Thermochemistry

Calorimetry

Calorimetry is the study of measuring heat changes in chemical reactions. It is essential for understanding energy transfer in reactions, especially those carried out at constant pressure or constant volume.

• Constant Pressure Calorimetry: Most reactions occur at constant pressure (e.g., in open containers). If the number of moles of gas increases, the system does work on the surroundings (expansion). If the number decreases, the surroundings do work on the system (compression).

• Pressure-Volume (PV) Work: The work done is given by , where the negative sign indicates work done by the system on the surroundings.

• Example: Mixing AgNO3 and HCl in a coffee-cup calorimeter, the heat change is calculated using the mass, specific heat, and temperature change of the solution.

Key Equations:

• (where c is specific heat, m is mass, and is temperature change)

• (where C is heat capacity; )

• Sign convention: is positive for endothermic, negative for exothermic processes.

Example Calculations:

• Heat absorbed by a copper penny warming from -8.0°C to 37.0°C: (endothermic).

• Determining specific heat of a gold-colored rock: (not pure gold).

• Final temperature of Al block after absorbing heat: ; .

• Thermal equilibrium between Al and water: ; solve for using simultaneous equations.

Constant-Volume Calorimetry

Constant-volume calorimetry uses a bomb calorimeter, where no PV work is done (). The heat change measured is the change in internal energy ().

• ; at constant volume, , so .

• Bomb calorimeter is an isolated system; heat change of the system is zero: .

• Heat capacity of calorimeter () is determined using a standard substance.

• Example: Combustion of sucrose in bomb calorimeter, calculate per mole.

Hess's Law

Hess's Law states that the enthalpy change for a reaction is the same whether it occurs in one step or multiple steps, because enthalpy is a state function.

• Allows calculation of for reactions using known enthalpy changes of related reactions.

• Manipulate equations (reverse, multiply, add) and apply the same operations to their values.

• Example: Calculating for using given reactions and their enthalpy changes.

Enthalpy () and Internal Energy ()

Enthalpy and internal energy are related, but not always equal. The difference arises from PV work done by gases.

• (since )

• is the change in moles of gas:

• Example: Conversion of SO2 to SO3, calculate given and .

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 most stable forms at 1 atm and 25°C.

• for elements in their standard state is zero.

• Examples: (C(s)) = 0, $\Delta H_f^\circ$(O2(g)) = 0, $\Delta H_f^\circ$(H2O(l)) = -285.8$ kJ/mol.

• Allows calculation of reaction enthalpy without direct measurement.

Key Equation:

Direct and Indirect Methods for Determining

Direct method involves synthesizing a compound from its elements and measuring the enthalpy change. Indirect method uses Hess's Law to calculate from known reactions.

• Direct Example: Formation of CO from C and O2.

• Indirect Example: Formation of CO from C and H2O using multiple reactions and their enthalpy changes.

Application: Combustion and Environmental Impact

Thermochemistry is used to calculate the mass of CO2 released during combustion of fuels, such as octane in gasoline.

• Balance the combustion reaction.

• Calculate moles of fuel and corresponding moles of CO2 produced.

• Convert moles of CO2 to mass (kg).

Example Problems

• Temperature Change in Calorimeter: Calculate final temperature after reaction using .

• Enthalpy of Reaction: Calculate for mixing solutions in a calorimeter.

• Specific Heat Determination: Find specific heat of a metal using heat exchange with water.

• Enthalpy per Mole: Calculate per mole for combustion reactions.

Table: Standard Enthalpy of Formation Values

Additional info: The notes include stepwise examples of Hess's Law, calorimetry calculations, and environmental applications, providing a comprehensive overview of thermochemical principles relevant to general chemistry.