Advanced Chemistry Comprehensive Final Exam Review Guide

Measurement, Error Analysis, and Foundations

• Significant Figures (Sig Figs)

  • Placeholder zeros are removed when determining significant figures.

  • zeros located after the decimal point must be remembered and kept as they are necessary for indicating precision.

  • Calculation Rules: When performing calculations with significant figures, keep all non-zero numbers and continue until there is only one number in the ones place.

• Percent Error Calculation

  • Procedure: Divide your obtained result by the theoretical result, take the absolute value of the quotient, and multiply by 100.

  • Formula: $\text{Percent Error} = \left| \frac{\text{Result}}{\text{Theoretical Result}} \right| \times 100$

• Dimensional Analysis

  • Utilize conversion factors systematically so that units cancel out (numerator vs. denominator) until the desired unit remains.

Chemical Nomenclature and Formulas

• Ionic Nomenclature

  • Cation: Write the full name of the cation (positive ion) first.

  • Anion: Write the name of the anion (negative ion) second, changing its ending to "-ide."

  • Oxidation Numbers: Remember to include oxidation numbers (Roman numerals) for transition metals or other elements if required.

• Covalent Nomenclature

  • Cation First: Write the name of the cation-like element first. Use the correct prefix for the number of atoms present, unless there is only one atom of the first element (do not use "mono-").

  • Anion Second: Write the anion-like element second. Use the correct prefix for the number of atoms and add the "-ide" suffix to the end.

• Chemical Formula Construction

  • Write the symbols for the elements and then apply subscripts to ensure the formula is electrically neutral (e.g., $H_2O$, $CO_2$).

• Empirical and Molecular Formulas

  • Empirical Formula (EF): Defined as the simplified molecular formula representing the smallest whole-number ratio of elements in a compound.

  • Molecular Formula (MF): The actual formula of a compound, which is a multiple of the empirical formula.

  • Calculating EF from Percent Composition:

    1. Assume a $100\,g$ sample of the substance so that percentages convert directly to grams.

    2. Divide the grams of each part by its respective molar mass to determine the number of moles.

    3. Set up a preliminary formula using these mole values as subscripts.

    4. Divide each subscript by the smallest mole value obtained.

    5. Write the final results as the subscripts for the EF.

  • Calculating MF from EF:

    1. Take the EF and multiply each subscript by the molar mass of its corresponding element.

    2. Sum these values to find the molar mass of the empirical unit.

    3. Divide the actual molar mass of the compound by the empirical unit mass to find the multiplier.

    4. Multiply all subscripts in the EF by this multiplier to obtain the MF.

Phases of Matter and Phase Diagrams

• Phase Changes

  • Solid to Gas: Sublimation

  • Solid to Liquid: Melting

  • Liquid to Solid: Freezing

  • Liquid to Gas: Evaporation/Boiling

  • Gas to Liquid: Condensation

  • Gas to Solid: Deposition

• Phase Diagram Components

  • Axis Labels: Heat and phase diagrams are typically graphed on Pressure (y-axis) vs. Temperature (x-axis).

  • Solid Phase: Located on the left side of the diagram.

  • Liquid Phase: Located in the middle section of the diagram.

  • Gas Phase: Located on the right side of the diagram.

  • Triple Point: The specific point where all three states of matter (solid, liquid, gas) exist simultaneously in equilibrium.

  • Critical Point: The specific conditions of temperature and pressure beyond which a liquid can no longer exist.

• Standard Temperature and Pressure (STP)

  • Standard Temperature: $0\,^{\circ}\text{C}$ or $273\,K$.

  • Standard Pressure: $1\,atm$, $101.3\,kPa$, or $760\,mmHg$.

  • Molar Volume at STP: One mole of any gas at STP occupies a volume of $22.4\,L$.

Chemical Equilibrium and Kinetics

• Equilibria

  • Represented in chemical equations by a double arrow (e.g., $\rightleftharpoons$).

  • Indicates a reaction or process where the forward and backward rates are equal.

  • In phase diagrams, it represents the ability to change states between phases.

  • A state of equilibrium implies the system is balanced.

