Chemistry Review Guide: Atomic Structure, Atomic Models, Matter & Measurement

Atomic Models and Historical Development

• Major Scientists and Historical Atomic Models:

  • Democritus: Proposed that matter was composed of tiny, indivisible particles termed "Atomos".
  • J.J. Thomson: Discovered the electron through experiments utilizing cathode rays. Proposed the "Plum Pudding Model".
  • Ernest Rutherford: Discovered the dense atomic nucleus via the gold foil experiment. Proposed the "Nuclear Model".
  • Niels Bohr: Proposed that electrons reside and orbit within specific energy levels. Proposed the "Planetary/Bohr Model".

• Comparison Between Thomson's Plum Pudding Model and Rutherford's Nuclear Model:

  • Thomson's Plum Pudding Model:
  • Confirms electrons are present within the atom.
  • Posits that positive charge is continuously spread throughout the entire structure of the atom.
  • Contains no nucleus.
  • Electrons are embedded directly within the diffuse positive material like raisins in a pudding.
  • Rutherford's Nuclear Model:
  • Posits that the atom contains a small, extremely dense center known as the nucleus.
  • The positive charge of the atom is concentrated strictly inside the nucleus.
  • Establishes that the vast majority of the volume of an atom consists of empty space.
  • Electrons are positioned outside and around the central nucleus.
  • Key Comparative Insight: Both Thomson's and Rutherford's models acknowledge the presence of electrons, but Rutherford's model introduced the fundamental discovery of the atomic nucleus.

Order of Subatomic Particle Discovery and Atomic Structure

• Historical Order of Discovery:

  • Electron $\rightarrow$ Proton $\rightarrow$ Neutron

• Subatomic Particle Properties:

  • Proton:
  • Charge: Positive ($+$)
  • Location: Located inside the nucleus
  • Fundamental Significance: Determines the chemical identity of the element
  • Neutron:
  • Charge: Neutral ($0$)
  • Location: Located inside the nucleus
  • Fundamental Significance: Adds directly to the mass of the atom without affecting charge
  • Electron:
  • Charge: Negative ($-$)
  • Location: Located outside the nucleus
  • Fundamental Significance: Responsible for overall atomic charge and chemical bonding behavior

• Anatomy of the Atom:

  • The Nucleus: Located at the center of the atom, containing protons and neutrons bound together.
  • Electron Cloud / Exterior: The region surrounding the nucleus where electrons exist.

Atomic Number, Mass Number, and Isotopes

• Atomic Number:

  • Definition: Equal to the exact number of protons in an atom's nucleus.
  • Role: Identifies the element uniquely.
  • Neutral Atom Rule: In any neutral atom, the number of protons equals the number of electrons ($\text{Protons} = \text{Electrons}$).

• Mass Number:

  • Formula: $\text{Mass Number} = \text{Protons} + \text{Neutrons}$
  • Neutron Calculation: $\text{Neutrons} = \text{Mass Number} - \text{Protons}$

• Worked Example — Potassium-40:

  • Given: Potassium-40 ($K-40$) with Atomic Number = $19$ and Mass Number = $40$.
  • Number of Protons: $19$
  • Number of Electrons: $19$
  • Number of Neutrons: $40 - 19 = 21$

• Isotopes:

  • Definition: Atoms of the exact same element that contain the same number of protons but different numbers of neutrons.
  • Key Rules:
  • Same number of protons = same element.
  • Different number of neutrons = different isotope of that element.
  • Electrons play no role in determining whether atoms are isotopes.
  • Comparative Example:
  • Atom A: $15$ protons, $12$ neutrons.
  • Atom B: $15$ protons, $16$ neutrons.
  • Conclusion: Atom A and Atom B are isotopes of the same element because they share identical proton counts ($15$) but differ in neutron counts ($12$ vs. $16$).

• Reading Isotope Notation:

  • Example — Uranium-235 ($U-235$):
  • Mass Number = $235$
  • Atomic Number of Uranium = $92$
  • Number of Protons = $92$
  • Number of Electrons (in a neutral atom) = $92$
  • Number of Neutrons = $235 - 92 = 143$
  • Practice Problem — Atom with Mass Number = $31$ and Atomic Number = $15$:
  • Number of Protons = $15$
  • Number of Electrons = $15$
  • Number of Neutrons = $31 - 15 = 16$

Periodic Table Properties and Isotopic Mass Distinctions

• Standard Periodic Table Information:

  • Element Name (e.g., Potassium)
  • Element Symbol (e.g., $K$)
  • Atomic Number (e.g., $19$)
  • Atomic Mass (e.g., $\approx 39.098\,amu$)

• Example — Potassium ($K$):

  • Atomic Number = $19$
  • Protons = $19$
  • Electrons = $19$
  • Atomic Mass = $39.098\,amu$
  • Most Common Mass Number = $39$
  • Neutrons in Potassium-39 = $39 - 19 = 20$

• Distinction Between Mass Number and Atomic Mass:

  • Mass Number: A whole-number integer representing the sum of protons and neutrons in a single, specific individual atom or isotope (e.g., Carbon-12 has a mass number of $12$).
  • Atomic Mass: A weighted average mass of all naturally occurring isotopes of an element, typically expressed as a decimal value (e.g., Carbon has an atomic mass of $\approx 12.01\,amu$).

