Glossary

9.4 Thermodynamics of mixing

4 min read•july 30, 2024

Thermodynamics of mixing explores how substances combine and interact. It's crucial for understanding solutions, from everyday mixtures like salt water to complex industrial processes. This topic dives into ideal and non-ideal solutions, intermolecular forces, and energy changes.

We'll examine how mixing affects , entropy, and enthalpy. We'll also look at phase diagrams, which show how mixtures behave under different conditions. These concepts are key to predicting and controlling mixture properties in various applications.

Ideal vs Non-ideal Solutions

Thermodynamic Properties

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  • An is a mixture in which the interactions between the components are identical to those within the pure components
    • The for an ideal solution is zero
  • In an ideal solution, the chemical potential of each component is proportional to the natural logarithm of its , as described by
  • Non-ideal solutions exhibit deviations from Raoult's law due to differences in intermolecular interactions between the components
    • These deviations can be positive or negative

Quantifying Non-ideality

  • The is a measure of the deviation from ideality in a
    • It relates the actual chemical potential of a component to its ideal chemical potential
  • Excess thermodynamic properties quantify the deviations from ideal behavior in non-ideal solutions
    • Examples include excess Gibbs free energy, excess enthalpy, and excess entropy

Intermolecular Interactions in Mixtures

Effects on Thermodynamic Properties

  • Intermolecular interactions, such as van der Waals forces, hydrogen bonding, and dipole-dipole interactions, influence the thermodynamic properties of mixtures
  • Attractive intermolecular interactions between unlike components in a mixture can lead to negative deviations from Raoult's law
    • This results in a decrease in the vapor pressure of the solution
  • Repulsive intermolecular interactions between unlike components can result in positive deviations from Raoult's law
    • This leads to an increase in the vapor pressure of the solution
  • The strength and nature of intermolecular interactions determine the magnitude and sign of the excess thermodynamic properties in non-ideal solutions

Formation of Azeotropes

  • The presence of strong intermolecular interactions can lead to the formation of azeotropes
    • Azeotropes are mixtures with a constant boiling point and composition
    • Examples include ethanol-water (95% ethanol) and hydrochloric acid-water (20.2% HCl)

Gibbs Free Energy of Mixing

Determining Spontaneity

  • The Gibbs free energy of mixing (ΔG_mix) is a thermodynamic quantity that determines the spontaneity of the mixing process at constant temperature and pressure
  • For an ideal solution, the Gibbs free energy of mixing is given by:
    • ΔGmix=RTΣ(xilnxi)ΔG_mix = RT Σ(x_i ln x_i)
    • where R is the gas constant, T is the absolute temperature, and x_i is the mole fraction of component i
  • In non-ideal solutions, the Gibbs free energy of mixing includes an additional term, the excess Gibbs free energy (G^E), which accounts for the deviations from ideality:
    • ΔGmix=RTΣ(xilnxi)+GEΔG_mix = RT Σ(x_i ln x_i) + G^E
  • A negative value of ΔG_mix indicates that mixing is spontaneous, while a positive value suggests that mixing is non-spontaneous

Temperature Dependence

  • The of ΔG_mix can lead to upper or lower critical solution temperatures
    • Above the upper critical solution temperature, the components become completely miscible
    • Below the lower critical solution temperature, the components also become completely miscible
    • Examples include nicotine-water (upper critical solution temperature of 210°C) and triethylamine-water (lower critical solution temperature of 18.5°C)

Entropy and Enthalpy Changes in Solutions

Entropy of Mixing

  • The entropy of mixing (ΔS_mix) is always positive for ideal solutions, as mixing increases the randomness of the system
    • It is given by: ΔSmix=−RΣ(xilnxi)ΔS_mix = -R Σ(x_i ln x_i)
  • In non-ideal solutions, the excess entropy of mixing (S^E) contributes to the total entropy change:
    • ΔSmix=−RΣ(xilnxi)+SEΔS_mix = -R Σ(x_i ln x_i) + S^E

