General Chemistry Chapter 1-2 Lecture Notes

Phase Changes, Chemical Reactions, and Thermochemistry

• Phase Transitions and Heat Flow:

  • Sublimation: The direct physical transition of a substance from the solid phase to the gas phase without passing through the liquid phase.

  • Example: A chunk of solid carbon dioxide ($CO_2$) sublimating directly into a gas, producing a visible white mist.

  • Exothermic Processes: Phase changes and reactions in which thermal energy (heat) is released or given off to the surroundings.

  • Condensation: Phase transition from gas to liquid.

  • Freezing: Phase transition from liquid to solid.

  • Deposition: The direct physical transition from gas to solid without entering the liquid phase.

    • Example: Frost forming on an automobile windshield, where water vapor in the surrounding air deposits directly into solid ice.

• Chemical Changes vs. Physical Changes:

  • Chemical Change Definition: A process in which starting materials are transformed into entirely new chemical substances with distinct physical and chemical properties and altered atomic bonding arrangements.

  • Propane Combustion Reaction:

  • Propane ($C_3H_8$) Structure: Contains three carbon atoms bonded sequentially in a continuous chain. Carbon forms four covalent bonds. The two terminal carbon atoms are each single-bonded to three hydrogen atoms, while the central carbon atom is single-bonded to two hydrogen atoms. Propane contains exclusively carbon-carbon ($C-C$) single bonds and carbon-hydrogen ($C-H$) single bonds.

  • Diatomic Oxygen ($O_2$) Structure: Composed of two oxygen atoms connected by a double covalent bond ($O=O$), representing four shared electrons (two pairs) alongside lone pairs of non-bonding electrons.

  • Reaction Process: Combustion of propane converts the hydrocarbon into carbon dioxide ($CO_2$) gas, water ($H_2O$) gas, and heat.

  • Primary Purpose of Combustion: To produce thermal energy (heat) to perform useful mechanical or physical work, such as powering internal combustion car engines, operating grills for tailgate parties, or burning coal.

  • Carbon Dioxide ($CO_2$) Structure: Linear geometry with a central carbon atom double-bonded to two surrounding oxygen atoms ($O=C=O$), with non-bonding lone pair electrons on the oxygen atoms.

  • Water ($H_2O$) Structure: Three-dimensional bent molecular geometry with an oxygen atom single-bonded to two hydrogen atoms and carrying non-bonding lone pairs.

• Step-by-Step Balancing of the Propane Combustion Reaction:

  • Unbalanced Equation:     $C_3H_8(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g) + \text{heat}$

  • Carbon Balance: Propane contains $3$ carbon atoms. Place a coefficient of $3$ in front of $CO_2$ to give $3$ carbon atoms on the product side:     $C_3H_8(g) + O_2(g) \rightarrow 3CO_2(g) + H_2O(g) + \text{heat}$

  • Hydrogen Balance: Propane contains $8$ hydrogen atoms. Water contains $2$ hydrogen atoms per molecule. Place a coefficient of $4$ in front of $H_2O$ ($4 \times 2 = 8$) to balance hydrogen:     $C_3H_8(g) + O_2(g) \rightarrow 3CO_2(g) + 4H_2O(g) + \text{heat}$

  • Diatomics Rule: Diatomic elements (elements that exist naturally in their most stable form as two identical atoms combined) must always be saved for last during equation balancing.

  • Oxygen Balance: Calculate total oxygen atoms on the product side:     $(3 \times 2) + (4 \times 1) = 6 + 4 = 10 \text{ oxygen atoms}$     Since diatomic oxygen ($O_2$) supplies $2$ oxygen atoms per molecule, set the coefficient in front of $O_2$ to $5$ ($5 \times 2 = 10$).

  • Balanced Chemical Equation:     $C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(g) + \text{heat}$

• Stoichiometric Interpretations of the Balanced Equation:

  • Molar Stoichiometry: $1 \text{ mole}$ of $C_3H_8$ gas reacts with $5 \text{ moles}$ of $O_2$ gas to produce $3 \text{ moles}$ of $CO_2$ gas, $4 \text{ moles}$ of $H_2O$ gas, and a specific quantity of thermal energy.

  • Molecular Stoichiometry: $1 \text{ molecule}$ of $C_3H_8$ reacts with $5 \text{ molecules}$ of $O_2$ to yield $3 \text{ molecules}$ of $CO_2$ and $4 \text{ molecules}$ of $H_2O$ plus heat.

