11.3 Mixing processes and heat effects

Mixing processes in thermodynamics involve combining substances and analyzing the resulting energy changes. These processes can be endothermic or exothermic, affecting the system's temperature and overall energy state.

Understanding mixing processes is crucial for grasping solution thermodynamics. By examining enthalpy, entropy, and Gibbs free energy of mixing, we can predict the spontaneity and heat effects of various mixing scenarios in real-world applications.

Thermodynamic Properties of Mixing

Enthalpy and Entropy of Mixing

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• Enthalpy of mixing ($\Delta H_{mix}$) represents the change in enthalpy when two or more substances are mixed together at constant temperature and pressure
  • Can be positive (endothermic) or negative (exothermic) depending on the interactions between the components
  • For ideal solutions, $\Delta H_{mix} = 0$ because there are no interactions between the components
• Entropy of mixing ($\Delta S_{mix}$) quantifies the increase in disorder or randomness when substances are mixed together
  • Always positive for mixing processes because mixing increases the randomness of the system
  • For ideal solutions, $\Delta S_{mix} = -R\sum x_i \ln x_i$, where $R$ is the gas constant and $x_i$ is the mole fraction of component $i$

Gibbs Free Energy and Excess Enthalpy

• Gibbs free energy of mixing ($\Delta G_{mix}$) determines the spontaneity of the mixing process at constant temperature and pressure
  • Calculated using the equation $\Delta G_{mix} = \Delta H_{mix} - T\Delta S_{mix}$
  • Mixing is spontaneous when $\Delta G_{mix} < 0$, non-spontaneous when $\Delta G_{mix} > 0$, and at equilibrium when $\Delta G_{mix} = 0$
• Excess enthalpy ($H^E$) is the difference between the actual enthalpy of mixing and the enthalpy of mixing for an ideal solution
  • Accounts for the non-ideal interactions between the components in a real solution
  • Positive $H^E$ indicates stronger interactions between like molecules (endothermic), while negative $H^E$ indicates stronger interactions between unlike molecules (exothermic)
  • For ideal solutions, $H^E = 0$ because there are no non-ideal interactions

Heat Effects in Mixing Processes

Heat of Solution

• Heat of solution ($\Delta H_{sol}$) is the enthalpy change associated with dissolving a solute in a solvent to form a solution
  • Can be positive (endothermic) or negative (exothermic) depending on the interactions between the solute and solvent
  • Endothermic heat of solution (positive $\Delta H_{sol}$) occurs when the energy required to break solute-solute and solvent-solvent interactions is greater than the energy released from forming solute-solvent interactions (e.g., dissolving ammonium nitrate in water)
  • Exothermic heat of solution (negative $\Delta H_{sol}$) occurs when the energy released from forming solute-solvent interactions is greater than the energy required to break solute-solute and solvent-solvent interactions (e.g., dissolving sodium hydroxide in water)

Endothermic and Exothermic Mixing

• Endothermic mixing processes absorb heat from the surroundings, resulting in a decrease in temperature
  • Occurs when the interactions between the components being mixed are weaker than the interactions within the pure components
  • Examples include mixing ethanol and water, where the temperature of the mixture decreases due to the breaking of hydrogen bonds in the pure components
• Exothermic mixing processes release heat to the surroundings, resulting in an increase in temperature
  • Occurs when the interactions between the components being mixed are stronger than the interactions within the pure components
  • Examples include mixing sulfuric acid and water, where the temperature of the mixture increases due to the formation of strong interactions between the acid and water molecules