Energy, Enthalpy, and Thermochemistry: Study Notes

Energy, Enthalpy, and Thermochemistry

Introduction to Thermodynamics

Thermodynamics is the study of energy and its interconversions, particularly as they relate to chemical and physical processes. Understanding energy changes is fundamental to predicting whether reactions will occur and how much energy will be released or absorbed.

• Thermodynamics: The study of energy, work, and heat, and their transformations.

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

• Potential Energy: Energy due to position or composition (e.g., chemical bonds).

• Kinetic Energy: Energy due to motion.

• First Law of Thermodynamics: Energy cannot be created or destroyed, only converted from one form to another.

Additional info: Energy can be stored in chemical bonds and released during chemical reactions.

Energy

Types and Concepts

Energy in chemistry is often discussed in terms of kinetic and potential energy, and how these forms change during chemical reactions.

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

• Surroundings: Everything outside the system.

• Exothermic process: Releases energy to the surroundings (temperature increases).

• Endothermic process: Absorbs energy from the surroundings (temperature decreases).

• Activation Energy: The minimum energy required to initiate a reaction.

Example: Combustion of methane is exothermic, releasing heat to the surroundings.

Chemical Energy

Energy Changes in Chemical Reactions

Chemical energy is stored in the bonds of substances and is released or absorbed during chemical reactions.

• Identify q (heat), w (work), and ΔE (change in internal energy).

• ΔE = q + w

• ΔE is positive if energy flows into the system, negative if energy flows out.

Example: When a gas expands against a piston, it does work on the surroundings.

State Functions

Definition and Importance

A state function is a property whose value depends only on the current state of the system, not on the path taken to reach that state.

• Examples: Internal energy (E), enthalpy (H), pressure (P), volume (V), temperature (T).

• Work and heat are not state functions.

Internal Energy (E)

Definition and Calculation

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

• ΔE = q + w

• q: heat absorbed by the system

• w: work done on the system

• Sign conventions: q > 0 (endothermic), q < 0 (exothermic); w > 0 (work done on system), w < 0 (work done by system)

Example: If a system absorbs 100 J of heat and does 40 J of work on the surroundings, ΔE = 100 J - 40 J = 60 J.

Expansion and Compression of Gases

Work Done by Gases

When a gas expands or is compressed, work is done by or on the system.

• Work (w) = -PΔV

• P: external pressure

• ΔV: change in volume (Vfinal - Vinitial)

• Expansion: ΔV > 0, w < 0 (system does work on surroundings)

• Compression: ΔV < 0, w > 0 (work done on system)

Example: If a gas expands from 2.0 L to 5.0 L against a constant pressure of 1.0 atm, w = -1.0 atm × (5.0 L - 2.0 L) = -3.0 L·atm.

Additional info: 1 L·atm = 101.3 J

Heat, q

Flow of Energy Due to Temperature Difference

Heat is the transfer of energy due to a temperature difference between the system and its surroundings.

• Sign conventions: q > 0 (endothermic), q < 0 (exothermic)

• Units: Joules (J), calories (cal), 1 cal = 4.184 J

• Calculation: q = mCΔT

• m: mass (g), C: specific heat capacity (J/g·°C), ΔT: change in temperature (°C)

Example: Heating 100 g of water (C = 4.18 J/g·°C) from 25°C to 75°C: q = 100 × 4.18 × (75 - 25) = 20,900 J

Measurement of Heat Flow: Calorimetry

Coffee-Cup Calorimeter

Calorimetry is the measurement of heat flow in a chemical or physical process. A coffee-cup calorimeter is used for reactions at constant pressure (usually in solution).

• qsolution = m × C × ΔT

• qreaction = -qsolution

• Assumes no heat loss to the surroundings.

Example: Dissolving NaCl in water and measuring the temperature change to determine the enthalpy of solution.

Bomb Calorimeter

Used for reactions involving gases, high temperatures, or substances that dissolve poorly in water. Operates at constant volume.

• qreaction = -Ccalorimeter × ΔT

• Ccalorimeter: heat capacity of the calorimeter

Example: Combustion of a hydrocarbon in a bomb calorimeter to determine its energy content.

Enthalpy (H)

Definition and Properties

Enthalpy is a state function that represents the heat content of a system at constant pressure.

• ΔH = qp (heat at constant pressure)

• ΔH > 0: endothermic process

• ΔH < 0: exothermic process

Example: The enthalpy change for the combustion of methane is negative, indicating an exothermic reaction.

Thermochemical Equations

Writing and Interpreting

Thermochemical equations show the enthalpy change associated with a chemical reaction.

• Must specify physical states of reactants and products.

• ΔH values depend on the states of substances.

• ΔH is proportional to the amount of substance reacted.

Example: $\mathrm{H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l)}$ $\Delta H = -285.8\ \mathrm{kJ}$

Rules of Thermochemistry

Key Principles

• The magnitude of ΔH is directly proportional to the amount of reactant or product.

• Reversing a reaction changes the sign of ΔH.

• ΔH is the same whether a reaction occurs in one step or several steps (Hess's Law).

Example: If the reaction is reversed, the sign of ΔH is also reversed.

Hess's Law

Combining Reactions

Hess's Law states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in.

• Allows calculation of ΔH for reactions that are difficult to measure directly.

• ΔHoverall = sum of ΔH for individual steps.

Example: Calculating ΔH for the formation of CO2 from C and O2 using known enthalpies of intermediate reactions.

Enthalpy of Formation (ΔHf°)

Standard Enthalpy of Formation

The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states.

• Standard state: 1 atm pressure, 25°C (298 K), 1 M concentration for solutions.

• ΔHf° for an element in its standard state is zero.

Example: $\mathrm{C(graphite) + 2H_2(g) \rightarrow CH_4(g)}$ $\Delta H_f^\circ = -74.8\ \mathrm{kJ/mol}$

Using Standard Enthalpies of Formation

The enthalpy change for a reaction can be calculated using standard enthalpies of formation:

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

Example: Calculating ΔH for the combustion of benzene using tabulated ΔHf° values.

Table: Selected Standard Enthalpies of Formation (ΔHf°)

The following table summarizes standard enthalpy of formation values for selected substances (values in kJ/mol):

Substance	ΔHf° (kJ/mol)
H2O(l)	-285.8
CO2(g)	-393.5
CH4(g)	-74.8
O2(g)	0
C(graphite)	0
NH3(g)	-45.9
NaCl(s)	-411
Additional info: Many more values are available in standard tables.

Summary

• Thermodynamics and thermochemistry provide the framework for understanding energy changes in chemical reactions.

• Key concepts include internal energy, enthalpy, heat, work, and the use of calorimetry.

• Standard enthalpies of formation and Hess's Law are essential tools for calculating reaction enthalpies.