10.2 Heat Capacity and Enthalpy Changes

Heat capacity is a crucial concept in thermodynamics, measuring how much heat a substance can absorb or release. It's key for understanding energy changes in chemical processes, from heating water to complex industrial reactions.

Enthalpy changes, calculated using heat capacity, help us predict energy flow in chemical systems. This knowledge is essential for designing efficient processes, whether you're brewing coffee or running a power plant.

Heat Capacity Fundamentals

Heat capacity of substances

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• Heat capacity measures heat required to raise temperature by one degree
• Specific heat capacity quantifies heat capacity per unit mass expressed in J/(kg·K) or cal/(g·℃)
• Molar heat capacity denotes heat capacity per mole of substance measured in J/(mol·K) or cal/(mol·℃)
• Constant pressure heat capacity (Cp) determined at constant pressure
• Constant volume heat capacity (Cv) measured at constant volume
• For ideal gases, $C_p = C_v + R$ relates Cp and Cv
• Mixture heat capacity calculated as weighted average of component heat capacities $C_{p,mix} = \sum x_i C_{p,i}$ (water and ethanol)

Enthalpy changes from heat capacity

• Enthalpy change quantifies heat absorbed or released at constant pressure
• Calculated using formula $\Delta H = m \cdot C_p \cdot \Delta T$
• Sensible heat involves temperature change without phase transition (heating water)
• Latent heat associated with phase changes (ice melting)
• Heat capacity varies with temperature $C_p = a + bT + cT^2 + dT^3$
• Enthalpy change found by integrating heat capacity $\Delta H = \int_{T_1}^{T_2} C_p dT$

Temperature effects on enthalpy

• Higher temperatures generally increase enthalpy changes
• Kirchhoff's equation $\frac{d\Delta H}{dT} = \Delta C_p$ relates temperature and enthalpy change
• Standard state conditions set at 25℃ (298.15 K) and 1 atm pressure
• Reference state enthalpy defines formation enthalpy at standard state
• Temperature correction applied using $\Delta H_T = \Delta H_{298} + \int_{298}^T \Delta C_p dT$

Hess's law for enthalpy calculations

• Hess's law states enthalpy change of reaction independent of pathway
• Applies to multi-step reactions by summing individual step enthalpy changes
• Reversing reaction changes enthalpy change sign
• Scaling reaction multiplies enthalpy change by same factor
• Formation reactions form compounds from elements in standard states
• Combustion reactions involve complete oxidation forming CO2 and H2O (methane combustion)
• Born-Haber cycle applies Hess's law to calculate lattice energies (NaCl formation)