• Kinetic Factors Affecting Reactivity

  • Factors that influence how fast a reaction occurs (reaction rate):

    1. Concentration: Higher concentration typically increases rates.

    2. Temperature: Higher temperatures increase kinetic energy (energy of motion), leading to more frequent and energetic collisions.

    3. Pressure: Especially relevant for gases.

    4. Surface Area: Increasing the surface area of a solid reactant increases the rate of reaction.

    5. Presence of a Catalyst: Lowering activation energy to speed up the reaction.

    6. Size of Object: Affects the available surface area for reaction.

• Activation Energy and Activated Complex

  • Enthalpy ($\Delta H$): The difference between the start (reactants) and end (products) energy states.

  • Activation Energy ($E_a$): The "hump" or energy barrier that must be overcome for a reaction to take place; described as a "jumpstart."

  • Activated Complex: The peak of the energy hump in a reaction diagram.

Stoichiometry and Gas Laws

• General Stoichiometry

  • Grams to Moles: Divide the mass by the molar mass ($n = \frac{m}{M_{mass}}$).

  • Molar Ratio:

    1. Moles of one part divided by the total number of moles (determines percentage).

    2. Moles of one substance relative to moles of another substance from a balanced equation (used as a conversion factor).

  • Balancing Equations: The number of atoms in the products must always equal the number of atoms in the reactants.

  • Stoichiometry Calculation Steps: If given grams, divide by molar mass to get moles, apply the molar ratio from the balanced equation, and then multiply by the molar mass of the desired substance to return to grams.

• Gas Laws and Formulas

  • Ideal Gas Law: $PV = nRT$

    • $P$ = Pressure

    • $V$ = Volume

    • $n$ = Number of moles

    • $R$ = Unique gas constant factor

    • $T$ = Temperature (must be in Kelvin)

  • Combined Ideal Gas Law: $\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}$

  • Molar Mass and Density Variations:

    • $PV = \frac{m \times R \times T}{M}$

    • $PM = D \times R \times T$

  • Dalton’s Law of Partial Pressures: The total pressure ($P_{\text{total}}$) is equal to the sum of the partial pressures of each individual gas.

    • $P_{\text{total}} = P_1 + P_2 + \text{...}$

• Behavior of Gases

  • Kinetic Molecular Theory: Gases consist of particles in constant motion, are compressible, have high kinetic energy, take the shape and volume of their container, and have no significant interactions between particles.

  • Ideal Gases (under STP): Characterized by elastic collisions, negligible particle volume (no volume), and no intermolecular interactions.

Intermolecular Forces (IMFs) and Physical Properties

• Types of Intermolecular Forces

  • London Dispersion Forces (LDFs): Minor forces created by instantaneous, temporary dipole moments when electrons are not dispersed equally. All molecules (polar and nonpolar) possess LDFs.

  • Dipole-Dipole Forces: Forces between two oppositely charged poles of polar molecules. These form only between polar molecules (consider lone pairs when determining polarity).

  • Hydrogen Bonds: The strongest IMF. Formed between a hydrogen atom on one molecule and a high-electronegativity atom (specifically Oxygen or Fluorine, also Nitrogen) on a different molecule. In water, the negative oxygen is pulled by the hydrogen of an adjacent molecule.

• IMF Strengths (Weakest to Strongest)

  • $\text{London Dispersion Forces} \rightarrow \text{Dipole-Dipole} \rightarrow \text{Hydrogen Bonds}$

• Physical Properties Governed by IMFs

  • Boiling Point (BP): The temperature where a liquid's vapor pressure equals the atmospheric pressure. Stronger IMFs lead to higher boiling points.

  • Melting Point (MP): The temperature where solid and liquid phases exist at equilibrium at atmospheric pressure. Stronger IMFs increase melting points.

  • Viscosity: A liquid's resistance to flow. Stronger IMFs lead to higher viscosity.

  • Vapor Pressure: Increases exponentially with temperature. At the boiling point, vapor pressure equals external pressure. Stronger IMFs lead to lower vapor pressure at a given temperature.

• Solubility and Polarity

  • Like Dissolves Like:

    • Polar solutions dissolve in other polar solutions but separate from nonpolar ones.