Enthalpy of Mixing

  • The enthalpy of mixing (ΔH_mix) is zero for ideal solutions, as there are no net changes in the intermolecular interactions during mixing
  • For non-ideal solutions, the enthalpy of mixing is equal to the excess enthalpy (H^E), which arises from the differences in intermolecular interactions between the components:
    • ΔHmix=HEΔH_mix = H^E
  • The signs and magnitudes of S^E and H^E depend on the specific intermolecular interactions in the non-ideal solution and can be positive or negative
    • Examples of positive H^E include acetone-chloroform and ethanol-benzene mixtures
    • Examples of negative H^E include acetone-water and ethanol-water mixtures

Phase Diagrams of Mixtures

Interpretation of Phase Diagrams

  • Phase diagrams represent the equilibrium states of mixtures as a function of composition, temperature, and pressure
  • The liquidus line in a phase diagram separates the liquid phase from the liquid-solid region
  • The solidus line separates the solid phase from the liquid-solid region
  • The lever rule allows the determination of the relative amounts of phases present in a mixture at equilibrium based on the composition and temperature

Special Points and Regions

  • Eutectic points in phase diagrams represent the composition and temperature at which the liquid phase directly transforms into a solid mixture of two phases upon cooling
    • Examples include lead-tin (solder) and silver-copper eutectic alloys
  • The presence of miscibility gaps in phase diagrams indicates regions where the components are not completely miscible, leading to the formation of two separate liquid or solid phases
    • Examples include water-phenol and zinc-lead systems

Predicting Mixture Behavior

  • Phase diagrams can be used to predict the solubility, melting point depression, and boiling point elevation of mixtures
    • Melting point depression example: salt-water mixtures
    • Boiling point elevation example: ethylene glycol-water antifreeze mixtures
  • Phase diagrams also help identify the occurrence of azeotropes and critical solution temperatures in mixtures

Key Terms to Review (18)

