Chemistry Honors - Unit 2 (Density, Atomic Theory & Nuclear Chemistry)

I. Density, Atomic Theory & Nuclear Chemistry

Density

• Definition: Density is defined as mass per unit volume and is represented by the symbol m or the Greek letter “rho” \rho .

• Formula: Density D = \frac{m}{V}, where:

  • D = Density

  • m = Mass

  • V = Volume

• Units:

  • English system: lb/ft3

  • Metric system:

    • Solids & liquids: g/cm3

    • Gases: g/L

    • SI: \frac{kg}{m^3}

  in})^3 \times (\frac{12 in}{1 ft})^3 \times (\frac{1 lb}{453.6 g}) = 1.20 \times 10^3 \frac{lb}{ft^3}

Specific Gravity

• Definition: Specific gravity measures the mass of an object compared to the mass of an equal volume of water.

• Since the density of water is 1.00 g/mL, specific gravity is numerically equal to density but has no units.

Example

Gold has a density of 19.3 g/mL. The specific gravity of gold is \frac{19.3 \frac{g}{mL}}{1.00 \frac{g}{mL}} = 19.3

Additional Information:

• It is expressed as a pure number and is usually used with liquids.

• At typical laboratory values (0 °C to 30 °C), the density of water is approximately 1.00 g/mL.

Finding the Density of Irregular Shapes

1. Measure the mass of the object.

2. Put water in a graduated cylinder and record initial volume V_i.

3. Carefully put the object in the graduated cylinder and record the final volume V_f.

4. Calculate the volume of the object: V = Vf - Vi .

5. Calculate density: D = \frac{m}{V} = \frac{m}{Vf - Vi} .

   00

   in}{2.54 cm}= 4.77 in

IV. Accuracy and Precision: Methods of expressing laboratory error:

• Accuracy and precision (percent) error are determined to assess how close measurements are to true values.

Key Terms

• Å = Angstrom = 10^{-10} m

Reasons for Uncertainty:

• Tolerance = Construction of the Device

• Human error = Incorrect usage of the device

• Malfunctioning equipment

• Conditions = Temperature, pressure, etc

Accuracy

• Definition: The closeness of a measurement or calculation to the true or accepted value, expressed in terms of error.

  • O = Observed, Your experimental value

  • A = Accepted, True value

Absolute Error (E_a)

E_a = |O - A|

Relative Error (E_r) (Percent % Error)

Er = \frac{|O - A|}{A} \times 100 = \frac{Ea}{A} \times 100

V. Elements

• Definition: A substance in which all of the atoms have the same number of protons in the nucleus.

• Symbols of elements - J.J. Berzelius (a Swedish chemist) is credited with creating the modern symbols.

• Atomic number: Number of protons

• Cannot be decomposed into simpler substances by chemical or physical means (Excluding nuclear processes).

Mixture

2 or more elements or compounds physically joined.

• Alloy:

  • Brass: Cu + Zn

  • Bronze: Cu + Sn

Compound

2 or more elements chemically bonded to one another.
Ex. H_2O

Periodic Table:

• Vertical columns – Groups or Families (Chemically similar)

• Rows - Periods

VI. Properties of Matter

Substances:

• Substances can be either pure elements or compounds.

• Substances are identified by enumerating their physical and chemical properties.

• All specimens of a given substance will have the same chemical and physical properties.

Examples of substances:

• elements (Al, C, S, Au)

• compounds (NaCl, H2O)

Mixtures:

Mixtures: Two or more pure substances.

• Homogeneous mixtures = uniform, constant composition = solution

• Heterogeneous mixtures = non-uniform (varying composition).

Physical Properties of Substances:

Features which distinguish one substance from another.

1. Density, used for solids.

2. Specific gravity, used for liquids.

3. Hardness, Ability to resist scratching.

4. Odor

5. Color: Cu- Blue-green; Ba- aqua blue.

6. Taste: Don’t taste acids or bases

7. Solubility in solvents

8. Physical state: s, ℓ, g (under certain conditions); M.P., F.P., B.P.

9. Properties of metals

   • Malleability (thin sheet)

   • Ductility (wire)

   • Conduction of heat (electricity)

10. Accidental physical properties: Not used to identify a substance.

    • Examples: mass & volume

Chemical Properties

Chemical Properties: Describe the ability of a substance to form other substances under given conditions.

