

  • Lead: $Pb^{2+}$ (Lead(II) / Plumbous), $Pb^{4+}$ (Lead(IV) / Plumbic)

• Naming Polyatomic Ionic Compounds and Oxyanions:

  • Oxyanions contain oxygen and another element.

  • Two-oxyanion series: The anion with more oxygen gets suffix -ate; the anion with less oxygen gets suffix -ite.

  • Four-oxyanion series: per- prefix for maximum oxygen, hypo- prefix for minimal oxygen.

• Hydrated Ionic Compounds:

  • Ionic compounds containing specific numbers of water molecules per formula unit (waters of hydration can be removed by heat).

  • Form: [Ionic compound name] [Greek prefix]hydrate

  • Example: $MgSO_4 · 7H_2O$ = Magnesium sulfate heptahydrate.

• Naming Acids:

  • Acids release $H^+$ ions in aqueous solution.

  • Binary Acids ($H$ + nonmetal):

  • hydro- + [Base name of nonmetal + -ic] + acid

  • Example: $HBr$ = Hydrobromic acid; $HCl$ = Hydrochloric acid.

  • Oxyacids ($H$ + oxyanion):

  • Oxyanion ending in -ate $\rightarrow$ [Base name of oxyanion + -ic] + acid (e.g., $H_2SO_4$ = Sulfuric acid from sulfate; $H_3PO_4$ = Phosphoric acid).

  • Oxyanion ending in -ite $\rightarrow$ [Base name of oxyanion + -ous] + acid (e.g., $H_2SO_3$ = Sulfurous acid from sulfite).

• Naming Molecular Compounds:

  • Composed of nonmetals covalently bonded.

  • [Greek prefix][1st element] [Greek prefix][Base name of 2nd element + -ide]

  • Element with smallest group number (leftmost on periodic table) listed first.

  • Prefix mono- is omitted on the first element if singular, but kept on the second element.

  • Examples: $P_4S_{10}$ = Tetraphosphorus decasulfide; $CO_2$ = Carbon dioxide; $CO$ = Carbon monoxide.

• Organic Chemistry:

  • The study of carbon-containing compounds (over 99% of 30+ million known compounds contain carbon).

  • Carbon always forms 4 chemical bonds, forming chains, branches, and ring backbones.

  • Hydrocarbons: Simple organic molecules containing only carbon and hydrogen. Simplest hydrocarbon = Methane ($CH_4$).

Quantitative Worked Examples

• Calculating Mass in Reactions (Conservation of Mass):

  • Antoine Lavoisier burned a $1.25\text{ g}$ strip of magnesium ($Mg$), resulting in $2.07\text{ g}$ of magnesium oxide ($MgO$).

  • Mass of oxygen consumed: $2.07\text{ g } MgO - 1.25\text{ g } Mg = 0.82\text{ g } O$.

• Calculating Mass of an Element in a Compound (Definite Proportions):

  • A $78.80\text{ g}$ sample of hematite contains $55.08\text{ g}$ of iron ($Fe$). Determine grams of $Fe$ and $O$ in a $260.82\text{ g}$ rock.

  • Set up proportion:     $\frac{55.08\text{ g Fe}}{78.80\text{ g sample}} = \frac{x\text{ g Fe}}{260.82\text{ g rock}}$     78.80x = 14365.9656 −−−> x = 182.3\text{ g of Fe}

  • Mass of oxygen: $260.82\text{ g} - 182.3\text{ g} = 78.5\text{ g of O}$.

• Calculating Atomic Mass of an Unknown Metal:

  • A metal ($M$) weighing $1.563\text{ g}$ is burned in $127.4\text{ mL}$ of $O_2$ gas (density = $1.429\text{ g/L}$) to produce metal oxide $MO$.

  • Step 1: Calculate mass of $O_2$ gas consumed:     $\text{Mass of } O_2 = 127.4\text{ mL} \times \frac{1\text{ L}}{1000\text{ mL}} \times \frac{1.429\text{ g}}{1\text{ L}} = 0.1820546\text{ g } O_2$

  • Step 2: Set up atomic ratio for formula $MO$ ($\text{atomic mass of } O = 16.00\text{ amu}$):     $\frac{\text{Atomic mass of } M}{16.00\text{ amu}} = \frac{1.563\text{ g } M}{0.1820546\text{ g } O}$     0.1820546x = 25.008 −−−> x = 137.4\text{ amu}

  • The calculated atomic mass ($137.4\text{ amu}$) identifies the metal $M$ as Barium ($Ba$).

• Calculating Molecular and Formula Mass:

  • Phosphorus Oxyfluoride ($POF_3$):

  • $1 \times P = 1 \times 30.97\text{ amu} = 30.97\text{ amu}$

  • $1 \times O = 1 \times 16.00\text{ amu} = 16.00\text{ amu}$

  • $3 \times F = 3 \times 19.00\text{ amu} = 57.00\text{ amu}$

  • $\text{Total Molecular Mass} = 103.97\text{ amu}$

  • Copper(II) Phosphate ($Cu_3(PO_4)_2$):

  • $3 \times Cu = 3 \times 63.55\text{ amu} = 190.65\text{ amu}$

  • $2 \times P = 2 \times 30.97\text{ amu} = 61.94\text{ amu}$

  • $8 \times O = 8 \times 16.00\text{ amu} = 128.00\text{ amu}$

  • $\text{Total Formula Mass} = 380.59\text{ amu}$