Aqueous Dissolution and Physical vs. Chemical Changes

• Chemical Nomenclature and Ionization:

  • Compound Formula: $K_3PO_4$

  • Symbol $K$ represents Potassium.

  • Polyatomic ion $PO_4^{3-}$ is Phosphate (carrying a $-3$ overall charge).

  • Contrast with $PO_3^{3-}$, which is Phosphite. Suffixes like -ite and -ate are critical in systematic chemical nomenclature.

  • Compound Name: Potassium phosphate.

• Dissolution in Water:

  • Dissolution Reaction:     $K_3PO_4(s) \rightarrow 3K^+(aq) + PO_4^{3-}(aq)$

  • The subscript $3$ on potassium in the solid compound becomes a stoichiometric coefficient of $3$ for the aqueous potassium ion ($3K^+$).

  • The notation $(aq)$ stands for aqueous, indicating that the ion is hydrated and dissolved in water.

• Classification of Dissolution as a Physical Change:

  • Dissolving an ionic compound such as potassium phosphate in water is a physical change, NOT a chemical change.

  • Reason: The process merely separates the solid ionic crystal lattice into its individual constituent aqueous ions. If the solvent water is evaporated, the original chemical compound ($K_3PO_4$) is recovered intact without any change in chemical identity.

  • Comparable Example: Dissolving table sugar in water is also a physical change, as evaporating the water restores the original sugar molecules without chemical alteration.

The Scientific Method, Gas Laws, and Proportionality

• Terminology of the Scientific Method:

  • Fact: A factual statement derived directly from direct observation or physical experience.

  • Hypothesis: A tentative statement proposed without immediate proof to explain a set of facts or their observed relationships; commonly characterized as an educated guess.

  • Theory: A comprehensive formulation of apparent relationships among observed phenomena that has been extensively verified through experimentation.

  • Relationship to Hypothesis: A theory is conceptually similar to a hypothesis, but carries substantially greater credibility and acceptance because it is backed by a large body of supporting experimental evidence.

  • Rule of Modification: If new experimental evidence contradicts an established theory, the theory must be modified or entirely discarded.

  • Unified Principle: A broad theory that explains a whole body of observations and the fundamental laws derived from them.

  • Law: A concise statement that summarizes and explains a broad range of direct observations regarding the behavior of matter. Scientific laws are suggested by experiments and suggest new experimental directions.

  • Observation: Direct empirical facts recorded regarding the physical behavior of matter.

• Mathematical Relationships in Scientific Laws (Ideal Gas Law Example):

  • Formula:     $PV = nRT$

  • $P$ = Pressure

  • $V$ = Volume

  • $n$ = Quantity of gas in moles

  • $R$ = Universal gas law constant

  • $T$ = Absolute temperature in Kelvin

  • Proportionality Rules Relative to the Equal Sign:

  • Inversely Proportional: Two mathematical variables located on the same side of the equal sign and both in the numerator are inversely proportional (behaves like a seesaw: as one variable increases, the other must decrease proportionately).

    • Example: Pressure ($P$) and Volume ($V$). If pressure is doubled, volume is reduced to half, provided mole quantity ($n$) and temperature ($T$) remain constant.

  • Directly Proportional: Two variables located on opposite sides of the equal sign are directly proportional.

    • Example: Gas quantity in moles ($n$) and Volume ($V$), or moles ($n$) and Pressure ($P$). Adding additional gas molecules into a flexible container (such as a balloon) causes the volume to expand proportionately. If volume is fixed (such as inside a rigid automobile tire), increasing gas moles causes internal pressure to rise.

  • Utility: Understanding these structural proportionality rules provides a common-sense mathematical check on calculations.

Physical Properties and Scientific Notation

• Definitions and Categories of Physical Properties:

  • Physical properties are characteristics that can be observed or measured without altering the underlying chemical composition or undergoing a chemical reaction.

  • Key Examples:

  • Density: A physical constant for pure substances at constant temperature (especially liquids).

  • Color

  • Boiling point

  • Physical state: Solid, liquid, or gas.

• Exponential / Scientific Notation Mechanics:

  • Purpose: Serves to express extremely large or extremely small numbers conveniently as powers of 10 ($a \times 10^b$).

  • Standard Scientific Format: Exactly one non-zero integer digit ($1, 2, 3, 4, 5, 6, 7, 8, \text{ or } 9$) must precede the decimal point.

  • Directional Rules for Decimal Point Movement:

  • Moving the decimal point to the right yields a negative exponent ($\text{Right} \rightarrow \text{Negative}$).

  • Moving the decimal point to the left yields a positive exponent ($\text{Left} \rightarrow \text{Positive}$).