• Chemical change: A change from one substance into another.

• Physical Change: The composition of a substances is not changed, and the substance retains its own identity.

• Chemical Change: The substance loses its identity, and the new substance formed has new chemical and physical properties.

rrow 2 MgO

Evidence of chemical changes:

• Color change

• Gas production

• Solid

• Heat/temperature change.

Solution, Colloid and Suspension (stopped here, keep editing)

Separating Mixtures by Physical Means

• Filtration: A colander is used to separate pasta from the water in which it was cooked.

• Distillation: During a distillation, a liquid is boiled to produce a vapor that is then condensed into a liquid, takes advantage of different boiling points. NaCl boils at 1415 °C

• Magnetism.

• Paper chromatography: Components of dyes such as ink may be separated by paper chromatography.

• Decanting

Physical or Chemical?

• A physical change does not alter the composition or identity of a substance.

• A chemical change alters the composition or identity of the substance(s) involved.

  • Physical Change

    • ice melting

    • sugar dissolving in water

  • Chemical Change

    • hydrogen burns in air to form water

Atomic Theory

I. Atomic Theory

• Matter is composed of tiny particles called atoms.

Matter

• compound (elements -> atoms)

• element (atoms)

Composition of an Atom

• Nucleus ( p+ (3 quarks) , n (3 quarks))

• Electrons

I. Historical Perspective:

A. Early Ideas

1. Democritus (400 B.C.)
   a) Greek philosopher
   b) Matter is composed of indivisible particles called atoms.
   c) “atomos” means indivisible.
   d) His theory was forgotten because
   1) Plato and Aristotle disagreed
   2) He had no experimental theory
   3) He used thought not experiments.

2. Alchemy
   a) 2 goals:
   1) Elixir of life.
   2) Transmutation: Lead into gold.
   b) Importance of alchemists is that they shifted from thought to observation and experimentation!

3. 1500’s – 1700’s: With the development of true scientific methods, scientists discovered many important things about matter.
   a) Such as: electricity, magnetism, chemical reactions; this information would help establish important scientific principles that would be used to develop the Atomic Theory.

4. Dalton’s Atomic Theory (1808)
   a) John Dalton re-proposes the atomic theory and supports his ideas with chemical behavior. (Look on study guide for postulates).
   b) 3 Important Laws Dalton based his Atomic Theory
   1) Law of Conservation of Mass: (Antoine Lavoisier 1789). Mass is neither created nor destroyed.
   2) Law of Definite Proportions (Joseph Proust 1799, Proust’s law): Compound always contains the same elements in the same proportion by mass.
   Example: H2O
   2 H2 + O2 \rightarrow 2 H_2O
   H = 1 g, O = 16 g. Ratio = 2 g : 16 g
   8 g : 64 g
   3) Law of Multiple Proportions (John Dalton): When two elements can form multiple compounds, the ratio of masses will remain constant for each compound.
   Example: CO : CO2
   C = 12 g, O = 16 g
   CO: 12 g : 16 g
   CO2: 12 g : 32 g

Postulates:
a) Elements are composed of small, indivisible particles called atoms.
b) Each element is made up of atoms that are identical to each other.
c) Chemical reactions are simple rearrangements of atoms in small, whole number ratios.
Problems with the Atomic Theory?
a) Atoms are divisible
b) Atoms of an element are not necessarily identical because of isotopes
(5) Thomson Model of the Atom Theory
a) J.J. Thomson discovered that atoms are made of particles, in other words, they are made of smaller things.
b) J.J. did experiments with Cathode Ray Tube (CRT) and he found that:
1) Cathode rays are e- particles that he called electrons.
2) This showed that atoms are not indivisible!
c) He determined the constant charge to mass ratio of the electron.
d) He knew atoms were neutral so he proposed a model of the atom called the Plum Pudding Model. The plums were e-.
e) Robert A. Millikan determined the charge of the e- with his oil drop experiment.
e^- \text{ charge } = -1.60 \times 10^{-19} C
e^- \text{ mass } = 9.10 \times 10^{-28} g