Calculating Average Atomic Mass

• General Formula:   $\text{Average Atomic Mass} = \sum (\text{Isotope Mass} \times \text{Decimal Abundance})$

• Step-by-Step Procedure:

  1. Convert all percentage abundances into decimal form by dividing by $100$ (e.g., $75\% \rightarrow 0.75$, $25\% \rightarrow 0.25$).
  2. Multiply each individual isotope's mass by its corresponding decimal abundance.
  3. Sum the resulting products together to obtain the final weighted average atomic mass.

• Worked Calculation Example:

  • Problem: An element consists of two naturally occurring isotopes:
  • Isotope A: Mass = $10.0\,amu$, Abundance = $20\%$
  • Isotope B: Mass = $11.0\,amu$, Abundance = $80\%$
  • Step 1 (% Abundance Conversion):
  • Isotope A decimal abundance = $20\% / 100 = 0.20$
  • Isotope B decimal abundance = $80\% / 100 = 0.80$
  • Step 2 (Mass Contribution per Isotope):
  • Isotope A contribution = $10.0\,amu \times 0.20 = 2.0\,amu$
  • Isotope B contribution = $11.0\,amu \times 0.80 = 8.8\,amu$
  • Step 3 (Final Atomic Mass Calculation):
  • $\text{Average Atomic Mass} = 2.0\,amu + 8.8\,amu = 10.8\,amu$

Bohr Model and Atomic Spectra

• Key Principles of Bohr's Atomic Model:

  • Electrons occupy specific, quantized energy levels surrounding the nucleus.
  • Electrons can transition or move between these distinct energy levels.
  • To move from a lower energy level to a higher energy level (excited state), an electron must absorb energy.
  • When an electron falls back from a higher energy level (excited state) to a lower energy state, it emits energy in the form of light.

• Spectroscopic Evidence:

  • Key Rule: Excited State $\rightarrow$ Lower Energy State = Light Emission.
  • The specific colors and spectral lines of light emitted by atoms provide direct empirical evidence for the existence of quantized electron energy levels.

Nuclear Forces, Stability, and Radioactivity

• Forces Within the Nucleus:

  • Protons carry positive charges and exert electrostatic repulsion against one another.
  • The Strong Nuclear Force acts over very short distances to overcome electrostatic repulsion and bind protons and neutrons together in the nucleus.

• Nuclear Instability and Radioactivity:

  • If electrical repulsion among protons exceeds the holding power of the strong nuclear force, the nucleus becomes unstable.
  • An unstable nucleus undergoes radioactive decay, emitting energy and particles to achieve stability.

• Nuclear Fusion:

  • Definition: A nuclear reaction in which smaller, lighter atomic nuclei combine to form a larger, heavier nucleus.
  • Natural Occurrence: Occurs naturally in stellar cores, such as inside the Sun.
  • Element Formation: Responsible for synthesizing elements heavier than hydrogen.
  • Core Rule: Fusion = combining nuclei; Fission = splitting nuclei.

Classification of Matter and Separation Techniques

• Classification of Matter:

  • Element: A pure substance composed entirely of one single type of atom.
  • Examples: Oxygen, Gold, Carbon.
  • Compound: A pure substance consisting of two or more different elements chemically bonded in fixed proportions.
  • Example: Water ($H_2O$), composed of hydrogen and oxygen chemically combined.
  • Mixture: A physical combination of two or more substances that retain their individual chemical identities.
  • Homogeneous Mixture: A mixture with uniform composition throughout.
    • Example: Salt water.
  • Heterogeneous Mixture: A mixture with non-uniform composition throughout, containing distinct phases or visible parts.
    • Example: Sand mixed in water.

• Physical Separation Techniques:

  • Filtration: A technique used to separate an insoluble solid from a liquid phase (e.g., separating sand from water).
  • Distillation: A technique used to separate liquid components of a mixture based on differences in their respective boiling points.

Physical and Chemical Properties

• Physical Properties:

  • Definition: Characteristics that can be observed or measured without altering the chemical composition or identity of the substance.
  • Examples: Color, odor, density, boiling point, melting point.

