Thermochemistry and Calorimetry: Study Notes and Practice Problems

Thermochemistry and Calorimetry

Introduction to Thermochemistry

Thermochemistry is the study of the energy and heat associated with chemical reactions and physical transformations. It involves understanding how energy is transferred between a system and its surroundings, and how to quantify these changes using concepts such as enthalpy, internal energy, and work.

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

• Surroundings: Everything outside the system.

• State Functions: Properties that depend only on the state of the system (e.g., enthalpy, internal energy).

Work, Heat, and Internal Energy

Energy can be transferred as heat (q) or work (w). The change in internal energy (ΔE) of a system is given by:

• First Law of Thermodynamics: $\Delta E = q + w$

• Work at constant pressure: $w = -P_{ext} \Delta V$

• Sign conventions: Work done by the system is negative; work done on the system is positive.

Enthalpy and Calorimetry

Enthalpy (H) is a state function that is especially useful for processes occurring at constant pressure. The change in enthalpy (ΔH) is equal to the heat exchanged at constant pressure:

• $\Delta H = q_p$ (heat at constant pressure)

• For exothermic reactions, $\Delta H < 0$; for endothermic reactions, $\Delta H > 0$.

Calculating Work and Heat in Gas Expansions

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

• $w = -P_{ext} (V_f - V_i)$

• Example: If a gas expands from 15 L to 35 L against 1.5 atm, $w = -1.5 \times (35 - 15) = -30$ L·atm. Convert to joules: $1$L·atm$= 101.3$ J.

Phase Changes and Heat Calculations

Calculating the heat required for phase changes or temperature changes involves specific heat capacity and enthalpy of phase change:

• Specific heat capacity ($c$): Amount of heat required to raise the temperature of 1 g of substance by 1°C.

• Heat for temperature change: $q = m c \Delta T$

• Heat for vaporization: $q = n \Delta H_{vap}$

Calorimetry and Bomb Calorimeters

Calorimetry is the measurement of heat flow. In a bomb calorimeter, the heat capacity of the calorimeter must be considered:

• Heat capacity ($C$): Amount of heat required to raise the temperature of the entire calorimeter by 1°C.

• $q = C \Delta T$

Standard Enthalpy of Formation and Hess's Law

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. Hess's Law allows calculation of enthalpy changes for reactions by combining known enthalpy changes:

• Hess's Law: The total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps.

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

Endothermic vs. Exothermic Processes

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

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

Sample Calculations and Applications

• Calculating final temperature after heat absorption: $q = m c \Delta T \implies \Delta T = \frac{q}{m c}$

• Comparing temperature changes for different metals: For equal heat absorbed, the metal with the lowest specific heat will have the highest temperature change.

• Molar heat capacity: $C_{molar} = c \times M$ (where $M$ is molar mass)

Representative Table: Standard Enthalpies of Formation

The following table lists standard enthalpies of formation for selected species (used in Hess's Law calculations):

Species	$\Delta H_f^\circ$ (kJ/mol)
Fe2O3 (s)	-824.2
Fe3O4 (s)	-1118.4
CO (g)	-110.5
CO2 (g)	-393.5

Example Problems

• Work done by a gas: Calculate $w$ when a gas expands from 1.0 L to 10.1 L against 0.50 atm.

• Heat required to raise temperature: Calculate $q$ for 10.5 moles of Al from 30.5°C to 225°C, given $c = 0.900$ J/g·°C.

• Enthalpy change for combustion: Use given $\Delta H_f^\circ$ values to calculate $\Delta H_{rxn}$ for combustion of ethanol or octane.

• Identifying endothermic/exothermic reactions: Use sign of $\Delta H$ to classify processes.

Additional info:

• Some questions require conversion between units (e.g., L·atm to J).

• Specific heat values and enthalpy data are essential for quantitative thermochemistry problems.

• Standard enthalpy of formation for elements in their standard state is zero.