Chapter 2 Atoms, Ions, and Molecules: The Building Blocks of Matter

Back in the Day

• Prior to the 18th Century, beliefs about matter's structure relied on ancient Greek ideas.

• Leucippus and Democritus (5th century BCE) proposed that:

  • All matter comprises small, indestructible particles called atoms (GR. atmos = indivisible).

  • Atoms are qualitatively alike but differ in size, shape, and mass.

  • Atoms exist within a void and are in constant motion.

  • Changes in matter result from the combination or separation of atoms.

• Later Greek philosophers, especially Aristotle, opposed this view, believing matter to be infinitely divisible.

Dalton’s Postulates

• All atoms of a given element possess identical properties, distinct from those of other elements. (Note: This postulate will later be revised.)

• A compound consists of atoms from two or more different elements, chemically combined in fixed proportions.

• A chemical reaction involves the rearrangement of atoms in reacting substances, forming new combinations in the products.

  • Atoms are not created, destroyed, or transformed into other elements during ordinary chemical reactions.

• Dalton’s Atomic Theory explains the Law of Conservation of Matter and the Law of Definite Proportions.

Law of Definite Proportions

• A pure compound always contains definite and constant proportions of its elements by mass, regardless of its source.

• Example: Sodium chloride (NaCl) always contains 39.3% Na and 60.7% Cl by mass.

Law of Multiple Proportions

• If two elements form multiple compounds, the masses of one element that combine with a fixed mass of the other occur in small whole-number ratios.

• Example:

  • Gold(I) chloride: 1.000 g gold combines with 0.1800 g chlorine.

  • Gold(III) chloride: 1.000 g gold combines with 0.5400 g chlorine.

  • For a fixed mass of gold, the combining masses of chlorine are in a 3:1 ratio.

Atomic Structure

• All atoms share the same fundamental structure.

  • They consist of a central nucleus surrounded by one or more electrons.  The nucleus comprises protons and neutrons.

• Modern understanding of atomic structure largely stems from experiments in the late 1800s and early 1900s.

• Several experiments utilized a Crookes’ Tube (named after Sir William Crookes).

Discovery of the Electron

• J.J. Thomson, a physicist at Cambridge University, is credited with discovering the electron.

• When a Crookes’ tube is evacuated and connected to a high voltage, a stream of rays flows from the cathode (-) to the anode (+).

• These rays are deflected by electric and magnetic fields, indicating they are negatively charged.

• These rays are a stream of negatively charged particles, later termed electrons.

• In 1897, Thomson measured the charge-to-mass ratio ($e/m$) of the electron to be approximately $10^8$ C/g (accepted value today is $1.7591 \times 10^8$ C/g).

• The $e/m$ ratio was independent of the cathode material.

Millikan’s Oil Drop Experiment

• In 1909, Robert Millikan conducted the oil drop experiment to determine the mass and charge of the electron.

• X-rays ionize gas molecules; the electrons are absorbed by oil droplets.

• At a specific applied voltage, gravitational and electrostatic forces balance, holding the droplets stationary.

• The charge of the oil droplets can be determined from the mass of the drop and the applied charge.

• The charge on the droplets was always found to be $1.602 \times 10^{-19}$ C or a multiple thereof; this is the charge of the electron.

• Given $e = 1.602 \times 10^{-19}$ C and $e/m = 1.7591 \times 10^8$ C/g, the mass of the electron (m) is $9.109 \times 10^{-28}$ g or $9.109 \times 10^{-31}$ kg.

Discovery of the Proton

• In 1886, Eugen Goldstein used a Crookes’ tube with holes in the cathode and observed rays originating at the anode (+) and passing through the cathode's holes.

• Wilhelm Wien demonstrated that these rays consisted of positively charged particles.

• The $e/m$ ratio was much smaller than that of the electron and varied based on the gas in the tube.

• Both $e$ and $m$ vary, and each particle had a positive charge equal in magnitude to the electron's charge (or a multiple).

• The mass was smallest when hydrogen was the fill gas, determined to be $1.673 \times 10^{-27}$ kg.

• These particles, obtained when hydrogen was used, are known as protons and are fundamental to atomic structure.

Thomson's Plum-Pudding Model

• Electrons are distributed throughout a diffuse, positively charged sphere.

