Chapter 6: Thermochemistry – Study Notes

Thermochemistry

Introduction to Thermochemistry

Thermochemistry is the study of the energy and heat changes that accompany chemical reactions and physical transformations. It is a branch of thermodynamics, which deals with the general study of energy and its interconversions. Understanding thermochemistry is essential for predicting the energy requirements and releases in chemical processes.

The Nature of Energy

Definitions and Concepts

• Energy: The capacity to do work.

• Thermodynamics: The study of energy and its interconversions.

• Thermochemistry: The study of relationships between chemistry and energy, especially heat.

Ways to Transfer Energy

• Heat (q): Flow of energy caused by a temperature difference between system and surroundings.

• Work (w): Energy transfer resulting from a force acting through a distance.

Types of Energy

Kinetic Energy

Kinetic energy is the energy associated with the motion of an object.

• Formula: $KE = \frac{1}{2}mv^2$ where m is mass (kg) and v is velocity (m/s).

• SI unit: Joule (J), where $1\,J = 1\,kg\cdot m^2\cdot s^{-2}$

• Thermal energy: A form of kinetic energy associated with the temperature of an object, resulting from the motion of atoms and molecules.

Example: Higher temperature corresponds to greater molecular motion.

Potential Energy

Potential energy is energy associated with the position or composition of an object.

• Gravitational potential energy: $PE = mgh$ (where g is acceleration due to gravity, h is height).

• Elastic potential energy: $PE = \frac{1}{2}kx^2$ (where k is the spring constant, x is displacement).

• Chemical energy: A form of potential energy associated with the relative positions of electrons and nuclei in atoms and molecules.

Units of Energy

Energy Conversion Factors

Energy can be measured in several units. The SI unit is the joule (J).

Unit	Equivalent in Joules (J)
1 calorie (cal)	4.184 J
1 Calorie (Cal) or kilocalorie (kcal)	1000 cal = 4184 J
1 kilowatt-hour (kWh)	3.60 × 106 J

Example Calculation

Calculate the average kinetic energy (in J and cal) of a nitrous oxide (N2O) molecule with a given speed.

• Given: Average speed = 37 m/s, molar mass = 44.02 g/mol

• Use $KE = \frac{1}{2}mv^2$

Law of Conservation of Energy

First Law of Thermodynamics

• The total energy of the universe is constant.

• Energy can neither be created nor destroyed, only transferred between system and surroundings.

Definitions

• System: The part of the universe under study.

• Surroundings: Everything else outside the system.

Internal Energy (U)

Definition and Calculation

• Internal energy is the sum of the kinetic and potential energies of all particles in a system.

• Mathematically: $U = U_{kinetic} + U_{potential}$

• Change in internal energy: $\Delta U = q + w$

Sign Conventions

Quantity	Positive (+)	Negative (–)
q (heat)	System gains thermal energy	System loses thermal energy
w (work)	Work done on the system	Work done by the system
$\Delta U$	Energy flows into the system	Energy flows out of the system

State Functions vs. Path Functions

Definitions

• State function: A property whose value depends only on the state of the system, not on how it got there (e.g., internal energy, altitude).

• Path function: A property that depends on the specific path taken to reach a state (e.g., distance traveled).

Example: Change in temperature ($\Delta T = T_f - T_i$) is a state function.

Quantifying Heat and Work

Heat (q)

• Exchange of thermal energy between system and surroundings due to a temperature difference.

• Thermal energy always moves from higher to lower temperature until thermal equilibrium is reached.

Heat Capacity and Specific Heat

• Heat capacity (C): Quantity of heat required to change the temperature of a system by 1°C.

• Formula: $q = C \times \Delta T$

• Specific heat capacity (C_s): Heat required to raise the temperature of 1 g of a substance by 1°C.

• Formula: $q = m \times C_s \times \Delta T$

• Molar heat capacity (C_m): Heat required to raise the temperature of 1 mol of a substance by 1°C.

• Formula: $q = n \times C_m \times \Delta T$

Substance	Specific Heat Capacity (J g–1 °C–1)
Lead	0.128
Gold	0.129
Silver	0.235
Copper	0.385
Iron	0.449
Aluminum	0.900
Water	4.184
Granite (Pyrox)	0.790
Sand	0.84

Thermal Energy Transfer

• When two substances at different temperatures are combined, thermal energy flows from the hotter to the cooler substance until equilibrium is reached.

• Mathematically: $q_{sys} = -q_{surr}$ or $-q_{metal} = q_{water}$

• For heat transfer problems: $m_{metal} C_{s,metal} \Delta T_{metal} = m_{water} C_{s,water} \Delta T_{water}$

Quantifying Heat and Work: Work

Pressure-Volume Work

• Work is done when a force acts through a distance.

• Pressure-volume work occurs when a system changes volume against an external pressure.

• Formulas:

  • $w = -P_{ext} \Delta V$

  • For gases: $w = -\Delta nRT$ (where $\Delta n$ is the change in moles of gas, $R$ is the gas constant, $T$ is temperature in K)

Measuring Internal Energy Changes

Constant-Volume Calorimetry (Bomb Calorimeter)

• Used to measure $\Delta U$ for combustion reactions at constant volume.

• Heat absorbed by calorimeter: $q_{cal} = C_{cal} \times \Delta T$

• At constant volume: $\Delta U = q_v$

• For reactions: $q_{rxn} = -q_{cal}$

• To obtain per mole: $q_r = \frac{\Delta U}{n}$

Heat at Constant Pressure: Enthalpy (H)

Definition and Calculation

• Enthalpy ($H$) is the sum of the internal energy and the product of pressure and volume: $H = U + PV$

• Change in enthalpy: $\Delta H = \Delta U + P\Delta V$

• At constant pressure: $\Delta H = q_p$ (heat at constant pressure)

• If there is a change in the amount of gas, $\Delta H = \Delta U + \Delta nRT$

Endothermic vs. Exothermic Reactions

Type	Sign of $\Delta H$	Description
Endothermic	$\Delta H > 0$	Absorbs heat from surroundings; feels cold
Exothermic	$\Delta H < 0$	Releases heat to surroundings; feels warm

Stoichiometry Involving Enthalpy ($\Delta H$)

Thermochemical Equations

• Thermochemical equations show the enthalpy change for the stoichiometric amounts of reactants and products.

• Example: $C_3H_8(g) + 5 O_2(g) \rightarrow 3 CO_2(aq) + 4 H_2O(l)$, $\Delta H = -2044$ kJ/mol

• To calculate heat for a given mass:

  • Convert mass to moles

  • Multiply by $\Delta H$ per mole

Example Calculation: For 47.9 kg of $O_2$, $q = 47.9 \times 10^3 \text{ g} \times \frac{1 \text{ mol}}{32.00 \text{ g}} \times \frac{-2044 \text{ kJ}}{5 \text{ mol}} = -6.12 \times 10^5$ kJ

Summary Table: Key Equations

Concept	Equation
Kinetic Energy	$KE = \frac{1}{2}mv^2$
Change in Internal Energy	$\Delta U = q + w$
Heat (using heat capacity)	$q = C \times \Delta T$
Heat (using specific heat)	$q = m \times C_s \times \Delta T$
Pressure-Volume Work	$w = -P_{ext} \Delta V$
Enthalpy Change	$\Delta H = \Delta U + P\Delta V$
Work for Gases	$w = -\Delta nRT$

Additional info: These notes are based on lecture slides and cover all foundational aspects of thermochemistry, including definitions, equations, and example applications. Practice problems and further examples are recommended for mastery.