  • Leading Zeros / Left Zeros Rule:

  • Zeros located to the left of the first non-zero integer are classified as leading or left zeros.

  • Leading zeros are never significant. Their sole purpose is to establish the position of the decimal point.

  • Example: In the number $0.00002$, there is only $1$ significant figure. Expressed in standard scientific notation, moving the decimal point $5$ places to the right yields:       $2 \times 10^{-5}$

  • Example: In the number $2000000$ (without an explicit decimal point), it is ambiguous and contains $1$ significant figure. Moving the decimal point $6$ places to the left yields:       $2 \times 10^6$

Significant Figure Rules and Calculator Mechanics

• Rules for Determining Significant Figures (Sig Figs):

  • Non-Zero Digits: All non-zero digits are unconditionally significant.

  • $233.1 \text{ m}$ contains $4$ significant figures.

  • $2.3 \text{ g}$ contains $2$ significant figures.

  • Leading / Left Zeros: Zeros preceding the first non-zero digit are never significant.

  • $0.0055$ contains $2$ significant figures.

  • $0.00002$ contains $1$ significant figure.

  • Trapped / Captive / Sandwich Zeros: Zeros located between non-zero digits are always significant.

  • $2.045$ contains $4$ significant figures.

  • $8.0506$ contains $5$ significant figures.

  • Trailing Zeros with Decimal Points: Zeros at the end of a number that contains an explicit decimal point are always significant.

  • $3.00$ contains $3$ significant figures.

  • $0.00450$ contains $3$ significant figures (the leading zeros are non-significant; the four, five, and final zero are significant).

  • Trailing Zeros without Decimal Points: Zeros at the end of a whole number without a visible decimal point are ambiguous.

  • $36000$ is treated as having $2$ significant figures (ambiguous).

  • $36000.$ (with an explicit trailing decimal point) contains $5$ significant figures.

  • $36000.00$ contains $7$ significant figures.

  • $5000 \text{ mL}$ without a decimal point contains $1$ significant figure; $5000. \text{ mL}$ with a decimal point contains $4$ significant figures.

• Calculator Mechanics and Rules for Operations:

  • Scientific Notation Input: Use dedicated exponential keys (E, EE, or 2nd + EE/E) on scientific calculators rather than manually multiplying by $10$ raised to a power.

  • Proper Physical Operation: Always hold the calculator stably and operate the keypad with two hands to avoid mechanical entry errors.

  • Multiplication and Division Sig Fig Rule: When performing multiplication or division, the count of significant figures in the final calculated result is governed entirely by the entry that possesses the fewest significant figures.

  • Mathematical Rules for Exponents:

  • When multiplying numbers in scientific notation, add the exponents together ($10^a \times 10^b = 10^{a+b}$).

  • When dividing numbers in scientific notation, subtract the exponent in the denominator from the exponent in the numerator ($\frac{10^a}{10^b} = 10^{a-b}$).

  • Standard Rounding Rules:

  • Identify the target final significant digit.

  • Inspect the adjacent digit directly to its right.

  • If the adjacent digit is less than $5$, retain the target digit without change.

  • If the adjacent digit is $5$ or greater, increment the target digit upward by $1$

Step-by-Step Mathematical Calculations and Quick Checks

• Calculator Multiplication Example:

  • Computation:     $(4.73 \times 10^5) \times (1.37 \times 10^2)$

  • Evaluation:

  • Both factors contain $3$ significant figures, requiring $3$ significant figures in the final output.

  • Multiply coefficients: $4.73 \times 1.37 = 6.4801$

  • Add exponents: $5 + 2 = 7$

  • Unrounded product: $6.4801 \times 10^7$

  • Rounding to $3$ significant figures (inspecting the digit $0$ following the $8$): $6.48 \times 10^7$

• Quick Check 1.1a:

  • Computation:     $(6.49 \times 10^7) \times (7.22 \times 10^{-3})$

  • Step-by-Step Solution:

  • Coefficient multiplication: $6.49 \times 7.22 = 46.8578$

  • Exponent addition: $7 + (-3) = 4$

  • Intermediate combination: $46.8578 \times 10^4$

  • Applying $3$ significant figures: The third digit is $8$; the following digit is $5$, requiring rounding up to $46.9 \times 10^4$

  • Convert to standard scientific notation by shifting the decimal point $1$ place to the left (adding $1$ to the exponent):       $4.69 \times 10^5$

• Quick Check 1.1b:

  • Computation:     $(3.4 \times 10^{-5}) \times (8.2 \times 10^{-11})$

  • Step-by-Step Solution:

  • Both factors contain $2$ significant figures.