Rutherford’s Gold Foil Experiment

• Hans Geiger and Ernest Marsden, working with Ernest Rutherford, bombarded a thin gold foil with alpha particles to test Thomson’s atomic model.

• Most α-particles passed through undeflected, some deflected at small angles, and a few recoiled.

Rutherford’s Results

• Atoms consist mostly of empty space, with a tiny, massive, positively charged center called the nucleus.

Discovery of the Neutron

• In 1932, James Chadwick discovered the neutron, an electrically neutral particle slightly heavier than the proton.

• The existence of neutrons had been predicted for over a decade before their discovery.

The Nuclear Atom

• The atomic model features a tiny, positively charged nucleus holding almost all of the atom's mass.

  • Proton: positively charged subatomic particle.

  • Neutron: electrically neutral subatomic particle.

• Atomic Number: The number of protons in an atom's nucleus.

The Atomic Mass Unit

• The unit used to express the relative masses of atoms and subatomic particles.

• Equal to 1/12 the mass of a carbon-12 atom.

• 1 amu (u) = 1 dalton (Da)

Subatomic Particles

• Neutron:

  • Symbol: n

  • Mass: 1.00867 u ≈ 1

  • Mass: $1.67493 \times 10^{-27}$ kg

  • Charge: 0

  • Relative Charge: 0

• Proton:

  • Symbol: p

  • Mass: 1.00728 u ≈ 1

  • Mass: $1.67262 \times 10^{-27}$ kg

  • Charge: $+1.602 \times 10^{-19}$ C

  • Relative Charge: +1

• Electron:

  • Symbol: e-

  • swa: $5.485799 \times 10^{-4}$ u ≈ 0

  • Mass: $9.10939 \times 10^{-31}$ kg

  • Charge: $-1.602 \times 10^{-19}$ C

  • Relative Charge: -1

• Most of an atom's mass resides in the nucleus because protons and neutrons are much heavier than electrons.

• The nucleus occupies a minuscule fraction of the atom's volume.

• The density of the nucleus is about $1 \times 10^{16}$ g/cm³.

Atomic Number and Mass Number

• ATOMIC NUMBER (Z) = Number of protons in the nucleus. All atoms of the same element have the same atomic number.

• MASS NUMBER (A) = Sum of protons and neutrons in the nucleus. Always an integer, but the mass of an individual atom generally is not.

• $A = Z + N$, where N = number of neutrons.

• Atoms of an element always have the same number of protons but may have different numbers of neutrons.

• Thus, atoms of an element can have different mass numbers.

Isotopes: Experimental Evidence

• Positively charged neon ions passed through electric and magnetic fields show multiple bright spots.

• This indicates Ne+ ions with different masses.

• Isotopes: Atoms with the same atomic number (Z) but different mass numbers (A).

• Isotopes are atoms with the same number of protons but different numbers of neutrons.

Isotopes: Mass Spectral Results

• Three kinds of neon gas atoms were observed:

  • 90.48% = 19.992435 amu

  • 0.27% = 20.993842 amu

  • 9.25% = 21.991383 amu

• Aston proposed the theory of “isotopes”.

• Isotopes: Atoms of an element with the same number of protons but different numbers of neutrons.

• Nuclide: A specific isotope of an element.

Symbols of Isotopes or Nuclides

• $^A_ZX$

  • X: element symbol

  • Z: nuclear charge or atomic number (# protons)

  • A: atomic mass of the nuclide (sum of protons and neutrons)

• A nuclide is a specific nucleus characterized by a specific atomic number and a specific mass number.

Symbols of Isotopes: Example

• Most elements have two or more isotopes, atoms that have the same atomic number (Z) but different mass numbers (A).

• Example:

  • $^{22}_{10}Ne$: 10 protons, 12 neutrons (22 – 10)

  • $^{20}_{10}Ne$: 10 protons, 10 neutrons (20 – 10)

• Hydrogen isotopes have unique names:

  • $^1_1H$: protium

  • $^2_1H$: deuterium

  • $^3_1H$: tritium

Identifying Isotopes and Ions

• Table with missing information (example):

  • Symbol: $^{23}Na^+$

  • Protons: 11

  • Neutrons: 12

  • Electrons: 10

  • Mass Number: 23

The Periodic Table

• In 1869, Dmitri Mendeleev and J. Lothar Meyer independently discovered that arranging elements in rows by increasing atomic weight allowed elements in the same column to have similar chemical properties.

