Thermochemistry: First Law of Thermodynamics, Enthalpy, Hess’s Law, and Calorimetry

Thermochemistry

Introduction

Thermochemistry is the study of energy changes, particularly heat, that occur during chemical reactions and physical changes. It is a fundamental topic in general chemistry, providing insight into how energy is transferred and conserved in chemical processes.

Basics of Energy

Types of Energy

Energy is the capacity to do work or supply heat. In chemistry, energy is classified into two main types:

• Kinetic Energy (KE): The energy an object possesses due to its motion. For gases, the average kinetic energy per molecule is given by $KE = \frac{3}{2}RT$ (where $R$ is the gas constant and $T$ is temperature in Kelvin). For matter in general, $KE = \frac{1}{2}mv^2$.

• Potential Energy (PE): The energy stored due to an object's position, composition, or condition. In chemistry, this often refers to energy stored in chemical bonds.

The total energy of a system is the sum of its kinetic and potential energies:

$E_{total} = KE + PE$

Units of Energy

• Joule (J): The SI unit of energy. $1\,J = 1\,kg\,m^2/s^2$.

• Calorie (cal): The amount of energy required to raise the temperature of 1 g of water by 1°C. $1\,cal = 4.184\,J$ (exact).

• Calorie (Cal): Also known as a kilocalorie, $1\,Cal = 1000\,cal = 4184\,J$.

• L-atm: Used when calculating work involving gases.

First Law of Thermodynamics

Law of Conservation of Energy

The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another. The total energy of the universe remains constant.

$\Delta E_{universe} = 0$

For a system and its surroundings:

$\Delta E_{system} + \Delta E_{surroundings} = 0$

Internal Energy and State Functions

• Internal Energy (E): The sum of all kinetic and potential energies of the particles in a system.

• State Function: A property that depends only on the current state of the system, not on the path taken to reach that state. Internal energy ($E$) is a state function.

Energy Transfer: Heat and Work

Energy can be transferred between a system and its surroundings as heat ($q$) or work ($w$):

$\Delta E = q + w$

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

• Work (w): Energy transferred when an object is moved by a force.

Sign conventions:

• If heat enters a system, $q$ is positive.

• If heat leaves a system, $q$ is negative.

• If work is done on the system, $w$ is positive.

• If work is done by the system, $w$ is negative.

Heat, Temperature, and Thermal Energy

Definitions

• Heat: The transfer of thermal energy between objects due to a temperature difference.

• Temperature: A measure of the average kinetic energy of the particles in a substance.

• Thermal Energy: The total kinetic energy of the particles in a substance.

Exothermic and Endothermic Processes

• Exothermic Process: Releases heat to the surroundings. Example: Combustion of octane.

• Endothermic Process: Absorbs heat from the surroundings. Example: Dissolving ammonium nitrate in water (cold pack).

Heat Capacity and Specific Heat

Definitions

• Heat Capacity (C): The amount of heat required to raise the temperature of an object by 1°C. Depends on the object's mass and material.

• Specific Heat (c): The amount of heat required to raise the temperature of 1 gram of a substance by 1°C. An intrinsic property of the material.

Relationship:

$q = C \Delta T$

For specific heat:

$q = m c \Delta T$

Where:

• $q$ = heat absorbed or released (J)

• $m$ = mass (g)

• $c$ = specific heat (J/g·°C)

• $\Delta T$ = change in temperature (°C)

Comparison Table: Heat Capacity vs. Specific Heat

Property	Heat Capacity (C)	Specific Heat (c)
Depends on	Mass & Material	Material only
Units	J/°C	J/g·°C
Example	Large frying pan has larger C	Both pans have same c if same material

Energy Transfer Between Objects

Heat Exchange Principle

When two objects at different temperatures are placed in contact, heat flows from the hotter object to the colder one until thermal equilibrium is reached.

The heat lost by the hot object equals the heat gained by the cold object:

$q_{hot} + q_{cold} = 0$

Or, $q_{hot} = -q_{cold}$

Calculating Heat Energy

Sample Calculation

• Given: 800 g of water is heated from 21°C to 85°C. Specific heat of water $c = 4.18\,J/g·°C$.