Measured mass of e- (1923 Nobel Prize in Physics)

(6) Rutherford Model of the Atom Theory
a) The discovery of radioactivity led to further advances in the atomic theory.
b) New Zealand physicist Ernest B. Rutherford and his associates (Geiger & Marsden) used radioactive alpha a particles to probe the atom
c) He discovered the + charged nucleus with the alpha scattering experiment.

e) His calculations regarding the deflected particles indicated that atoms have a small, + charged, “massive” nucleus. f) If the atom were a mile in diameter, the nucleus would be the size of a baseball…yet the nucleus contains virtually all of the atom’s mass. In other words, most of the atom is made up of empty space.

g) He proposed the still popular (yet wrong) planetary model:
1) electrons orbit the positive nucleus
2) like the planets around the sun.
h) Problems with a planetary atomic model;
It could not explain…
1) Electron collapse: classical physics theory says that a charged particle (like an electron) moving in a circular orbit would lose energy and slow down, eventually collapsing out of its orbit and crash into the nucleus.
2) Periodic chemical behavior
3) Atomic line spectra..
(7) The Bohr model of the atom: proposed by Danish physicist Neils Bohr would first explain (sort of) some of these problems, Only the hydrogen spectrum

Atomic Structure

A. 3 particles

1. Proton (p)
   a. located in the nucleus
   b. unit charge = "+1"
   c. mass = 1.67265 x 10^{-24} g (Proton)
   d. relative mass = 1(relative to the other particles)
   e. charge = + 1.6022 x 10^{-19} C (Coulomb)
   f. the mass is 1,836 x the mass of a electron.
   g. discovered by Rutherford
   h. made of 3 quarks

2. Electron (e)
   a. located outside the nucleus in energy levels (shells).
   b. unit charge = -1
   c. mass = 9.11 x 10^{-28} g (9.10953 x 10^{-28} g)
   d. relative mass = 0 tiny compared to n & p
   e. charge = -1.6022 x 10^{-19} C (Coulomb)
   f. the mass is 1/1,836 the mass of a proton.
   g. discovered by Thomson.

3. Neutron (n)
   a. located in the nucleus.
   b. unit charge = 0 neutral
   c. mass = 1.67495 x 10^{-24} g slightly more massive than a proton.
   d. relative mass = 1
   e. discovered by Chadwick in 1932 (Why so late? No charge – Harder to detect)
   f. made of 3 quarks

B. Nucleus

1. The central core of the atom.

2. Contains the neutrons and protons: nucleon = a particle in the nucleus (n or p)

3. Nuclide = the nucleus of an atom.

4. Contains almost all the mass of the atom.

5. Has a small volume compared to the total atomic volume. (Ping pong ball in the Astro dome).

6. Density of nucleus = 10^{13-14} g/cm3!

7. Radionuclide: an unstable nucleus. Why some nuclei stable and others are unstable? (radioactive)

8. Nuclear stability is due to…
   a. Nuclear binding energy (strong force) - Holds protons and neutrons together.
   b. n/p ratio = stable atoms have a favorable n/p ratio. Examples:
   Larger atoms n>p
   Smaller atoms n=p
   Examples Fe26 56 He2 4

C. Atomic Size

1. Atomic diameters = 1 – 5 Å or 100 – 500 pm1 Angstrom =10^{-10} m, 1 picometer =10^{-12} m

2. Diameter of atomic nuclei = 10^{-4} Å = 10^{-14} m

3. How many carbon atoms are there in a pencil line 1.00 inch long? (radius = 0.77 Å) (Assume 1 atom wide).

Solution

\frac{1.00 in}{line} \times \frac{39.37 in}{m} \times \frac{1m}{10^{-10} Å} \times \frac{1 atom}{1.54 Å} = \frac{1.65 \times 10^8 atoms}{line}

Mass Relationships

A. Atomic Number (Z)

1. Equal to the number of protons
   a. Equals the number of electrons in a neutral atom.

   i) Example
   o) Oxygen
   oo) Oxide ion (ions: charged particles)
   b. Each type of element has a specific number of protons…this determines the element’s identity.

