Thermochemistry: Study Notes for General Chemistry

Ch.7 - Thermochemistry

Nature of Energy

Thermochemistry is the study of energy and its transformations during chemical reactions and physical changes. Energy is the capacity to do work or produce heat.

• Energy: Exists in various forms, including kinetic and potential energy.

• Thermochemistry: Focuses on energy changes associated with chemical reactions.

Type of Energy	Description
Kinetic Energy	Energy due to motion
Potential Energy	Energy due to position or composition

• Energy Conversion Factors: 1 calorie (cal) = 4.184 joules (J); 1 kilowatt-hour (kWh) = 3.60 × 106 J

Kinetic and Potential Energy

Mechanical energy is the sum of kinetic and potential energy in an object.

• Kinetic Energy Formula: $KE = \frac{1}{2}mv^2$

• Potential Energy Formula: $PE = mgh$

• m: mass (kg), v: velocity (m/s), g: acceleration due to gravity (9.8 m/s2), h: height (m)

Example: Calculate the kinetic energy of an electron (m = 9.11 × 10-31 kg) moving at 1.58 × 106 m/s.

First Law of Thermodynamics

The first law states that energy cannot be created or destroyed, only transformed between system and surroundings.

• System: The part of the universe being studied.

• Surroundings: Everything outside the system.

• Internal Energy (E): The total energy of a system.

Example: A chemical reaction in a metal sample releases 11.1 kJ of energy; the temperature change is measured to determine energy transfer.

Heat and Work

Energy transfer between system and surroundings occurs as heat (q) or work (w).

• Heat (q): Energy transferred due to temperature difference.

• Work (w): Energy transferred when a force moves an object.

• Sign conventions: Heat absorbed by system (+q), heat released (-q); work done on system (+w), work done by system (-w).

Internal Energy

Internal energy change ($\Delta E$) is the sum of heat and work exchanged with the surroundings.

• Formula: $\Delta E = q + w$

• For pressure-volume work: $w = -P\Delta V$

• Units: Joules (J)

Example: Calculate $\Delta E$ for a reaction at constant pressure of 2.0 atm, volume compression from 15.0 L to 5.0 L, releasing 72.0 kJ of heat.

Endothermic and Exothermic Reactions

Reactions are classified by whether they absorb or release heat.

• Endothermic: Absorbs heat from surroundings; $q > 0$

• Exothermic: Releases heat to surroundings; $q < 0$

Reaction Type	Heat Flow	Example
Endothermic	Absorbs heat	Melting ice
Exothermic	Releases heat	Combustion of gasoline

Heat Capacity

Heat capacity is the amount of heat required to change the temperature of a substance.

• Molar Heat Capacity (C): $C = \frac{q}{n\Delta T}$

• Specific Heat Capacity (c): $c = \frac{q}{m\Delta T}$

• q: heat (J), n: moles, m: mass (g), ΔT: temperature change (°C)

Example: If 15.7 g of silver raises its temperature by 17.2 °C when it absorbs 648.5 J, what is its molar heat capacity?

Measurement: Specific Heat Capacity

Specific heat capacity formula allows calculation of heat absorbed or released:

• Formula: $q = mc\Delta T$

Example: How much heat is released when 120.0 g H2O cools from 95 °C to 43 °C? (c = 4.184 J/g·°C)

Constant-Pressure Calorimetry

Calorimetry measures heat changes in chemical reactions. A coffee-cup calorimeter operates at constant pressure.

• Formula: $q_{solution} = m \times c \times \Delta T$

• Heat capacity of calorimeter: $C_{cal} = \frac{q_{cal}}{\Delta T}$

Example: 60.0 g of lead at 98.0 °C is added to 50.0 g H2O at 30.0 °C; temperature rises to 36.0 °C. Calculate heat capacity of calorimeter.

Constant-Volume Calorimetry (Bomb Calorimeter)

Bomb calorimeters measure heat of combustion at constant volume.

• Formula: $q_{cal} = C_{cal} \Delta T$

• Heat of combustion: $\Delta E_{rxn} = q_{cal}$

Example: Burning 12.1 g of a sample increases temperature by 15.2 °C; $C_{cal} = 1560$ J/°C. Find heat capacity.

Thermal Equilibrium

Thermal equilibrium occurs when substances in contact reach the same temperature and no net heat flows between them.

• Heat transfers until equilibrium is reached.

• Final temperature can be calculated using heat capacities and masses.

Example: 50.0 g of metal at 250 °C is placed in solution at 90 °C; calculate final temperature.

Thermochemical Equations

Thermochemical equations relate the stoichiometry of a reaction to its enthalpy change ($\Delta H$).

• Balanced chemical equations include $\Delta H$ values.

• Stoichiometry allows calculation of heat change for given amounts of reactants/products.

Example: 2 Mg (s) + O2 (g) → 2 MgO (s); $\Delta H = -1204$ kJ

Formation Equations and Standard States

Standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when one mole of a compound forms from its elements in their standard states.

• Standard state: Most stable form of an element at 1 atm and 25 °C.

• Formation equations use elements in standard states as reactants.

Element	Standard State
Oxygen	O2 (g)
Hydrogen	H2 (g)
Carbon	C (s, graphite)

Example: Write the formation equation for methane, CH4(g).

Enthalpy of Formation

Enthalpy of formation is determined using calorimetry or tabulated values.

• Formula: $\Delta H_{rxn} = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})$

Example: Calculate $\Delta H_{rxn}$ for the oxidation of ammonia using standard enthalpies of formation.

Hess's Law

Hess's Law states that the enthalpy change for a reaction is the same whether it occurs in one step or multiple steps.

• Allows calculation of $\Delta H$ for complex reactions by combining known reactions.

• Reverse reaction: Change sign of $\Delta H$; multiply/divide reaction: multiply/divide $\Delta H$ accordingly.

Example: Calculate $\Delta H$ for the formation of barium trioxide from given reactions.

Applying Hess's Law

To use Hess's Law, manipulate and sum equations so that the desired overall reaction is obtained.

• Identify partial reactions and their $\Delta H$ values.

• Sum $\Delta H$ values for the overall reaction.

Example: Given reactions for CO and H2O, calculate $\Delta H$ for the overall reaction.

Summary Table: Specific Heat Capacities

Substance	Specific Heat Capacity (J/g·°C)
Water	4.184
Copper	0.385
Ethanol	2.44
Wood	1.76

Additional info: These notes cover all major concepts in college-level thermochemistry, including energy, heat, work, calorimetry, enthalpy, and Hess's Law, with formulas, examples, and tables for reference.