• The modern periodic table orders elements by increasing atomic number, with similar chemical properties appearing in columns.

Mendeleev’s Periodic Table (1872)

• Elements were ordered by increasing atomic mass.

• Arranged elements in columns based upon similar chemical and physical properties.

• Left spaces open for elements not yet discovered.

Mendeleev’s Periodic Table (1872) Success

• Mendeleev’s table successfully predicted undiscovered elements.

• For instance, germanium (discovered in 1886) was predicted as eka-silicon.

• Mendeleev accurately predicted the properties of this element based on the elements surrounding it.

The Modern Periodic Table

• Elements are arranged by increasing atomic number.

• Elements in columns (groups) have similar chemical and physical properties.

• Horizontal rows are called periods (1 to 7).

• Columns are called groups (1 to 18).

Categories of Elements

• Metals:

  • Shiny, solid conductors of heat and electricity

  • Malleable and ductile

  • Exception: Mercury is liquid.

• Nonmetals:

  • Solids (brittle), liquids, and gases

  • Nonconductors

• Metalloids:

  • Shiny (like metals) but brittle (like nonmetals)

  • Semiconductors

Categories of Elements

• Main group (representative elements)

• Transition metals

• Inner-transition metals

Commonly Used Names of Groups

• Group 1: Alkali metals

• Group 2: Alkaline earth metals

• Group 15: Pnictogens

• Group 16: Chalcogens

• Group 17: Halogens

• Group 18: Noble gases

Atomic Mass (Atomic Weight)

• Samples of naturally occurring elements usually mixtures of two or more different isotopes.

• The atomic weight of an element is a weighted average of the masses of all the naturally occurring isotopes of that element.

• $Atomic Weight = \sum(f<em>i \times m</em>i)$, where:

  • $f_i$ = fractional abundance of an isotope

  • $m_i$ = mass of an atom of that isotope

Atomic Mass (Atomic Weight) Example

• Neon has three naturally occurring stable isotopes:

  • Neon-20: 19.9924 amu, 90.4838%

  • Neon-21: 20.9940 amu, 0.2696%

  • Neon-22: 21.9914 amu, 9.2465%

• Atomic weight of neon:

  • $(19.9924 \text{ amu} \times 0.904838) + (20.99395 \text{ amu} \times 0.002696) + (21.9914 \text{ amu} \times 0.092465) = 20.1799 \text{ amu}$

Atomic Mass (Atomic Weight) Significance

• No single atom of neon has a mass of 20.1799 amu, but a representative sample of neon behaves as if it's made of atoms with this average mass.

• Periodic table atomic weights are weighted averages of the atomic masses of stable, naturally occurring isotopes.

• Only about twenty elements have only one stable, naturally occurring isotope: 9Be, 19F, 23Na, 27Al, 31P, 45Sc, 55Mn, 59Co, 75As, 89Y, 93Nb, 103Rh, 127I, 133Cs, 141Pr, 159Tb, 165Ho, 169Tm, 197Au and 209Bi

Molecular Weight and Formula Weight

• It's simple to extend the concept of atomic weight to molecular and formula weights.

• A molecular formula indicates the actual number of atoms of each element in a molecule.

• The molecular weight (MW) of a molecular compound is the sum of the atomic weights of all atoms in the molecule.

Molecular Weight Example

• Ethanol (C2H5OH) has 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom per molecule.

• Molecular weight of ethanol:

  • 2 C: 2 (12.011 amu) = 24.022 amu

  • 6 H: 6 (1.0079 amu) = 6.0474 amu

  • 1 O: 1 (15.9994 amu) = 15.9994 amu

  • Total: 46.069 amu

• The molecular weight of ethanol is 46.069 amu.

Formula Weight

• Ionic compounds like NaCl, CaSO4, and Zn(NO3)2 do not exist as individual molecules, so we use formula weights instead of molecular weights.

• Formula weights are computed like molecular weights.

Formula Weight Definition

• The formula weight (FW) of a compound is the sum of the atomic weights of all atoms in a formula unit of the substance.

• Example: Formula weight of Zn(NO3)2

  • 1 Zn: 1 (65.39 amu) = 65.39 amu

  • 2 N: 2 (14.0067 amu) = 28.0134 amu

  • 6 O: 6 (15.9994 amu) = 95.9964 amu

  • Total: 189.40 amu

• The formula weight of zinc nitrate is 189.40 amu.

