Energy and Chemical Change: Principles of Thermochemistry

Core Concepts of Energy and Chemical Change

• Thermochemistry: The scientific study of energies that are either given off by or absorbed by chemical reactions.

• Thermodynamics: The broader study of heat transfer and heat flow within systems.

• Energy ($E$): Defined as the ability to do work or to transfer heat.

• Kinetic Energy ($KE$): The energy associated with an object's motion. It is mathematically expressed as:     $\text{KE} = \frac{1}{2}mv^2$

• Potential Energy ($PE$):     * Defined as stored energy.     * It exists due to natural attractions and repulsions, such as gravity, positive and negative charges, and mechanical springs.

• Chemical Energy:     * A form of potential energy possessed by chemical substances.     * It is stored within chemical bonds.     * Bond Energy Principles:         * Breaking chemical bonds always requires an input of energy (increases $PE$).         * Forming chemical bonds always releases energy (decreases $PE$).         * Example Reaction: $H_2 + O_2 \rightarrow H_2O$

Factors Affecting Potential Energy

• Increasing Potential Energy:     * Occurs when pulling apart objects that attract each other:         * A book being lifted (attracted to Earth by gravity).         * Moving the North and South poles of magnets away from each other.         * Separating positive and negative charges.     * Occurs when pushing together objects that repel each other:         * Compressing a mechanical spring.         * Forcing two like poles of magnets (e.g., North and North) together.         * Pushing two like charges (e.g., two electrons) together.

• Decreasing Potential Energy:     * Occurs when objects that attract each other come together:         * A book falling toward the Earth.         * North and South poles of magnets moving toward each other.         * Positive and negative charges coming together.     * Occurs when objects that repel each other move apart:         * Two North poles of magnets moving away from each other.         * Releasing a compressed spring.         * Two like charges moving away from each other.

Law of Conservation of Energy and Units

• Law of Conservation of Energy: Energy can neither be created nor destroyed; it can only be converted from one form to another. The total energy of the universe remains constant.     * $\text{Total Energy} = \text{Potential Energy} + \text{Kinetic Energy}$

• Joule ($J$): The kinetic energy possessed by a $2\,kg$ object moving at a speed of $1\,m/s$.     * $1\,J = \frac{1}{2} \times 2\,kg \times (1\,m/s)^2$     * $1\,J = 1\,kg \cdot m^2/s^2$     * If the calculated value exceeds $1000\,J$, kilojoules ($kJ$) are used: $1\,kJ = 1000\,J$.

• calorie ($cal$): The amount of energy required to raise the temperature of $1\,g$ of $H_2O$ by $1\,^{\circ}C$.     * $1\,cal = 4.184\,J$ (exactly).     * $1\,kcal = 1000\,cal$.     * $1\,kcal = 4.184\,kJ$.

• Nutritional Calorie ($Cal$): Note the capital "C".     * $1\,Cal = 1000\,cal = 1\,kcal$.     * $1\,Cal = 4.184\,kJ$.

Temperature, Heat, and Internal Energy

• Temperature:     * Proportional to the average kinetic energy of the particles within an object.     * Higher average kinetic energy results in higher temperature and faster molecular motion.     * Relationship: $\text{Avg KE} \propto \text{Kelvin Temperature (T)}$.

• Heat ($q$):     * The total amount of energy transferred between objects due to a temperature difference.     * Heat always passes spontaneously from warmer objects to colder objects until thermal equilibrium is reached (both objects at the same temperature).

• Internal Energy ($E$):     * The sum of all potential and kinetic energies of all particles within a system ($E = PE + KE$).     * Change in Internal Energy ($\Delta E$):         * $\Delta E = E_{\text{final}} - E_{\text{initial}}$         * Positive sign ($+$): The system absorbs energy from surroundings ($E_{\text{final}} > E_{\text{initial}}$). Examples include photosynthesis or charging a battery.         * Negative sign ($-$): The system releases energy to surroundings.

Kinetic Molecular Theory (KMT)

• KMT and Temperature: Temperature relates to the average kinetic energy. In a large collection of gas molecules, there is a wide distribution of KEs.     * A small number of molecules have $KE = 0$ (momentarily stopped by collisions).     * A small number have very high $KE$.     * Most molecules possess intermediate $KE$ values.

• Effect of Temperature Rise: At higher temperatures, the distribution shifts toward higher kinetic energy and higher average speeds.     * At $0\,K$, kinetic energy is zero ($KE = 0, v = 0$).

• States of Matter: Atoms and molecules in liquids and solids are also in constant motion (jiggling/vibrating in place).     * At the same temperature, gases, liquids, and solids have the same average kinetic energy distributions but different potential energies.

Systems and State Functions

• System: The specific part of the universe being studied (e.g., a reaction in a beaker).

• Surroundings: Everything else in the universe outside the system.