  • Coefficient multiplication: $3.4 \times 8.2 = 27.88$

  • Exponent addition: $-5 + (-11) = -16$

  • Intermediate combination: $27.88 \times 10^{-16}$

  • Applying $2$ significant figures: The second digit is $7$; the following digit is $8$, requiring rounding up to $28 \times 10^{-16}$

  • Convert to standard scientific notation by shifting the decimal point $1$ place to the left (adding $+1$ to the exponent $-16$):       $2.8 \times 10^{-15}$

• Division Practice Example 1:

  • Computation:     $\frac{6.02 \times 10^{23}}{3.10 \times 10^5}$

  • Step-by-Step Solution:

  • Both entries contain $3$ significant figures.

  • Coefficient division: $\frac{6.02}{3.10} = 1.941935...$

  • Exponent subtraction: $23 - 5 = 18$

  • Intermediate value: $1.941935 \times 10^{18}$

  • Rounding to $3$ significant figures (the digit after $4$ is $1$): $1.94 \times 10^{18}$

• Division Practice Example 2:

  • Computation:     $\frac{3.14}{2.30 \times 10^{-5}}$

  • Step-by-Step Solution:

  • Note that $3.14$ is equivalent to $3.14 \times 10^0$

  • Both entries contain $3$ significant figures.

  • Coefficient division: $\frac{3.14}{2.30} = 1.365217...$

  • Exponent subtraction: $0 - (-5) = 5$

  • Intermediate value: $1.365217 \times 10^5$

  • Rounding to $3$ significant figures: The third digit is $6$; the following digit is $5$, requiring rounding up to $7$

  • Final Result: $1.37 \times 10^5$

Units of Measurement and the Metric System

• Fundamental Base Units of the Metric / SI System:

  • Length: Meter ($\text{m}$)

  • Volume: Liter ($\text{L}$) — Volume is defined dimensionally as $\text{length} \times \text{width} \times \text{height}$

  • Mass: Gram ($\text{g}$) — Note: The base metric unit for mass is the gram, not the kilogram.

  • Time: Second ($\text{s}$ or $\text{sec}$)

  • Temperature: Kelvin ($\text{K}$) — The absolute temperature scale. Never use a degree symbol ($^\bullet$) with Kelvin.

  • Amount of Substance: Mole ($\text{mol}$)

• Metric Prefixes and Equivalent Statements (Mandatory Memorization):

  • Tera ($\text{T}$): $1 \times 10^{12}$ ($1 \text{ Tg} = 1 \times 10^{12} \text{ g}$ or $1 \text{ g} = 1 \times 10^{-12} \text{ Tg}$)

  • Giga ($\text{G}$): $1 \times 10^9$ ($1 \text{ Gg} = 1 \times 10^9 \text{ g}$ or $1 \text{ g} = 1 \times 10^{-9} \text{ Gg}$)

  • Mega ($\text{M}$): $1 \times 10^6$ ($1 \text{ Mg} = 1 \times 10^6 \text{ g}$ or $1 \text{ g} = 1 \times 10^{-6} \text{ Mg}$)

  • Kilo ($\text{k}$): $1 \times 10^3$ ($1 \text{ kg} = 1 \times 10^3 \text{ g}$ or $1 \text{ g} = 1 \times 10^{-3} \text{ kg}$)

  • Deci ($\text{d}$): $1 \times 10^{-1}$ ($1 \text{ dg} = 1 \times 10^{-1} \text{ g}$ or $1 \text{ g} = 10 \text{ dg}$)

  • Centi ($\text{c}$): $1 \times 10^{-2}$ ($1 \text{ cg} = 1 \times 10^{-2} \text{ g}$ or $1 \text{ g} = 100 \text{ cg}$)

  • Milli ($\text{m}$): $1 \times 10^{-3}$ ($1 \text{ mg} = 1 \times 10^{-3} \text{ g}$ or $1 \text{ g} = 1000 \text{ mg}$)

  • Micro ($\text{u}$ or $\text{u}\text{g}$): $1 \times 10^{-6}$ ($1 \text{ ug} = 1 \times 10^{-6} \text{ g}$ or $1 \text{ g} = 1 \times 10^6 \text{ ug}$)

  • Nano ($\text{n}$): $1 \times 10^{-9}$ ($1 \text{ ng} = 1 \times 10^{-9} \text{ g}$ or $1 \text{ g} = 1 \times 10^9 \text{ ng}$)

  • Pico ($\text{p}$): $1 \times 10^{-12}$ ($1 \text{ pg} = 1 \times 10^{-12} \text{ g}$ or $1 \text{ g} = 1 \times 10^{12} \text{ pg}$)

  • Femto ($\text{f}$): $1 \times 10^{-15}$ ($1 \text{ fg} = 1 \times 10^{-15} \text{ g}$ or $1 \text{ g} = 1 \times 10^{15} \text{ fg}$)

• Scale Navigation Rules:

  • Looking up the metric scale (expressing base unit in terms of larger prefix): Exponent is negative.