Activity coefficient: The activity coefficient is a factor used in chemistry to quantify how the behavior of a substance in a solution deviates from ideal behavior. It reflects the effective concentration of a species in a mixture, taking into account interactions between particles that can alter their activity. This concept is crucial for understanding properties such as partial molar quantities and the thermodynamics of mixing, as it helps explain how real solutions behave compared to ideal solutions.
Azeotropic mixture: An azeotropic mixture is a combination of two or more liquids that has a constant boiling point and composition throughout the distillation process. This unique behavior occurs when the vapor phase of the mixture has the same composition as the liquid phase, making it impossible to separate the components through simple distillation. Azeotropes can affect both phase behavior and thermodynamic properties when mixing different substances, influencing how we understand phase diagrams and the energy changes involved in mixing.
Configurational Entropy: Configurational entropy is a measure of the number of different arrangements or configurations that a system can adopt, reflecting the degree of disorder or randomness in the distribution of its particles. This concept plays a critical role in understanding how systems evolve and mix, linking statistical mechanics with thermodynamic properties, and providing insights into the behavior of gases, liquids, and solids during mixing processes.
Critical Point: The critical point is a specific temperature and pressure at which the properties of a substance's gas and liquid phases become indistinguishable, marking the end of the liquid-gas phase boundary. At this point, the substance enters a supercritical fluid state, where it exhibits unique characteristics that differ from those of traditional liquids and gases.
Enthalpy of mixing: Enthalpy of mixing is the change in enthalpy that occurs when two or more substances are mixed together. This term is crucial for understanding both ideal and non-ideal solutions, as it helps explain how the interactions between different molecules can affect the overall energy of the system. The enthalpy of mixing can vary depending on the nature of the components being mixed and their interactions, which also ties into thermodynamics principles governing mixing processes.
Gibbs Free Energy: Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. This concept is vital for predicting the spontaneity of processes, as it combines the system's enthalpy and entropy to determine whether a reaction or process can occur naturally without external input.
Henry's Law: Henry's Law states that at a constant temperature, the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid. This relationship highlights how changes in pressure and temperature can significantly affect the solubility of gases, which is crucial for understanding various physical and chemical processes, including those involving solutions and mixtures.
Ideal solution: An ideal solution is a type of solution where the enthalpy of mixing is zero and the properties of the solution can be predicted by Raoult's Law. In an ideal solution, the interactions between the different types of molecules are similar to the interactions among like molecules, meaning that the physical properties such as vapor pressure, boiling point, and concentration behave in a predictable manner. This concept helps in understanding the behavior of mixtures and their effects on various physical properties.
Liquid-liquid mixture: A liquid-liquid mixture is a combination of two or more immiscible liquids, where they do not fully mix or dissolve in each other, resulting in distinct phases. The behavior and properties of these mixtures are influenced by the interactions between the molecules of the different liquids, which can lead to changes in thermodynamic parameters such as enthalpy and entropy when they mix.
Mixing entropy: Mixing entropy is a measure of the increase in disorder or randomness that occurs when two or more substances are mixed together. It reflects how the arrangement of particles becomes more disordered as they intermingle, contributing to the overall thermodynamic stability of the system. Understanding mixing entropy is essential in thermodynamics, especially when analyzing the behavior of ideal solutions and mixtures, and it plays a crucial role in determining the spontaneity of mixing processes.
Mole fraction: Mole fraction is the ratio of the number of moles of a particular component to the total number of moles of all components in a mixture. This dimensionless quantity is critical for understanding the composition of solutions and helps in calculating properties related to both ideal and non-ideal solutions, as well as colligative properties and the thermodynamics involved in mixing substances.
Non-ideal solution: A non-ideal solution is a mixture where the behavior of the components deviates from the ideal predictions due to interactions between molecules. These deviations can arise from various factors such as differences in molecular size, shape, and polarity, leading to non-linear relationships in properties like vapor pressure and concentration. Understanding non-ideal solutions is crucial for applying concepts like partial molar quantities, thermodynamics of mixing, and colligative properties effectively.
Pressure effects: Pressure effects refer to the influence of pressure on the behavior and properties of substances, particularly in relation to phase transitions and mixing. These effects play a crucial role in determining how components interact and distribute themselves in a mixture, influencing solubility, chemical equilibria, and overall thermodynamic stability. Understanding pressure effects is essential for predicting the behavior of mixtures under varying conditions, especially in processes involving gases and liquids.
Raoult's Law: Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent present. This law applies to ideal solutions where interactions between different molecules are similar to those between like molecules, leading to predictable behaviors in mixtures. In contrast, non-ideal solutions exhibit deviations from Raoult's Law due to differences in intermolecular forces, which can impact colligative properties and thermodynamics of mixing.
Solid-liquid mixture: A solid-liquid mixture is a heterogeneous combination of solid particles dispersed within a liquid medium. These mixtures can be found in various applications, including chemical processes and natural phenomena, where the solid phase may either remain suspended or settle out over time. Understanding the behavior of solid-liquid mixtures is crucial for grasping the thermodynamics of mixing, as it reveals insights into solubility, stability, and the energy changes associated with the process.
Solute: A solute is a substance that is dissolved in a solvent to form a solution. In this process, the solute's particles disperse uniformly throughout the solvent, leading to a homogeneous mixture. Understanding how solutes interact with solvents is crucial in discussing the thermodynamics of mixing and two-component phase diagrams, as these concepts reveal how different substances behave when mixed together and how their phases change.
Temperature Dependence: Temperature dependence refers to the way in which a physical or chemical property of a substance changes with temperature. This concept is crucial in understanding various processes, such as heat capacity, phase changes, and reaction rates, which all exhibit different behaviors as temperature varies.
Tie line: A tie line is a horizontal line on a phase diagram that connects the compositions of two coexisting phases in a two-component system at equilibrium. This line helps to illustrate how the components of the mixture interact and how their relative amounts can be altered by changing temperature or pressure, which are crucial aspects when examining the thermodynamics of mixing.
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