• Boundary: The separation between system and surroundings (can be visible like beaker walls or invisible).

• Types of Systems:     1. Open System: Can exchange both mass and energy with the surroundings (e.g., an open beaker).     2. Closed System: Can exchange energy (heat/work) but not mass with the surroundings.     3. Isolated System: Cannot exchange mass or energy with the surroundings (e.g., a sealed Thermos bottle).

• Adiabatic Process: A process occurring in an isolated system where no heat or matter crosses the boundary.

• State Function: A property that depends only on the current state or condition of the object, independent of the path taken to reach that state.     * Examples: Internal energy ($E$), Pressure ($P$), Temperature ($t$ or $T$), and Volume ($V$).

Heat Capacity and Specific Heat

• Heat ($q$) Calculation: Heat cannot be measured directly but is calculated via temperature change ($\Delta t$).     * $q = C \times \Delta t$

• Heat Capacity ($C$):     * The amount of heat required to raise the temperature of an object by $1\,^{\circ}C$.     * Units: $J/^{\circ}C$ or $J \cdot {^{\circ}C}^{-1}$.     * Extensive property: Depends on sample size (mass) and identity of the substance.

• Specific Heat ($s$):     * The heat energy required to raise the temperature of $1\,g$ of a substance by $1\,^{\circ}C$.     * Units: $J/(g\cdot^{\circ}C)$ or $J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$.     * Intensive property: Independent of the amount of substance.     * Relationship: $C = s \times m$ or $s = \frac{C}{m}$.     * Equation: $q = s \times m \times \Delta t$

• Specific Heats of Common Substances (Table 6.1):     * Carbon (graphite): $0.711\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$     * Copper: $0.387\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$     * Ethyl alcohol: $2.45\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$     * Gold: $0.129\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$     * Granite: $0.803\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$     * Iron: $0.4498\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$     * Lead: $0.128\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$     * Olive oil: $2.0\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$     * Silver: $0.235\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$     * Water (liquid): $4.184\,J \cdot g^{-1} \cdot {^{\circ}C}^{-1}$

• High Specific Heat of Water: Water resists temperature changes effectively, which is vital for thermal regulation in the human body ($\sim 60\%$ water) and influences coastal vs. inland climates.

Chemical Reaction Energetics

• Exothermic Reaction:     * Products have less chemicanl energy than reactants.     * Heat is released to the surroundings ($q$ is negative).     * Reaction vessel feels warmer; temperature increases.     * Heat is treated as a product: $\text{Reactants} \rightarrow \text{Products} + \text{Heat}$.     * Example: $\text{CH}_4(g) + 2 ext{O}_2(g) \rightarrow ext{CO}_2(g) + 2 ext{H}_2 ext{O}(g) + \text{Heat}$

• Endothermic Reaction:     * Products have more chemical energy than reactants.     * Heat is absorbed from surroundings ($q$ is positive).     * Reaction vessel feels colder; temperature decreases.     * Heat is treated as a reactant: $\text{Reactants} + \text{Heat} \rightarrow \text{Products}$.     * Example (Photosynthesis): $6 ext{CO}<em>2(g) + 6 ext{H}_2 ext{O}(g) + \text{Solar Energy} \rightarrow ext{C}_6 ext{H}</em>{12} ext{O}_6(s) + 6 ext{O}_2(g)$

• Bond Strength: Stronger bonds require more energy to break and release more energy when formed. If products have stronger bonds than reactants, the reaction is typically exothermic (e.g., methane combustion).

Calorimetry and Work

• Calorimeter: An instrument used to measure heat of reaction by monitoring temperature changes in surroundings of known heat capacity.

• Conditions of Measurement:     * Constant Volume ($q_V$): Measured in a bomb calorimeter (closed, rigid container).     * Constant Pressure ($q_P$): Measured in a coffee cup calorimeter (open to atmosphere).

• Pressure-Volume ($P-V$) Work:     * Work done by a system as it expands against an opposing pressure ($P$).     * $\text{Work} = -P \times \Delta V$     * $\Delta V = V_{\text{final}} - V_{\text{initial}}$     * Expansions (\Delta V > 0) result in negative work (work done by the system).     * Contractions (\Delta V < 0) result in positive work (work done on the system).

• First Law of Thermodynamics:     * $\Delta E = q + w$     * $q$ is ($+$) and $w$ is ($+$) when energy enters the system.     * $q$ is ($-$) and $w$ is ($-$) when energy leaves the system.

Enthalpy ($H$)

• Definition: Heat of reaction at constant pressure ($q_P$).     * $H = E + PV$     * $\Delta H = \Delta E + P\Delta V$     * If only $P-V$ work is performed ($w = -P\Delta V$), then $\Delta H = q_P$.

