General Chemistry Essentials

Cheatsheet Content

### Matter and Atomic Structure #### Physical and Chemical Properties - **Physical Properties**: Characteristics observed or measured without changing the substance's chemical identity. - Examples: Density, melting point, boiling point, color, hardness, conductivity, state of matter (solid, liquid, gas). - **Chemical Properties**: Characteristics that describe how a substance reacts or changes into a different substance. This involves a change in composition. - Examples: Flammability, reactivity with acids/bases, oxidation, corrosion, heat of combustion. #### Classification of Matter - **Pure Substances**: Have a fixed chemical composition and distinct properties. - **Elements**: Cannot be broken down into simpler substances by chemical means (e.g., O₂, H, Fe). - **Compounds**: Formed when two or more elements are chemically combined in fixed proportions (e.g., H₂O, NaCl). - **Mixtures**: Combinations of two or more substances where each substance retains its distinct chemical identity. - **Homogeneous Mixture (Solution)**: Uniform composition and properties throughout; components are indistinguishable (e.g., salt water, air, brass). - **Heterogeneous Mixture**: Non-uniform composition with visible boundaries between components; properties vary from one region to another (e.g., oil and water, sand and sugar, granite). #### States of Matter - **Solid**: Definite shape and volume; particles are tightly packed and vibrate in fixed positions. - **Liquid**: Indefinite shape (takes shape of container) but definite volume; particles are close but can move past each other. - **Gas**: Indefinite shape and volume; particles are far apart and move randomly and rapidly. - **Plasma**: Ionized gas; extremely high energy state. #### Atomic Composition For an atom of element X with Atomic Number (Z) and Mass Number (A): - **Atomic Number (Z)**: Number of protons in the nucleus. Defines the element. - **Mass Number (A)**: Total number of protons and neutrons in the nucleus. - **Number of protons (p)** = Z - **Number of electrons (e)** = Z (for a neutral atom) - **Number of neutrons (n)** = A - Z - **Isotopes**: Atoms of the same element (same Z) but with different numbers of neutrons (different A). #### Periodic Table Basics - **Metals**: Located on the left and center of the periodic table. - Properties: Lustrous (shiny), malleable (can be hammered into sheets), ductile (can be drawn into wires), good conductors of heat and electricity, tend to form cations (lose electrons). - **Nonmetals**: Located on the upper right side of the periodic table. - Properties: Generally dull, brittle (if solid), poor conductors of heat and electricity (insulators), exist in various states (solid, liquid, gas), tend to form anions (gain electrons). - **Metalloids (Semimetals)**: Border the zigzag line between metals and nonmetals (e.g., Si, Ge, As). - Properties: Exhibit properties intermediate between metals and nonmetals. Often semiconductors. ### Measurements and Stoichiometry #### SI Prefixes and Units The International System of Units (SI) is the standard system of measurement. - **Base Units**: - Length: meter (m) - Mass: kilogram (kg) - Time: second (s) - Temperature: Kelvin (K) - Amount of substance: mole (mol) - Electric current: ampere (A) - Luminous intensity: candela (cd) - **Common Prefixes**: - Giga (G) = 10⁹ - Mega (M) = 10⁶ - Kilo (k) = 10³ - Hecto (h) = 10² - Deca (da) = 10¹ - Deci (d) = 10⁻¹ - Centi (c) = 10⁻² - Milli (m) = 10⁻³ - Micro (µ) = 10⁻⁶ - Nano (n) = 10⁻⁹ - Pico (p) = 10⁻¹² - **Derived Units**: Combinations of base units (e.g., density = kg/m³, volume = m³). #### Density and Temperature - **Density ($\rho$)**: Mass per unit volume. $$\rho = \frac{m}{V}$$ - Units: g/cm³, g/mL, kg/L. - **Temperature Conversions**: - Celsius to Kelvin: $$T(K) = T(^\circ C) + 273.15$$ - Celsius to Fahrenheit: $$T(^\circ F) = 1.8 \cdot T(^\circ C) + 32$$ - Fahrenheit to Celsius: $$T(^\circ C) = \frac{T(^\circ F) - 32}{1.8}$$ #### Chemical Bonding - **Ionic Bonding**: Formed by the electrostatic attraction between oppositely charged ions. - Typically occurs between a metal (loses electrons to form cations) and a nonmetal (gains electrons to form anions). - Example: NaCl (Na⁺Cl⁻). - **Covalent Bonding**: Formed by the sharing of electron pairs between atoms. - Typically occurs between two nonmetals. - **Nonpolar Covalent**: Equal sharing of electrons (e.g., O₂, Cl₂). - **Polar Covalent**: Unequal sharing of electrons due to difference in electronegativity (e.g., H₂O). - **Metallic Bonding**: Delocalized electrons shared among a lattice of metal atoms. Explains conductivity and malleability of metals. #### Stoichiometry and Moles - **Mole (mol)**: The SI unit for amount of substance. Contains Avogadro's number of particles. $$1 \text{ mol} = 6.022 \times 10^{23} \text{ particles (atoms, molecules, ions)}$$ - **Molar Mass (M)**: The mass of one mole of a substance (g/mol). Numerically equal to atomic mass (for elements) or molecular/formula mass (for compounds) in amu. $$\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$$ - **Molecular Mass / Formula Mass**: Sum of the atomic masses of all atoms in a molecule or formula unit. - **Percent Composition**: The mass percentage of each element in a compound. $$\text{% Element} = \frac{\text{mass of element in compound}}{\text{molar mass of compound}} \times 100\%$$ #### Balancing Chemical Equations - Ensure the number of atoms of each element is the same on both sides of the reaction arrow. - Coefficients represent the mole ratio of reactants and products. #### Limiting and Excess Reagents - **Limiting Reagent**: The reactant that is completely consumed in a chemical reaction. It determines the maximum amount of product that can be formed. - **Excess Reagent**: The reactant(s) present in an amount greater than required to react with the limiting reagent. - **To identify the Limiting Reagent**: 1. Write and balance the chemical equation. 2. Convert the given masses of reactants to moles using their molar masses. 3. For each reactant, divide its moles by its stoichiometric coefficient from the balanced equation. 4. The reactant with the smallest resulting value is the limiting reagent. - **Theoretical Yield**: The maximum amount of product that can be formed from the given amounts of reactants (calculated using the limiting reagent). - **Actual Yield**: The experimentally obtained amount of product. - **Percent Yield**: $$\text{% Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$$ ### Thermochemistry #### Systems and Energy - **System**: The specific part of the universe under study. - **Surroundings**: Everything else outside the system. - **Open System**: Exchanges both mass and energy with the surroundings (e.g., an open beaker of boiling water). - **Closed System**: Exchanges energy but not mass with the surroundings (e.g., a sealed flask of reacting chemicals). - **Isolated System**: Exchanges neither mass nor energy with the surroundings (e.g., an ideal thermos flask). - **Energy**: The capacity to do work or transfer heat. - **Kinetic Energy**: Energy of motion ($KE = \frac{1}{2}mv^2$). - **Potential Energy**: Stored energy due to position or composition. #### First Law of Thermodynamics - **Statement**: Energy cannot be created or destroyed in an isolated system. The total energy of the universe is constant. - **Internal Energy ($\Delta U$ or $\Delta E$)**: The sum of all kinetic and potential energies of the particles within a system. $$\Delta U = q + w$$ - Where: - $q$ = heat (energy transferred due to temperature difference) - $w$ = work (energy transferred when a force acts over a distance) - **Sign Conventions**: - $q > 0$: Heat absorbed by system (endothermic) - $q 0$: Work done on system - $w 0$ (expansion), system does work ($w 0$). #### Enthalpy ($H$) and Calorimetry - **Enthalpy ($H$)**: A thermodynamic property that is equal to the internal energy of the system plus the product of pressure and volume ($H = U + PV$). - **Enthalpy Change ($\Delta H$)**: Heat exchanged at constant pressure. - **Exothermic Reaction**: $\Delta H 0$. System absorbs heat from surroundings. Products are higher in energy than reactants. - **Standard Enthalpy of Formation ($\Delta H_f^\circ$)**: The enthalpy change when one mole of a compound is formed from its elements in their standard states (25°C, 1 atm). $\Delta H_f^\circ$ for an element in its standard state is zero. - **Specific Heat Capacity ($c$)**: The amount of heat required to raise the temperature of 1 gram of a substance by 1°C (or 1 K). Units: J/(g·°C) or J/(g·K). $$q = m \cdot c \cdot \Delta T$$ - Where: - $m$ = mass - $c$ = specific heat capacity - $\Delta T$ = change in temperature ($T_{\text{final}} - T_{\text{initial}}$) - **Heat Capacity ($C$)**: The amount of heat required to raise the temperature of an