The Mole

• We cannot measure the mass of individual atoms or molecules directly because the masses are too small.

• The SI unit for the amount of a substance is the mole (mol).

• A mole is the quantity of a given substance that contains as many formula units as there are atoms in exactly 0.012 kg (12 g) of 12C.

The Mole and Avogadro's Number

• The number of entities in a mole is a very large number called Avogadro’s Number (NA), named after Amedeo Avogadro.

• Avogadro’s Number (NA) = $6.0221367 \times 10^{23}$ or $6.022 \times 10^{23}$ (4 sig figs).

• A mole is a specific number of items ($6.022 \times 10^{23}$), similar to how a dozen refers to 12 items or a gross refers to 144 items.

How Big is a Mole?

• A mole of M&Ms would fill 18 tractor trailers.

How Big is a Mole? Volume Calculation

• Assuming the effective volume of an M&M is 1 cm3 and a typical tractor trailer volume is about 3600 ft3, one mole of M&Ms would occupy a volume of about $1.4 \times 10^8$ mi3.

• One mole of M&Ms would cover the entire surface of the earth ($5.1 \times 10^{14}$ m2) to a depth of nearly 1200 m!

Considerations When Using the Mole

• Always specify the formula unit to avoid ambiguity.

• 1 mol of H atoms = $6.022 \times 10^{23}$ H atoms

• 1 mol of H2 molecules = $6.022 \times 10^{23}$ H2 molecules (twice as much hydrogen as 1 mol of H atoms).

• For non-molecular substances, a mole corresponds to one mole of the formula unit.

• The formula unit of sodium sulfate is Na2SO4, thus one mole of Na2SO4 contains 2 moles of Na+ ions and 1 mole of SO42- ions.

• One formula unit of Al2O3 contains 2 Al3+ ions and 3 O2- ions; therefore, one mole of Al2O3 contains 2 moles of Al3+ ions and 3 moles of O2- ions.

Conversions Using Avogadro’s Number

• Avogadro’s number is used to convert between number of particles and the number of moles of a substance (or vice versa).

Molar Mass

• The molar mass of a substance is the mass of one mole of that substance.

• For any substance, the molar mass in g/mol is numerically equal to the formula weight in amu.

• Molar masses and formula weights are computed identically.

• For example, Cu has an atomic weight of 63.546 amu. The molar mass of Cu is 63.546 g/mol.

• 1 mol Cu = 63.546 g Cu = $6.022 \times 10^{23}$ Cu atoms

Molar Mass as a Conversion Factor

• The molar mass of a substance serves as a conversion factor between the number of moles of the substance and the mass of that substance.

• Example: What is the mass of 5.00 mol Cu?

Molar Mass Example 2

• Problem: How many moles of Ru are there in 37.9 g Ru?

• Solution:

  • $37.9 \text{ g Ru} \times \frac{1 \text{ mol Ru}}{101.07 \text{ g Ru}} = 0.375 \text{ mol Ru}$

• Problem: How many Ru atoms are in 0.375 mol Ru?

• Solution:

  • $0.375 \text{ mol Ru} \times \frac{6.022 \times 10^{23} \text{ Ru atoms}}{1 \text{ mol Ru}} = 2.26 \times 10^{23} \text{ Ru atoms}$

Molar Mass Example 3

• How many moles CaCO3 are contained in 23.6 g CaCO3?

• $FW = 40.078 + 12.011 + 3 (15.9994) = 100.087 \text{ g/mol}$

Conversions among Moles, Mass, and Particles

• A diagram illustrates conversions between mass, moles, and the number of atoms/molecules using molar mass (M) and Avogadro's number (NA).

Complex Molar Mass Problem

• Calculate how many moles of uranium are found in 100.0 grams of carnotite, K2(UO2)2(VO4)2 · 3H2O.

Mass Spectrometry

• Atoms or molecules are converted into ions (M+) and then separated based on their mass-to-charge ratios.

Mass Spectra

• A mass spectrum is a graphical display of intensity versus m/z value.

• Example provided for Benzene.

Mass Spectra Application Example

• The explosive compound TATP (triacetone triperoxide) can be detected by its mass spectrum.

• What is the mass of the molecular-ion peak in Figure 2.23?

• Show this mass is consistent with the formula of TATP: C9H18O6.