• Calculate: $q = m c \Delta T = 800\,g \times 4.18\,J/g·°C \times (85 - 21)°C$

Work: Pressure-Volume Work

Definition and Formula

When a gas expands or contracts against an external pressure, work is done:

$w = -P_{ext} \Delta V$

• $P_{ext}$ = external pressure (atm)

• $\Delta V$ = change in volume (L)

Sign conventions:

• Expansion: $w < 0$ (system does work on surroundings)

• Compression: $w > 0$ (surroundings do work on system)

Calorimetry

Definition and Types

Calorimetry is the measurement of heat flow in a chemical or physical process. A calorimeter is a device used for this purpose, often consisting of an insulated container and a thermometer.

• Constant Pressure Calorimeter: Used for reactions in solution, typically open to the atmosphere (e.g., coffee cup calorimeter).

• Bomb Calorimeter: Used for reactions at constant volume, such as combustion.

Calorimetry Equations

At constant pressure:

$q_{rxn} = -q_{solution}$

$q_{solution} = m_{solution} c_{solution} \Delta T_{solution}$

For enthalpy change per mole:

$\Delta H = \frac{q_{rxn}}{n}$

Enthalpy and Enthalpy Change

Definition

Enthalpy (H): The sum of the internal energy of a system and the product of its pressure and volume:

$H = E + PV$

The enthalpy change ($\Delta H$) for a reaction at constant pressure is:

$\Delta H = H_{products} - H_{reactants}$

• Endothermic: $\Delta H > 0$ (system absorbs heat)

• Exothermic: $\Delta H < 0$ (system releases heat)

Stoichiometry of Enthalpy Change

Relationship to Reaction Amounts

The enthalpy change for a reaction depends on the amounts (coefficients) of reactants and products. For example, if the reaction is multiplied by a factor, $\Delta H$ is also multiplied by that factor.

Hess’s Law

Statement and Application

Hess’s Law states that the enthalpy change for a reaction is the same, regardless of the pathway taken, as long as the initial and final conditions are the same. This allows calculation of $\Delta H$ for complex reactions by summing the $\Delta H$ values of component reactions.

Example:

• Step 1: $C + \frac{1}{2}O_2 \rightarrow CO$ $\Delta H_1$

• Step 2: $CO + \frac{1}{2}O_2 \rightarrow CO_2$ $\Delta H_2$

• Overall: $C + O_2 \rightarrow CO_2$ $\Delta H_{overall} = \Delta H_1 + \Delta H_2$

Standard Enthalpy of Formation

Definition

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 at 1 atm and 25°C.

Calculating Standard Enthalpy Change

The standard enthalpy change for a reaction is calculated using:

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

Where $n$ is the stoichiometric coefficient.

Sample Table: Standard Enthalpies of Formation

Compound	$\Delta H_f^\circ$ (kJ/mol)
H2O(l)	-285.8
CO2(g)	-393.5
NH3(g)	-46
NO(g)	90.3
NO2(g)	33.7
HNO3(aq)	-207.4
Additional info: Values inferred from standard tables; see Appendix 4 in most textbooks for a complete list.

Summary of Key Principles

• Energy is conserved in chemical reactions (First Law of Thermodynamics).

• Heat and work are two ways energy is transferred between system and surroundings.

• Heat capacity and specific heat are important for quantifying temperature changes.

• Calorimetry allows measurement of heat changes in reactions.

• Enthalpy change ($\Delta H$) is a state function and can be calculated using Hess’s Law and standard enthalpies of formation.

Example Application

Calculate the enthalpy change for the reaction:

$2NO_2(g) + H_2O(l) \rightarrow 2HNO_3(aq) + NO(g)$

Given standard enthalpies of formation:

• $\Delta H_f^\circ$(NO2(g)) = 33.7 kJ/mol

• $\Delta H_f^\circ$(H2O(l)) = -285.8 kJ/mol

• $\Delta H_f^\circ$(HNO3(aq)) = -207.4 kJ/mol

• $\Delta H_f^\circ$(NO(g)) = 90.3 kJ/mol

Apply the formula:

$\Delta H_{rxn}^\circ = [2 \times (-207.4) + 1 \times 90.3] - [2 \times 33.7 + 1 \times (-285.8)]$

Additional info: This calculation demonstrates the use of standard enthalpies of formation in determining reaction enthalpy.