entire object by 1°C (or 1 K). Units: J/°C or J/K. $$q = C \cdot \Delta T$$ #### Calorimetry - The experimental measurement of heat flow. - **Coffee-Cup Calorimeter (Constant Pressure)**: Measures heat changes for reactions in solution. Since pressure is constant, $q_P = \Delta H$. $$q_{\text{rxn}} = -(q_{\text{water}} + q_{\text{calorimeter}})$$ - If the calorimeter's heat capacity is negligible, $q_{\text{calorimeter}} \approx 0$. - **Bomb Calorimeter (Constant Volume)**: Measures heat changes for combustion reactions. Since volume is constant, $q_V = \Delta U$. $$q_{\text{rxn}} = -C_{\text{cal}} \cdot \Delta T$$ - $C_{\text{cal}}$ is the heat capacity of the bomb calorimeter. #### Hess's Law - **Statement**: If a reaction can be expressed as a series of steps, then the enthalpy change for the overall reaction is the sum of the enthalpy changes for each step. - This allows calculation of $\Delta H$ for reactions that are difficult to measure directly. - **Calculation using Standard Enthalpies of Formation**: $$\Delta H_{\text{rxn}}^\circ = \sum n \Delta H_f^\circ (\text{products}) - \sum m \Delta H_f^\circ (\text{reactants})$$ - Where $n$ and $m$ are the stoichiometric coefficients. ### Thermodynamics and Spontaneity #### Second Law of Thermodynamics - **Statement**: For any spontaneous process, the total entropy of the universe must increase. $$\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} > 0$$ - **Entropy ($S$)**: A measure of disorder or randomness in a system. - Higher entropy corresponds to greater disorder. - Factors increasing entropy: - Increase in number of moles of gas. - Phase transition from solid to liquid to gas. - Increase in temperature. - Dissolving a solid in a solvent. #### Third Law of Thermodynamics - **Statement**: The entropy of a perfect crystalline substance at absolute zero (0 K) is zero. - This provides a reference point for absolute entropy values. #### Entropy Change ($\Delta S$) - **Standard Molar Entropy ($S^\circ$)**: The absolute entropy of one mole of a substance in its standard state. - **Standard Entropy Change of Reaction ($\Delta S_{\text{rxn}}^\circ$)**: $$\Delta S_{\text{rxn}}^\circ = \sum n S^\circ (\text{products}) - \sum m S^\circ (\text{reactants})$$ - **Entropy Change of Surroundings ($\Delta S_{\text{surr}}$)**: $$\Delta S_{\text{surr}} = \frac{-q_{\text{sys}}}{T} = \frac{-\Delta H_{\text{sys}}}{T} \quad \text{(at constant P and T)}$$ #### Gibbs Free Energy ($G$) - **Definition**: A thermodynamic potential that measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. - **Gibbs Free Energy Equation**: Relates enthalpy, entropy, and temperature to spontaneity. $$\Delta G = \Delta H - T\Delta S$$ - Where: - $\Delta G$ = change in Gibbs free energy - $\Delta H$ = change in enthalpy - $T$ = absolute temperature (in Kelvin) - $\Delta S$ = change in entropy #### Criteria for Spontaneity (at constant T and P) - If $\Delta G 0$: The process is **non-spontaneous** (favors reactant formation; the reverse process is spontaneous). - If $\Delta G = 0$: The system is at **equilibrium** (no net change). #### Relationship between $\Delta H$, $\Delta S$, and Spontaneity | $\Delta H$ | $\Delta S$ | $\Delta G = \Delta H - T\Delta S$ | Spontaneity | |:----------:|:----------:|:----------------------------------:|:------------| | - | + | - (always) | Spontaneous at all temperatures | | - | - | - at low T, + at high T | Spontaneous at low temperatures | | + | + | + at low T, - at high T | Spontaneous at high temperatures | | + | - | + (always) | Non-spontaneous at all temperatures | #### Standard Gibbs Free Energy Change ($\Delta G^\circ$) - **Standard Gibbs Free Energy of Formation ($\Delta G_f^\circ$)**: The Gibbs free energy change when one mole of a compound is formed from its elements in their standard states. - **Standard Gibbs Free Energy of Reaction ($\Delta G_{\text{rxn}}^\circ$)**: $$\Delta G_{\text{rxn}}^\circ = \sum n \Delta G_f^\circ (\text{products}) - \sum m \Delta G_f^\circ (\text{reactants})$$ #### Gibbs Free Energy and Equilibrium Constant ($K$) - The relationship between $\Delta G^\circ$ and the equilibrium constant $K$ is: $$\Delta G^\circ = -RT \ln K$$ - Where: - $R$ = ideal gas constant (8.314 J/(mol·K)) - $T$ = absolute temperature (K) - $K$ = equilibrium constant - At equilibrium, $\Delta G = 0$, so: $$0 = \Delta G^\circ + RT \ln Q$$ $$\Delta G = \Delta G^\circ + RT \ln Q$$ - Where $Q$ is the reaction quotient.