Thermochemistry: Energy, Calorimetry, and Enthalpy in Chemical Reactions

Chapter 9: Thermochemistry

9.1 Energy Basics

Thermochemistry is the study of heat absorbed or released during chemical and physical changes. Understanding energy changes is essential for analyzing chemical reactions and their practical applications.

• Energy: The capacity to supply heat or do work.

• Work: A force acting over a distance. Formula: $\text{Energy} = \text{work} = \text{force} \times \text{distance}$

• Energy can be exchanged between objects through contact (collisions).

• Potential energy: Energy due to position, composition, or condition.

• Kinetic energy: Energy due to motion.

Law of Conservation of Energy

Energy cannot be created or destroyed, only transformed. This principle is the foundation of the first law of thermodynamics.

• First Law of Thermodynamics: The total energy in the universe is constant.

• Mathematical expression: $E = \text{constant}$ $\Delta E_{\text{universe}} = 0$ $\Delta E_{\text{system}} = -\Delta E_{\text{surroundings}}$ $\Delta E_{\text{system}} + \Delta E_{\text{surroundings}} = 0$

Thermal Energy and Temperature

Thermal energy is a form of kinetic energy associated with the random motion of atoms and molecules. Temperature quantitatively measures how 'hot' or 'cold' a substance is.

• Fast-moving molecules: High thermal energy, 'hot'

• Slow-moving molecules: Low thermal energy, 'cold'

Heat

Heat (q) is the transfer of thermal energy between two bodies at different temperatures. Heat always flows from the higher temperature substance to the lower temperature substance until thermal equilibrium is reached.

• Thermal equilibrium: Both objects reach the same temperature.

• Temperature: Measures the thermal energy within a sample.

Heat Units

Energy is measured in various units, with the SI unit being the joule (J).

• Calorie (cal): Energy required to raise 1 g of water by 1°C (or 1 K).

• Calorie (Cal): Large calorie, used for food energy; 1 Cal = 1 kilocalorie (kcal).

• Joule (J): Energy used when a force of 1 newton moves an object 1 meter. $1 \text{calorie} = 4.184 \text{joules}$

• Kinetic energy formula: $KE = \frac{1}{2}mv^2$

Heat Capacity

Heat capacity is the amount of heat required to change the temperature of a body of matter by 1°C (or 1 K).

• Formula: $C = \frac{q}{\Delta T}$

• Heat capacity is an extensive property (depends on amount).

• The temperature increase is proportional to the heat absorbed.

• Heat capacity depends on the type and amount of material.

Specific Heat Capacity

Specific heat capacity (c) is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C (or 1 K). It is an intensive property (depends only on the substance).

• Formula: $c = \frac{q}{m \Delta T}$

• For example, the specific heat of water is 4.184 J/g·°C.

Table: Specific Heats of Common Substances at 25°C and 1 bar

Substance	Symbol (state)	Specific Heat (J/g·°C)
Helium	He(g)	5.193
Water	H2O(l)	4.184
Ethanol	C2H5OH(l)	2.376
Ice	H2O(s)	2.093
Water vapor	H2O(g)	1.864
Nitrogen	N2(g)	1.040
Air		1.007
Oxygen	O2(g)	0.918
Aluminum	Al(s)	0.897
Carbon dioxide	CO2(g)	0.853
Argon	Ar(g)	0.522
Iron	Fe(s)	0.449
Copper	Cu(s)	0.385
Lead	Pb(s)	0.128
Gold	Au(s)	0.129
Silicon	Si(s)	0.712

Calculating Heat

The amount of heat entering or leaving a substance can be calculated using:

• Formula: $q = c \times m \times \Delta T$ $q = c \times m \times (T_f - T_i)$

• If $T_f > T_i$, $q$ is positive (heat gained).

• If $T_f < T_i$, $q$ is negative (heat lost).

Example:

A flask containing $8.0 \times 10^2$ g of water is heated from 21°C to 85°C. How much heat is absorbed?

• $q = (4.184 \text{ J/g·°C}) \times (8.0 \times 10^2 \text{ g}) \times (85 - 21)$

• $q = 2.1 \times 10^5 \text{ J}$

9.2 Calorimetry

Calorimetry is the technique used to measure the amount of heat involved in chemical or physical processes.

• Calorimeter: Device used to measure heat transfer.

• Processes measured in calorimeters often occur in solution.

• If the reaction is exothermic, heat is released to the solution.