• Chemical Properties:

  • Definition: Characteristics that describe a substance's capacity to undergo chemical reactions and transform into entirely new substances.
  • Examples: Reactivity, flammability, tendency to rust (oxidation), combustion.

• Decision Test:

  • Ask: Does observing or measuring this property change the substance into a new chemical substance?
  • No $\rightarrow$ Physical property.
  • Yes (or describes potential reactivity) $\rightarrow$ Chemical property.

Density Calculations and Water Displacement

• Density Mathematical Formulas:

  • Main Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$ ($D = \frac{M}{V}$)
  • Rearranged for Mass: $\text{Mass} = \text{Density} \times \text{Volume}$ ($M = D \times V$)
  • Rearranged for Volume: $\text{Volume} = \frac{\text{Mass}}{\text{Density}}$ ($V = \frac{M}{D}$)
  • Common Units: $g/mL$ or $g/cm^3$.

• Density Determination via Water Displacement:

  • Used to measure the volume of irregular solid objects.
  • Step 1: Record initial volume of water in a graduated cylinder.
  • Step 2: Submerge object fully and record final volume of water.
  • Step 3: Calculate object volume:     $\text{Volume of object} = \text{Final water volume} - \text{Initial water volume}$
  • Step 4: Calculate density:     $\text{Density} = \frac{\text{Mass}}{\text{Final water volume} - \text{Initial water volume}}$
  • Substance Identification: Unknown samples are identified by comparing calculated density values against known reference table standards.

Scientific Variables in Measurement

• Definitions:

  • Independent Variable: The factor deliberately manipulated or changed by the experimenter ("I change it").
  • Dependent Variable: The factor that responds to changes in the independent variable and is measured ("It depends on what was changed").

• Experimental Dataset Example:

  • Sunlight Exposure vs. Plant Growth Height:
  • $2\,\text{hours}$ of sunlight $\rightarrow 5\,\text{cm}$ height
  • $4\,\text{hours}$ of sunlight $\rightarrow 9\,\text{cm}$ height
  • $6\,\text{hours}$ of sunlight $\rightarrow 14\,\text{cm}$ height
  • $8\,\text{hours}$ of sunlight $\rightarrow 18\,\text{cm}$ height
  • Analysis:
  • Independent Variable: Amount of sunlight exposure (hours).
  • Dependent Variable: Plant growth height ($\text{cm}$).

Dimensional Analysis and Unit Conversions

• Methodology:

  • Uses conversion factors arranged as ratios to cancel unwanted units and convert to desired units.
  • General Formula:     $\text{Starting Value} \times \text{Conversion Factor} = \text{Converted Value}$
  • Cancellation Rule: The unit to be eliminated must be placed in the denominator of the conversion factor.

• Worked Conversion Example:

  • Problem: Convert $2.5\,\text{hours}$ into seconds.
  • Conversion Factor: $1\,\text{hour} = 3600\,\text{seconds}$.
  • Dimensional Setup:     $2.5\,\text{hr} \times \frac{3600\,\text{sec}}{1\,\text{hr}} = 9000\,\text{seconds}$
  • Explanation: Hours cancel out in numerator and denominator, leaving seconds as the final unit ($2.5 \times 3600 = 9000$).

Rules for Significant Figures

• Rule 1 (Nonzero Digits):

  • All nonzero numbers are always significant.
  • Example: $123$ contains $3$ significant figures.

• Rule 2 (Captured Zeros):

  • Zeros located between two nonzero digits are always significant.
  • Example: $100098.9$ contains $7$ significant figures.

• Rule 3 (Leading Zeros):

  • Leading zeros positioned before the first nonzero digit are NEVER significant; they merely act as place holders.
  • Example: $0.000098$ contains $2$ significant figures.

• Rule 4 (Trailing Zeros):

  • Trailing zeros at the end of a number are significant ONLY if a decimal point is explicitly present.
  • Example: $231000$ is ambiguous without a decimal point or scientific notation, whereas $231000.$ or $2.31000 \times 10^5$ explicitly confirms the trailing zeros.

