Thermochemistry: Heat, Calorimetry, and Enthalpy Changes

Thermochemistry

Heat, Calorimetry, and Enthalpy Changes

Thermochemistry is the study of energy changes, particularly heat, that accompany chemical reactions and physical changes. Understanding how to calculate heat transfer and enthalpy changes is essential for analyzing chemical processes.

1. Calculating Heat Transfer for Temperature Changes

• Specific Heat Capacity (c): The amount of heat required to raise the temperature of 1 gram of a substance by 1°C (or 1 K).

• Formula:

$q = m \cdot c \cdot \Delta T$

• q: Heat absorbed or released (J)

• m: Mass of the substance (g)

• c: Specific heat capacity (J/g·°C)

• ΔT: Change in temperature (°C or K)

Example: Calculate the heat needed to raise the temperature of 5.78 g of silver from 18°C to 35°C. Given: $c_{Ag} = 0.235$ J/g·°C.

2. Calorimetry with Water

• Water is commonly used in calorimetry due to its high specific heat capacity.

• Example: A bottle contains 45.5 g of water, cooled from 22.7°C to 4.3°C. Calculate the heat lost. $c_{H_2O} = 75.291$ J/mol·K (note: typically, water's specific heat is 4.18 J/g·°C; the value here is per mole).

Equation:

$q = m \cdot c \cdot \Delta T$

3. Enthalpy of Reaction (ΔH) and Combustion

• Enthalpy Change (ΔH): The heat change at constant pressure for a chemical reaction.

• Combustion Reactions: The complete reaction of a substance with oxygen to form oxides and release energy.

Example: Calculate the heat evolved in the complete combustion of 25.0 g of ethanol ($C_2H_5OH$):

$C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l)$ $\Delta H_{rxn} = -1367.3 \text{ kJ}$

• Convert mass to moles, then multiply by $\Delta H_{rxn}$ per mole.

Example: Calculate the mass of natural gas (methane, $CH_4$) burned to release 267 kJ of heat:

$CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$ $\Delta H_{rxn} = -802.3 \text{ kJ}$

4. Formation Reactions

• Formation Reaction: The formation of 1 mole of a compound from its elements in their standard states.

• Example: $C(graphite) + O_2(g) \rightarrow CO_2(g)$ is a formation reaction for $CO_2$.

5. Calculating Enthalpy Change Using Standard Enthalpies of Formation

• Standard Enthalpy of Formation ($\Delta H_f^\circ$): The enthalpy change when 1 mole of a compound is formed from its elements in their standard states.

• Formula:

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

• Example: Calculate $\Delta H_{rxn}$ for $4NH_3(g) + 7O_2(g) \rightarrow 4NO_2(g) + 6H_2O(g)$ using given $\Delta H_f^\circ$ values.

Substance	$\Delta H_f^\circ$ (kJ/mol)
NH3(g)	-45.90
NO2(g)	33.18
H2O(g)	-241.8

6. Enthalpy Change from Multiple Reactions (Hess's Law)

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

• Given reactions and their $\Delta H$ values, combine them to find the enthalpy change for a target reaction.

Example: Given:

• $C_2H_2(g) + 5/2 O_2(g) \rightarrow 2CO_2(g) + H_2O(l)$, $\Delta H = -1300. kJ$

• $2C(graphite) + O_2(g) \rightarrow 2CO_2(g)$, $\Delta H = -788.4 kJ$

• $H_2(g) + 1/2 O_2(g) \rightarrow H_2O(l)$, $\Delta H = -285.8 kJ$

Calculate $\Delta H$ for $2C(graphite) + H_2(g) \rightarrow C_2H_2(g)$.

Additional info: The worksheet covers key thermochemistry concepts, including heat calculations, enthalpy of reaction, formation reactions, and Hess's Law, with practical examples and relevant equations.