Thermochemistry: Heat, Work, Enthalpy, and Calorimetry

Chapter 7: Thermochemistry

Introduction to Thermochemistry

Thermochemistry is the study of energy changes, particularly heat, that occur during chemical reactions and physical changes. It is essential for understanding how energy is transferred and transformed in chemical systems.

• Thermal energy is the energy associated with the random motion of atoms and molecules.

• Heat (q) is the transfer of thermal energy between two bodies at different temperatures.

• Work (w) is energy transfer resulting from a force acting through a distance, often associated with volume changes in gases.

Quantifying Heat and Work

Calculating Heat Transfer

Heat transfer in a substance can be calculated using its mass, specific heat capacity, and temperature change.

• Specific heat capacity (C): The amount of heat required to raise the temperature of 1 gram of a substance by 1°C. Units: J/g·°C.

• Formula:

$q = m \times C \times \Delta T$

• $\Delta T = T_f - T_i$

Example: What is the final temperature of 295 g of Al (C = 0.900 J/g·°C) at 3.00°C after 85.0 kJ of heat is added?

• Convert 85.0 kJ to J: $85,000$ J

• Rearrange formula: $T_f = \frac{q}{mC} + T_i$

• Calculation: $T_f = \frac{85,000}{295 \times 0.900} + 3.00 = 323$°C

Internal Energy, Enthalpy, and Energy Changes

Internal Energy and Work

The change in internal energy ($\Delta E$) of a system is the sum of heat and work:

$\Delta E = q + w = q - P\Delta V$

• At constant volume ($\Delta V = 0$): $\Delta E = q$

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

Enthalpy ($H$)

Enthalpy is a state function representing the heat flow at constant pressure.

$\Delta H = H_{\text{final}} - H_{\text{initial}}$

• Exothermic process: Heat is released, $\Delta H < 0$

• Endothermic process: Heat is absorbed, $\Delta H > 0$

Classifying Processes: Endothermic vs. Exothermic

Examples

• An ice cube melts: $\Delta H > 0$ (endothermic)

• Combustion of butane: $\Delta H < 0$ (exothermic)

Thermochemical Equations and Stoichiometry

Thermochemical Equations

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

• Example: $\text{Pb (s) + PbO}_2 \text{(s) + 2 SO}_3 \text{(g)} \rightarrow 2 \text{PbSO}_4 \text{(s)}$   $\Delta H = -768$ kJ

Stoichiometry and Enthalpy Calculations

Enthalpy changes can be calculated for different amounts of reactants/products using stoichiometry.

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

Given	Conversion	Thermochemical Equation	Energy Change
Mass	Use molar mass	Balanced equation	Released/absorbed
Volume & Molarity	$M \times V =$ moles	Balanced equation	Released/absorbed

Example Calculations

• Enthalpy for 1 mol of PbSO4: $\Delta H = -384$ kJ (half the reaction, half the $\Delta H$)

• Enthalpy change for 5.56 g H2:

  • Convert grams to moles: $5.56 \text{ g H}_2 \times \frac{1 \text{ mol}}{2.02 \text{ g}}$

  • Use $\Delta H$ per 2 mol H2: $\Delta H = -787$ kJ

• Enthalpy change for 15.53 g SO3:

  • Convert grams to moles: $15.53 \text{ g SO}_3 \times \frac{1 \text{ mol}}{80.07 \text{ g}}$

  • Use $\Delta H$ per 2 mol SO3: $\Delta H = -74.5$ kJ

Thermal Energy Transfer

Heat Exchange Between Materials

When two substances at different temperatures are mixed, heat lost by one equals heat gained by the other:

$q_{\text{sys}} = -q_{\text{surr}}$

$m_{\text{metal}} \times C_{s,\text{metal}} \times \Delta T_{\text{metal}} = -m_{\text{water}} \times C_{s,\text{water}} \times \Delta T_{\text{water}}$

Example: Silver Block in Water

• Given: $C_s$ for water = 4.184 J/g·°C, $C_s$ for silver = 0.235 J/g·°C

• Initial temperatures: Silver = 58.7°C, Water = 24.9°C, Final = 26.9°C

• Calculation:

$m_{\text{silver}} \times 0.235 \times (26.9 - 58.7) = -100 \times 4.184 \times (26.9 - 24.9)$ $m_{\text{silver}} = \frac{-100 \times 4.184 \times (26.9 - 24.9)}{0.235 \times (26.9 - 58.7)} = 112$ g

Calorimetry: Measuring Heat Changes

Types of Calorimeters

• Constant Pressure Calorimeter: Measures heat change at constant pressure ($q = \Delta H$)

• Bomb Calorimeter: Measures heat change at constant volume ($q = \Delta E$)

Constant Volume Calorimetry

• Surroundings = calorimeter (reaction vessel)

• Heat gained by calorimeter = heat lost by reaction

$q_{\text{calorimeter}} = C_{\text{calorimeter}} \times \Delta T$ $q_{\text{rxn}} = -q_{\text{calorimeter}} = -C_{\text{calorimeter}} \times \Delta T$

Example: Combustion of Methylhydrazine

• Given: 4.00 g sample, $C_{\text{cal}} = 7.794$ kJ/°C, $\Delta T = 14.50$°C

• Calculation:

$q_{\text{rxn}} = -7.794 \times 14.50 = -113.0$ kJ Convert to per mole: $\frac{-113.0}{4.00} \times 46.1 = -1,300$ kJ/mol

Constant Pressure Calorimetry

• The reaction is the system; the solution is the surroundings.

• Heat of reaction at constant pressure is the change in enthalpy:

$\Delta H_{\text{rxn}} = -q_{\text{solution}} = -m_{\text{soln}} \times C_{s,\text{soln}} \times \Delta T$

Example: Neutralization Reaction

• Mix 50 mL of 1.0 M HCl and 50 mL of 1.0 M NaOH

• Total volume = 100 mL, density = 1.0 g/mL, $C_s$ = 4.18 J/g·°C

• Temperature change: $\Delta T = 27.5 - 21.0 = 6.5$°C

• Heat of reaction: $q_{\text{rxn}} = -4.18 \times 100 \times 6.5 = -2.7$ kJ

• Moles HCl: $0.050$ mol; $\Delta H$ per mole: $-2.7 / 0.050 = -54$ kJ/mol

Summary Table: Key Equations in Thermochemistry

Equation	Description
$q = mC\Delta T$	Heat transfer for temperature change
$\Delta E = q + w$	Change in internal energy
$\Delta H = \Delta E + P\Delta V$	Change in enthalpy at constant pressure
$q_{\text{rxn}} = -q_{\text{calorimeter}}$	Heat of reaction in calorimetry
$q_{\text{calorimeter}} = C_{\text{calorimeter}} \times \Delta T$	Heat absorbed by calorimeter

Additional info:

• All calculations require careful attention to units, especially when converting between kJ and J.

• Enthalpy changes are extensive properties and must be scaled according to the stoichiometry of the reaction.

• Calorimetry experiments are fundamental for determining enthalpy changes in chemical reactions.