Core Review Equations and Summary Formulas

• Atomic Structure Equations:

  • $\text{Mass Number} = \text{Protons} + \text{Neutrons}$
  • $\text{Neutrons} = \text{Mass Number} - \text{Protons}$
  • For Neutral Atoms: $\text{Protons} = \text{Electrons}$

• Density Formulas:

  • $D = \frac{M}{V}$
  • $M = D \times V$
  • $V = \frac{M}{D}$

• Average Atomic Mass Formula:

  • $\text{Average Atomic Mass} = \sum (\text{Isotope Mass} \times \text{Decimal Abundance})$

• Dimensional Analysis Formula:

  • $\text{Starting Value} \times \text{Conversion Factor} = \text{Converted Value}$

Master Self-Assessment and Check Questions

• Question 1: Who discovered the electron?
  • Answer: J.J. Thomson (using cathode ray tubes).
• Question 2: Who discovered the nucleus?
  • Answer: Ernest Rutherford (via the gold foil experiment).
• Question 3: What is the difference between Thomson's and Rutherford's models?
  • Answer: Thomson's Plum Pudding Model depicts positive charge spread evenly throughout the atom with embedded electrons and no nucleus. Rutherford's Nuclear Model places positive charge in a small, dense nucleus at the center, with electrons orbiting in mostly empty space.
• Question 4: What is the correct order of subatomic particle discovery?
  • Answer: Electron $\rightarrow$ Proton $\rightarrow$ Neutron.
• Question 5: What determines the identity of an element?
  • Answer: The number of protons (atomic number).
• Question 6: Where are protons and neutrons located?
  • Answer: Inside the nucleus at the center of the atom.
• Question 7: What is the charge of an electron?
  • Answer: Negative ($-$).
• Question 8: What is the difference between atomic number and mass number?
  • Answer: Atomic number is the number of protons in an atom. Mass number is the sum of protons plus neutrons in a specific atom.
• Question 9: How do you calculate the number of neutrons?
  • Answer: Subtract atomic number (protons) from mass number: $\text{Neutrons} = \text{Mass Number} - \text{Protons}$.
• Question 10: What makes two atoms isotopes?
  • Answer: Having the exact same number of protons but a different number of neutrons.
• Question 11: How many neutrons are in potassium-40?
  • Answer: $21$ neutrons ($40 - 19 = 21$).
• Question 12: How many protons are in phosphorus-31?
  • Answer: $15$ protons (atomic number of phosphorus is $15$).
• Question 13: What is the difference between atomic mass and mass number?
  • Answer: Mass number is a whole-number sum of protons and neutrons for a single isotope. Atomic mass is the weighted average mass of all naturally occurring isotopes.
• Question 14: What did Bohr add to our understanding of electrons?
  • Answer: He proposed that electrons occupy specific, quantized energy levels and can transition between them.
• Question 15: What happens when an excited electron falls to a lower energy level?
  • Answer: It emits energy in the form of light.
• Question 16: What makes a nucleus radioactive?
  • Answer: When the electrical repulsive force between protons exceeds the holding capacity of the strong nuclear force, rendering the nucleus unstable.
• Question 17: Where does nuclear fusion naturally occur?
  • Answer: In stellar cores, such as inside the Sun.
• Question 18: What is the difference between an element and a compound?
  • Answer: An element consists of only one type of atom, whereas a compound consists of two or more different elements chemically combined.
• Question 19: What is the difference between a homogeneous and heterogeneous mixture?
  • Answer: A homogeneous mixture is uniform throughout, while a heterogeneous mixture has a non-uniform composition with visually distinguishable parts/phases.
• Question 20: What is the difference between physical and chemical properties?
  • Answer: Physical properties can be measured/observed without forming a new substance, whereas chemical properties describe a substance's potential to react and transform into a new substance.
• Question 21: What is filtration used for?
  • Answer: Separating an insoluble solid from a liquid.
• Question 22: What is distillation based on?
  • Answer: Differences in the boiling points of liquid components in a mixture.
• Question 23: How do you calculate density?
  • Answer: Divide mass by volume: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$.
• Question 24: How do you determine volume using water displacement?
  • Answer: Subtract the initial water volume from the final water volume after submerging the object: $\text{Volume} = \text{Final Volume} - \text{Initial Volume}$.
• Question 25: What is an independent variable?
  • Answer: The variable that is deliberately manipulated or changed by the experimenter.
• Question 26: What is a dependent variable?
  • Answer: The variable that is measured and responds to changes in the independent variable.
• Question 27: How many seconds are in 2.5 hours?
  • Answer: $9000\,\text{seconds}$ ($2.5\,\text{hr} \times 3600\,\text{sec/hr} = 9000\,\text{sec}$).
• Question 28: How do you determine significant figures?
  • Answer: Count all nonzero numbers, captured zeros, and trailing zeros (only if a decimal point is explicitly present). Exclude leading zeros.
• Question 29: How do you calculate average atomic mass?
  • Answer: Multiply the mass of each isotope by its decimal abundance, then sum all products together.
• Question 30: Can you show all of your work for an atomic mass calculation?
  • Answer: Yes: Convert % abundance to decimal ($\% / 100$), multiply each isotope's mass by its decimal abundance, and sum the partial masses to obtain the total average atomic mass.