    • Nonpolar solutions dissolve in other nonpolar solutions but separate from polar ones.

Thermodynamics and Thermochemistry

• Heat and Temperature

  • Temperature / Kinetic Energy: Higher temperature correlates to higher kinetic energy.

  • Enthalpy ($\Delta H$): The total energy of a reaction.

    • $\Delta H = \sum H_{\text{products}} - \sum H_{\text{reactants}}$

  • Entropy ($\Delta S$): The measure of disorder or randomness.

    • $\Delta S = \sum S_{\text{products}} - \sum S_{\text{reactants}}$

    • Bond Breaking: Leads to more randomness, so $\Delta S$ is positive.

    • Bond Forming: Leads to more order, so $\Delta S$ is negative. Nature seeks higher entropy.

• Specific Heat and Calorimetry

  • Heat Formula: $Q = m \times s_h \times \theta T$

    • $Q$ = Total heat (Energy)

    • $m$ = Mass in grams

    • $s_h$ = Specific heat (Energy required to raise 1g by $1\,^{\circ}\text{C}$)

    • $\theta T$ = Change in temperature in $^{\circ}\text{C}$

  • Heat Curve Calculations: Total heat is found by summing segments:

    1. $Q = m \times s_h \times \theta T$ (heating segments).

    2. $Q = n \times \Delta H$ (phase change segments using moles and enthalpy of fusion/vaporization).

  • Calorimetry Equation:

    • $-m \times s_h \times \theta T_{\text{metal}} = m \times s_h \times \theta T_{\text{water}}$

    • $-(\text{mass metal})(\text{specific heat metal})(T_{\text{final}} - T_{\text{initial}}) = (\text{mass water})(\text{specific heat water})(T_{\text{final}} - T_{\text{initial water}})$

• Gibbs Free Energy and Spontaneity

  • Formula: $\Delta G = \Delta H - T \times \Delta S$

    • $T$ must be in Kelvin ($K$).

    • $\Delta S$ must often be converted to kJ by dividing by 1000 to match $\Delta H$.

  • Spontaneity Rules:

    1. \Delta G < 0: Spontaneous reaction.

    2. \Delta G > 0: Non-spontaneous reaction.

    3. $\Delta G = 0$: System at equilibrium.

• Energy Changes in Solvation

  • Breaking solute-solute or solvent-solvent bonds: Energy is added (endothermic, \Delta H > 0) and randomness increases (\Delta S > 0).

  • Creating solute-solvent interactions: Energy is released (exothermic, \Delta H < 0) and randomness decreases (\Delta S < 0).

Atomic Structure and Static Electricity

• Hybridization

  • Determined by Lewis structure and electron geometry shape:

    1. Methane ($CH_4$): Tetrahedral shape, $sp^3$ hybridization.

    2. $O_2$: Trigonal planar electronic geometry, $sp^2$ hybridization.

    3. Water ($H_2O$): Tetrahedral electronic geometry, bent shape, $sp^3$ hybridization.

    4. Ammonia ($NH_3$): Tetrahedral electronic geometry, trigonal pyramidal shape, $sp^3$ hybridization.

• Coulomb’s Law

  • Describes the electrostatic force between charges.

  • Formula: $F = k \times \frac{Q_1 \times Q_2}{r^2}$

    • $F$ = Force

    • $k$ = Constant

    • $Q_1, Q_2$ = Charges

    • $r$ = Distance

Advanced Logic and Calculations

• Hydrates

  • Procedure:

    1. Find mass of water by subtracting the mass of the "androgynous" (anhydrous) substance from the total mass of the hydrate.

    2. Convert the mass of water to moles ($mass / 18.02\,g/mol$).

    3. Convert the mass of the "andyhdrygous" (anhydrous) substance to moles using its molar mass.

    4. Divide the moles of water by the moles of the anhydrous substance to find the coefficient ($x$).

    5. Write the formula with a dot: $\text{Anhydrous} \cdot xH_2O$ (e.g., $Na_4Cl_3 \cdot 5H_2O$).

• Ionic Compound Diagram and Properties

  • Ionic compounds are hard, brittle, and have high melting points.

  • When force is applied, they split because like charges line up and repel (brittleness).

