Thermochemistry: Energy, Enthalpy, and Calorimetry

Thermochemistry

Introduction

Thermochemistry is the study of the energy and heat associated with chemical reactions and physical transformations. It is a fundamental topic in General Chemistry, providing insight into how energy is transferred and conserved in chemical processes.

Energy in Chemistry

Definition and Types of Energy

• Energy: The potential or capacity to move matter. In chemistry, energy is crucial for driving reactions and changes in state.

• Units of Energy: Common units include calories (cal), kilocalories (kcal), joules (J), and kilojoules (kJ).

• Conversion Factor: $1\ \text{cal} = 4.184\ \text{J}$

• Potential Energy: Stored energy due to position or composition.

• Kinetic Energy: Energy of motion, proportional to mass and the square of velocity.

Law of Conservation of Energy

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

Energy Unit Conversion Factors

The following table summarizes common energy unit conversions:

Unit	Equivalent
calorie (cal)	4.184 joules (J)
kilocalorie (kcal) or Calorie (Cal)	1000 cal = 4184 J
watt-hour (kWh)	$3.60 \times 10^6$ J

Energy Transfer

System and Surroundings

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

• Surroundings: Everything outside the system.

Energy is transferred between the system and surroundings until thermal equilibrium is reached (no temperature difference).

• Example (Ice Melting): The ice (system) absorbs energy (gets warmer), surroundings lose energy (get cooler).

• Example (Water Freezing): The water (system) loses energy (gets cooler), surroundings (e.g., freezer) absorb energy (get warmer).

Heat of Reaction

Definition of Heat (q)

• Heat (q): The energy that flows into or out of a system due to a temperature difference between the system and its surroundings.

Exothermic and Endothermic Reactions

• Exothermic Reaction: Releases heat to the surroundings ($q < 0$). The reaction vessel warms up.

• Endothermic Reaction: Absorbs heat from the surroundings ($q > 0$). The reaction vessel cools down.

Examples:

• $\mathrm{CH_4(g) + 2\ O_2(g) \rightarrow CO_2(g) + 2\ H_2O(g)}$    $q = -890\ \text{kJ}$ (exothermic)

• $\mathrm{NH_4NO_3(s) \rightarrow NH_4^+(aq) + NO_3^-(aq)}$    $q = 36\ \text{kJ}$ (endothermic)

Enthalpy (ΔH)

Definition and Properties

• Enthalpy (ΔH): The heat content of a system at constant pressure. For chemical reactions, $\Delta H$ is the heat of reaction at constant pressure.

• Mathematically: $\Delta H = q$ (at constant pressure)

Manipulating Enthalpy Changes

• If a reaction is multiplied by a factor, $\Delta H$ is multiplied by the same factor.

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

Examples:

• $\mathrm{N_2(g) + 3\ H_2(g) \rightarrow 2\ NH_3(g)}$    $\Delta H = -92\ \text{kJ}$

• Double the equation: $2\mathrm{N_2(g) + 6\ H_2(g) \rightarrow 4\ NH_3(g)}$    $\Delta H = -184\ \text{kJ}$

• Reverse the equation: $2\mathrm{NH_3(g) \rightarrow N_2(g) + 3\ H_2(g)}$    $\Delta H = +92\ \text{kJ}$

Stoichiometry of ΔH

• Enthalpy changes are typically reported per mole of reaction as written.

• To calculate the heat evolved or absorbed for a given amount of reactant, use stoichiometry:

Example:

• Given: $\mathrm{CH_4(g) + 2\ O_2(g) \rightarrow CO_2(g) + 2\ H_2O(g)}$    $\Delta H = -890\ \text{kJ}$

• Calculate heat for 7.33 g CH4:

$7.33\ \text{g CH}_4 \times \frac{1\ \text{mol CH}_4}{16.05\ \text{g}} \times \frac{-890\ \text{kJ}}{1\ \text{mol CH}_4} = -406\ \text{kJ}$

Calorimetry

Measuring Heat Changes

• Calorimetry: The measurement of heat flow in a chemical or physical process.

• Specific Heat (s): The amount of heat required to raise the temperature of 1 g of a substance by 1°C at constant pressure.

• Heat Capacity (C): The amount of heat required to raise the temperature of an object by 1°C.

Calorimetry Equations

• When using specific heat:

$q = sm\Delta T$

• When using heat capacity:

$q = C\Delta T$

• Where:

  • $q$ = heat (J or kJ)

  • $s$ = specific heat (J/g·°C)

  • $m$ = mass (g)

  • $C$ = heat capacity (J/°C or kJ/°C)

  • $\Delta T = T_{final} - T_{initial}$ (°C)

Example: Calculate the heat needed to raise 19.0 g of H2O from 11°C to 88°C. (Specific heat of water = 4.184 J/g·°C)

$q = (4.184\ \text{J/g·°C}) \times (19.0\ \text{g}) \times (88 - 11)\ ^\circ\text{C} = 6,110\ \text{J}$

Hess's Law

Definition and Application

• Hess's Law: The enthalpy change for a reaction is the same, regardless of the number of steps or pathway taken, as long as the initial and final conditions are the same.

• Allows calculation of $\Delta H$ for a reaction by combining known enthalpy changes of other reactions.

Example:

• Given reactions:

  • $\mathrm{S(s) + O_2(g) \rightarrow SO_2(g)}$    $\Delta H = -297\ \text{kJ}$

  • $\mathrm{2SO_2(g) + O_2(g) \rightarrow 2SO_3(g)}$    $\Delta H = -198\ \text{kJ}$

• Target reaction: $\mathrm{2S(s) + 3O_2(g) \rightarrow 2SO_3(g)}$

• Combine and manipulate the given reactions to obtain the target reaction and sum their $\Delta H$ values accordingly.

Standard Enthalpies of Formation (ΔH°f)

Definition

• Standard Enthalpy of Formation ($\Delta H^\circ_f$): The enthalpy change when one mole of a compound is formed from its elements in their standard states at 1 atm and 25°C.

• By convention, $\Delta H^\circ_f$ for all elements in their most stable form (including H2, O2, N2, etc.) is zero.

Calculating Reaction Enthalpy from Formation Enthalpies

• The standard enthalpy change for a reaction can be calculated using:

$\Delta H^\circ_{rxn} = \sum \Delta H^\circ_f \text{(products)} - \sum \Delta H^\circ_f \text{(reactants)}$

Example:

• Given: $\mathrm{CH_4(g) + 4Cl_2(g) \rightarrow CCl_4(l) + 4HCl(g)}$

• Given $\Delta H^\circ_f$ values (kJ/mol): CH4(g) = -74.9, Cl2(g) = 0, CCl4(l) = -139, HCl(g) = -92.3

• Calculation:

$\Delta H^\circ_{rxn} = [(-139) + 4(-92.3)] - [(-74.9) + 0] = -508.2\ \text{kJ}$

Important Notes

• Always check the physical states (solid, liquid, gas, aqueous) when using $\Delta H^\circ_f$ values.

• Use tabulated values for standard enthalpies of formation, typically found in appendices of chemistry textbooks.

Additional info: Some values and examples were inferred or expanded for clarity and completeness based on standard General Chemistry curriculum.