• If the reaction is endothermic, heat is absorbed from the solution.

System and Surroundings

• System: The substance(s) undergoing change.

• Surroundings: Everything else, including the calorimeter and solution.

Coffee-Cup Calorimeter

• Used for reactions at constant pressure (open to atmosphere).

• Often constructed from nested foam cups.

Bomb Calorimeter

• Used for reactions producing large amounts of heat and gases (e.g., combustion).

• Consists of a steel container submerged in water.

Calorimetry Principles

When a hot object (M) is placed in cool water (W) in a calorimeter, heat flows from M to W until thermal equilibrium is reached.

• The net change in heat is zero: $q_M + q_W = 0$

• Heat gained by M equals heat lost by W: $q_M = -q_W$

• For both substances: $m_{\text{metal}} \times c_{\text{metal}} \times \Delta T_{\text{metal}} = -m_{\text{water}} \times c_{\text{water}} \times \Delta T_{\text{water}}$

Example:

A 360-g piece of rebar is dropped into 425 mL of water at 24.0°C. The final temperature is 42.7°C. Calculate the initial temperature of the rebar.

• Set up: $(0.449 \text{ J/g·°C})(360 \text{ g})(42.7 - T_{\text{initial}}) = -(4.184 \text{ J/g·°C})(425 \text{ g})(42.7 - 24.0)$

• Solve for $T_{\text{initial}}$.

9.3 Enthalpy

Enthalpy (H) is a thermodynamic quantity equivalent to the total heat content of a system. It is especially useful for processes occurring at constant pressure.

• Formula: $H = U + PV$

• Enthalpy change ($\Delta H$) is measured for chemical and physical processes.

• At constant pressure: $\Delta H = \Delta U + P\Delta V$

• For reactions at constant pressure, $\Delta H$ equals the heat exchanged.

Thermochemical Equations

• Show both the chemical change and the enthalpy change.

• Example: $2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \quad \Delta H = -572 \text{ kJ}$

• If the equation is reversed, the sign of $\Delta H$ is reversed.

• If coefficients are multiplied, $\Delta H$ is multiplied by the same factor.

• $\Delta H < 0$: Exothermic reaction; $\Delta H > 0$: Endothermic reaction.

Standard Enthalpy of Formation

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

• Elements in their standard state have $\Delta H_f^\circ = 0$.

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

Calculating Standard Enthalpy Change for a Reaction

• Any reaction can be written as the sum of formation reactions.

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

Hess's Law

Hess's Law states that the enthalpy change for a reaction is the same whether it occurs in one step or several steps. This allows calculation of $\Delta H$ for reactions that are difficult to measure directly.

• If a reaction can be expressed as a series of steps, $\Delta H$ for the overall reaction is the sum of the $\Delta H$ values for each step.

• Enthalpy is a state function; only the initial and final states matter.

9.4 Strengths of Ionic and Covalent Bonds

The strength of chemical bonds affects the energy changes in reactions. Ionic compounds are stabilized by lattice energy, while covalent bonds are characterized by bond energies.

Lattice Energy

• Lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions.

• Formula: $\Delta H_{\text{lattice}} \propto \frac{z^+ z^-}{r}$ where $z^+$ and $z^-$ are the charges, and $r$ is the distance between ions.

• Lattice energy increases with higher ion charge and decreases with larger ion size.

Bond Energies

• Bond energy is the energy required to break one mole of a bond in the gas phase.

• Bond breaking is endothermic (energy in, $\Delta H > 0$); bond making is exothermic (energy out, $\Delta H < 0$).

• Formula: $\Delta H_{\text{reaction}} \approx \sum \text{(bond energies broken)} - \sum \text{(bond energies formed)}$

• Stronger bonds have higher bond energies and are shorter in length.

Trends in Bond Energies and Lengths

• More shared electrons (triple > double > single) = stronger, shorter bonds.

• Bonds get weaker and longer down a group due to increasing atomic size.

Example Table: Bond Energies

Bond	Bond Energy (kJ/mol)
C=C	602
C-H	413
O=O	495
C=O	799
O-H	457

Summary

• Thermochemistry connects energy changes to chemical reactions.

• Calorimetry allows measurement of heat changes in reactions.

• Enthalpy and Hess's Law provide tools for calculating energy changes.

• Bond and lattice energies explain the stability and energy requirements of compounds.

Additional info: These notes are based on textbook slides and include expanded academic context for clarity and completeness.