B. Mass Number (A)

1. Equals the number of protons + the number of neutrons.
   a. It is the number of nucleons.

2. # of neutrons = mass # − atomic # (n = A − Z)

3. Correct notation

Isotopes:

Atoms with the same atomic number but different mass numbers.
Same number of protons Different number of neutrons Isotopes are named by their mass #
Ex.

• Carbon-14

• Uranium-238

Example:

• Protium 1p+, 0n, 1e-

• Deuterium 1p+, 1n, 1e-

• Tritium 1p+, 2n, 1e-
  n=A-Z
  Ions: Charged atoms (or groups of atoms) that have lost or gained electrons.
  Example : O 8 18 2- (gained 2e-), Al 13 27 3+ (lost 3e-)

Nuclear Chemistry

Chemistry of the nucleus (p+ n). A. Radioactivity: The spontaneous emission of particles or EMR (Electromagnetic radiation) from the nucleus.1. Henri Becquerel: Discovered radioactivity (1896) using photographic plates and uranium ore.

2. Types of Radioactivity

a. Alpha (α): Nucleus of a helium atom
b. Beta (β): High-speed electron emission from the nucleus
c. Gamma ray (γ): Photon of high energy light(3) Penetrating power of radiation
a. Alpha can go through paper
b. Beta particles can go through 3 cm Al
c. Gamma rays can go through 3 mm Pbγ > β > α
B. Nuclear equations: Must obey Law of Conservation of mass (top line) and Law of Conservation of charge (bottom line).

Alpha emission {Z}^{A}X \rightarrow \,{Z-2}^{A-4}Y + \,{2}^{4}He Ex: {92}^{238}U \rightarrow \,{90}^{234}Th + \,{2}^{4}He

Beta Emission ( Too many Neutrons) {Z}^{A}X \rightarrow \,{Z+1}^{A}Y + \,_{-1}^{0}e

Too many neutrons

{6}^{14}C \rightarrow \,{7}^{14}N + \,_{-1}^{0}e

Positron Emission (Too many Protons) {Z}^{A}X \rightarrow \,{Z-1}^{A}Y + \,{+1}^{0}e Example: {19}^{40}K \rightarrow \,{18}^{40}Ar + \,{+1}^{0}e

Gamma Emission {29}^{64}Cu*\rightarrow \,{29}^{64}Cu + \,_{0}^{0}𝛾

Electron Capture {Z}^{A}X + \,{-1}^{0}e\rightarrow \,_{Z-1}^{A}Y

Decay Series

A radioactive decay often results in a daughter nucleus that is also radioactive. A radioactive decay series refers to successive decays which starts with one parent isotope and proceeds through a number of daughter isotopes. The series ends when a stable, non-radioactive isotope is produced.

Uranium Decay Series
Radon-222 - α, α, β, β, α decay

_{86}^{222}Rn\rightarrow … \,… \rightarrow _{82}^{210}Pb \rightarrow _{83}^{214}Bi \rightarrow _{84}^{214}Po \rightarrow _{82}^{214}Pb
Half-lives:1. 3.8d2. 3min.3. 27min.4. 20min.5. 180 μs

Nuclear Stability
Which isotope is the most stable, according to the figure?
Iron-56(Fe 56-26) Rule 2: Nuclei of low atomic numbers with a 1:1 ratio of neutrons to protons are very stable.
(See Figure 1)
Carbon-12(C 6 12)
Helium-4(He 2 4)

Radioactive Stability
Refer to Figure 1 Isotopes decay with α.
Isotopes decay with β+. Isotopes decay with β.
Most stable nuclei tend to contain an even number of both protons and neutrons. Example: Iron-56(Fe 26 56 26p+, 30n), Oxygen-16(O 8 16 8p+, 8n)

Mass Defect
Mass of constituents - Mass of Nucleus. The "missing" mass has converted into energy!
Mass conversion equation:
E = mc^2
Nuclear reactions, fission and fusion, involve small changes in mass that result in enormous releases of energy. The relationship between mass and energy is expressed in Einstein’s equation:
Masses of subatomic particles are:
e- 0.0005485