• Sign Conventions:     * Endothermic: $\Delta H$ is positive ($+$).     * Exothermic: $\Delta H$ is negative ($-$).

• Standard State in Thermochemistry:     * Pressure = $1\,atm$.     * Temperature = $25\,^{\circ}C$ ($298\,K$).     * Amount = $1\,mol$ (for formation) or coefficients in a balanced equation.

• Standard Heat of Reaction ($\Delta H^{\circ}$): Enthalpy change for a reaction at $1\,atm$ and $25\,^{\circ}C$.

Thermochemical Equations and Hess's Law

• Thermochemical Equations: Balanced chemical equations that include the associated $\Delta H^{\circ}$ value and specify the physical states of all participants.     * States matter: Changing from liquid water to gaseous water requires energy ($\Delta H_{\text{vap}} \approx 44\,kJ/mol$).

• Rules for Manipulating Equations:     1. If an equation is reversed, the sign of $\Delta H^{\circ}$ is reversed.     2. If coefficients are multiplied/divided by a factor, the $\Delta H^{\circ}$ is multiplied/divided by the same factor.     3. Physical states must match exactly to cancel substances from both sides.

• Hess's Law of Heat Summation: The enthalpy change for any reaction is the same whether it occurs in one step or several steps.     * $\Delta H^{\circ}<em>{\text{rxn}} = \sum \Delta H^{\circ}</em>{\text{steps}}$

• Standard Enthalpy of Formation ($\Delta H_f^{\circ}$):     * The heat change when one mole of a substance is formed from its elements in their standard states.     * Crucial Rule: The $\Delta H_f^{\circ}$ for any element in its most stable standard state is exactly $0$ (e.g., $\text{O}_2(g), \text{C}(s, \text{gr})$).

• Calculating $\Delta H^{\circ}<em>{\text{rxn}}$ using $\Delta H_f^{\circ}$:     * $\Delta H^{\circ}</em>{\text{rxn}} = \sum n\Delta H_f^{\circ}(\text{products}) - \sum m\Delta H_f^{\circ}(\text{reactants})$

Questions & Discussion

• Decrease in Potential Energy: Which occurs when a ball rolls downhill?     * Response: A ball rolling downhill represents a decrease in potential energy as it moves closer to the Earth's center (gravity).

• Kinetic Energy Accuracy: Which statement is true?     * Response: Atoms and molecules in gases, liquids, and solids possess KE since they are in constant motion. At the same temperature, they share the same average KE distribution.

• Internal Energy Calculation: A reaction contracts by $1.534\,L$ under $2.134\,atm$ pressure while releasing $200.7\,J$ of heat. Find $\Delta E$.     * Solution:         * $w = -P\Delta V = -2.134\,atm \times (-1.534\,L) = 3.274\,L \cdot atm$         * Conversion: $1.000\,L \cdot atm = 101.3\,J$         * $w = 3.274 \times 101.3 = 331.7\,J$         * $\Delta E = q + w = -200.7\,J + 331.7\,J = 131.0\,J$

• Specific Heat of Solid: A $43.29\,g$ solid at $99.8\,^{\circ}C$ is dropped into $152\,g$ of water at $22.5\,^{\circ}C$. The final temp is $24.3\,^{\circ}C$. Calculate specific heat ($s_{\text{solid}}$).     * Solution:         * $q_{\text{water}} = 152\,g \times 4.184\,J/g^{\circ}C \times (24.3 - 22.5) = 1.1 \times 10^3\,J$         * $q_{\text{solid}} = -1.1 \times 10^3\,J$         * $s_{\text{solid}} = \frac{-1.1 \times 10^3\,J}{43.29\,g \times (24.3 - 99.8)} = 0.35\,J/g^{\circ}C$

• Enthalpy of Formation Identification: Which corresponds to $\Delta H_f^{\circ}$ for $\text{NaHCO}_3(s)$?     * Response: $\text{Na}(s) + \frac{1}{2}\text{H}_2(g) + \frac{3}{2}\text{O}_2(g) + \text{C}(s, \text{gr}) \rightarrow \text{NaHCO}_3(s)$. (Note: Elements must be in standard states).

• Using $\Delta H_f^{\circ}$ for Reaction: Calculate for $4\text{NH}_3(g) + 7\text{O}_2(g) \rightarrow 4\text{NO}_2(g) + 6\text{H}_2 ext{O}(l)$ .     * Data: $\Delta H_f^{\circ}$ of $\text{NH}_3 = -46.0\,kJ/mol$, $\text{NO}_2 = 34\,kJ/mol$, $\text{H}_2 ext{O}(l) = -285.9\,kJ/mol$, $\text{O}_2 = 0$.     * Solution:         * $[4(34) + 6(-285.9)] - [4(-46.0) + 7(0)] = [136 - 1715.4] - [-184] = -1395.4\,kJ$.