  • They dissociate into ions in water. Only conduct electricity in aqueous solution or molten states; solids do not conduct.

• Particle Diagrams and Diatomics

  • In reaction diagrams, the number of atoms of each type must be equal on both sides.

  • Remember diatomic elements: $H_2$, $N_2$, $F_2$, $O_2$, $I_2$, $Cl_2$, $Br_2$.

Questions & Discussion

• Stoichiometry Problem (Limiting Reactant): $17.63\,g$ of $HBr$ reacts with $12.94\,g$ of $KOH$. Determine the limiting reactant and grams of $KBr$ produced.

• Energy Calculation: How much energy is required to heat $89.0\,g$ of ethanol ($C_2H_5OH$) from $17.0\,^{\circ}\text{C}$ to $65.0\,^{\circ}\text{C}$ with a specific heat of $2.40\,J/g\,^{\circ}\text{C}$?

• Manometer Calculations:

  • Neon gas with a height difference of $31.2$ inches of $Hg$. Calculate pressure in $kPa$.

  • Open-arm manometer with height difference of $26.93\,mmHg$ and standard air pressure. Calculate pressure in $kPa$.

• Gas Law Shifts:

  • A gas occupies $251\,mL$ at STP; find volume at $86\,^{\circ}\text{C}$ and $26.7\,inHg$.

  • $317\,mL$ of $O_2$ at $25\,^{\circ}\text{C}$ and $660\,mmHg$ cooled to fit a $125\,mL$ tank at standard pressure.

• Calorimetry Mix: Final temperature of a $52.5\,g$ cobalt chunk at $97\,^{\circ}\text{C}$ placed in $45.0\,g$ of water at $19\,^{\circ}\text{C}$.

• Equilibrium Stresses ($N_2O_3(g) \rightleftharpoons NO(g) + NO_2(g)$, \Delta H > 0):

  • Adding $N_2O_3$: Shifts right.

  • Decreasing Temperature: Shifts left (exothermic direction).

  • Adding Catalyst: No change.

  • Removing $NO_2$: Shifts right.

  • Tripling volume: Shifts right (toward more moles of gas).

• Titrations:

  • $115.0\,mL$ unknown $HClO_2$ titrated with $75.2\,mL$ of $0.275\,M\,NaOH$. Find concentration.

  • Volume of $0.0453\,M\,KOH$ to neutralize $24.99\,mL$ of $0.09233\,M$ Nitric Acid.

• Significant Figures (Sig Figs)

  • Significant figures are vital in scientific measurements as they reflect the precision of the measurements.

  • Placeholder zeros in a number are eliminated when identifying significant figures, and they do not count towards the total number of significant figures.

  • Zeros located after the decimal point are critical and must be retained since they play a significant role in demonstrating the accuracy and precision of the measurement.

  • Calculation Rules: When executing calculations involving significant figures, keep all non-zero numbers and proceed until only one non-zero figure remains in the ones place.

  • When adding or subtracting numbers, the result should be reported to the least number of decimal places in the original numbers.

  • In multiplication and division, the final answer should reflect the same number of significant figures as the measurement with the fewest significant figures.

• Percent Error Calculation

  • The percent error is a critical metric that helps quantify the accuracy of a measurement in comparison to a known or accepted value.

  • Procedure: To compute percent error, divide the absolute value of the difference between the obtained result and the theoretical result by the theoretical result, then multiply by 100 to express it as a percentage.

  • Formula: $\text{Percent Error} = \left\| \frac{\text{Result} - \text{Theoretical Result}}{\text{Theoretical Result}} \right\| \times 100$

  • A small percent error indicates that the measurement is close to the theoretical value, while a large percent error suggests a significant deviation, pointing to potential sources of error that could be systematic or random.

• Dimensional Analysis

  • Dimensional analysis is a powerful technique used to convert units and solve problems involving measurements.

  • Systematically apply conversion factors to ensure that units cancel out correctly (numerator versus denominator) throughout the process until only the desired unit remains.

  • This method not only aids in verifying the correctness of a calculation but also enhances clarity when working with different unit systems, such as converting volume from liters to milliliters or mass from grams to kilograms.