Principles of Thermochemistry and Calorimetry

Enthalpy and Reaction Energy

Heat of reaction is expressed as the change in enthalpy $\Delta H$ of a system, calculated as $\Delta H = H(\text{products}) - H(\text{reactants})$. This value is measured in $kJ/mol$. A positive $\Delta H$ indicates an endothermic process where energy is added, while a negative $\Delta H$ indicates an exothermic process where energy is released.

Standard Heat of Formation

The standard heat of formation $\Delta H^\theta_f$ is the heat change occurring when one mole of a compound is formed from its constituent elements in their natural states at $25^\circ C$ and $1\,atm$. By definition, all elements in their standard states have an enthalpy of zero. The standard heat of reaction is determined using the formula:

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

In the thermite reaction $Cr_2O_3 (s) + 2Al (s) \rightarrow 2Cr (s) + Al_2O_3 (s)$, weights are applied using $\Delta H^\theta_f (Cr_2O_3) = -1128.4\,kJ\,mol^{-1}$ and $\Delta H^\theta_f (Al_2O_3) = -1669.3\,kJ\,mol^{-1}$, resulting in a net $\Delta H$ of $-540.9\,kJ\,mol^{-1}$.

Heat of Combustion

Combustion reactions involve burning substances in oxygen to release energy, making them always exothermic. The standard heat of combustion $\Delta H^\theta_c$ is the heat released during the complete combustion of one mole of a fuel at standard pressure. For phosphorus, while the heat of formation for $P_4O_{10} (s)$ is $-2984\,kJ\,mol^{-1}$, the heat of combustion based on one mole of $P (s)$ is $-746\,kJ\,mol^{-1}$, as shown in the equation:

$P (s) + \frac{5}{4} O_2 (g) \rightarrow \frac{1}{4} P_4O_{10} (s)$

Calorimetry and Measurement

Calorimetry measures the quantity of heat exchanged between a system and its surroundings. A bomb calorimeter is a specific constant-volume device used to measure the heat of combustion by igniting fuel and measuring the temperature change of surrounding water. The calorie is a metric unit of energy, where $1\,\text{calorie}$ equals the specific heat capacity of water, defined as $4.184\,J\,^\circ C^{-1}\,g^{-1}$.

Specific Heat Capacity and Thermal Calculations

Temperature indicates the average kinetic energy of particles, while heat energy represents the total energy within an object. Each substance has a specific heat capacity ($C$), representing the energy required to raise the temperature of $1\,g$ of that substance by $1^\circ C$. Energy calculations are performed using the relationship:

$q = mC\Delta T$

Where $q$ is heat, $m$ is mass in grams, $C$ is specific heat capacity, and $\Delta T$ is the change in temperature. Examples of specific heat values include Gold ($0.13\,J\,g^{-1}\,^\circ C^{-1}$), Aluminium ($0.905\,J\,g^{-1}\,^\circ C^{-1}$), and Silver ($0.240\,J\,g^{-1}\,^\circ C^{-1}$).