  • Looking down the metric scale (expressing base unit in terms of smaller prefix units): Exponent is positive.

Conversions and Unit Equivalencies

• English System Conversion Factors (Mandatory Memorization):

  • $1 \text{ mile} = 5280 \text{ feet}$

  • $1 \text{ mile} = 1760 \text{ yards}$

  • $1 \text{ yard} = 3 \text{ feet}$

  • $1 \text{ foot} = 12 \text{ inches}$

• Metric to English Equivalent Statements (Provided on Exams — Practice Usage Required):

  • Length Factors:

  • $1 \text{ inch} = 2.54 \text{ centimeters}$

  • $1 \text{ meter} = 39.37 \text{ inches}$

  • $1 \text{ mile} = 1.609 \text{ kilometers}$

  • Mass / Weight Factors:

  • $1 \text{ ounce} = 28.35 \text{ grams}$

  • $1 \text{ pound} = 453.6 \text{ grams}$

  • $1 \text{ kilogram} = 2.205 \text{ pounds}$

  • $1 \text{ grain} = 15.43 \text{ grams}$ (legacy pharmaceutical unit)

  • Volume Factors:

  • $1 \text{ quart} = 0.946 \text{ liters}$

  • $1 \text{ gallon} = 3.785 \text{ liters}$

  • $1 \text{ liter} = 33.81 \text{ fluid ounces}$

  • $1 \text{ fluid ounce} = 29.57 \text{ milliliters}$

  • $1 \text{ liter} = 1.057 \text{ quarts}$

Mass vs. Weight and Clinical Applications

• Physical Distinction:

  • Mass: The total quantity of matter contained within an object. Mass is entirely independent of geographic or gravitational location.

  • Weight: The gravitational force exerted upon an object's mass ($\text{Weight} = \text{mass} \times \text{gravity}$). Weight varies depending on the local gravitational field strength.

  • Usage Note: Mass and weight are frequently used interchangeably in general chemistry contexts.

• Clinical Application: Body Mass Drug Dosages:

  • Medical dosages are calculated based on patient body mass (e.g., milligrams of drug per kilogram of body weight).

  • Dosage Benchmark Example: $2 \text{ mg}$ of drug per $3 \text{ kg}$ of body weight.

  • A $50 \text{ kg}$ ($110 \text{ lb}$) individual receives a dosage of $150 \text{ mg}$

  • An $82 \text{ kg}$ ($180 \text{ lb}$) individual receives a dosage of $246 \text{ mg}$

  • Pediatric Considerations: Dosage adjustment based on mass is vital for children to prevent toxicity and accidental overdose caused by administering adult-sized doses.

  • Geriatric Considerations: Elderly patients frequently suffer from impaired kidney or liver clearance functions. Delayed drug clearance causes pharmaceuticals to persist in the bloodstream longer than normal, leading to clinical complications such as dizziness, vertigo, severe migraine-like headaches, loss of balance, falls, and broken bones.

Course Policies, Exam Rules, and Best Practices

• Exam Rules and Grading Integrity:

  • Calculation Credit: Full mathematical calculations must be shown explicitly for every problem. Providing a final numerical answer without showing the complete supporting calculation will result in a score of zero ($0$) for the question, regardless of correctness.

  • Formatting Answers: Enclose final calculated answers inside a box on exam papers to facilitate clear identification during grading.

  • Multiple Methods: Multiple valid mathematical setups exist to solve the same chemistry problem correctly.

  • Prohibition of Unauthorized Materials: No cheat sheets, notes, or unauthorized reference materials are permitted during examinations. Violation of this rule constitutes an academic integrity violation, resulting in an immediate zero ($0$) on the exam and formal administrative reporting.

  • Class Attendance Policy: Students are expected to remain present for the full duration of every lecture until official dismissal. Leaving lecture early is subject to penalty, and specific exam questions are routinely created from material presented in the final minutes of lecture or end-of-chapter problems (e.g., end-of-chapter problems 54 and 55).