16: The Chemical Activity of the Components of a Solution
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We are frequently interested in equilibrium processes that occur in a solution at a constant temperature. If we are able to find the activities of the species making up the solution, we can describe the thermodynamics of such processes. Many experimental methods have been developed for the measurement of the activities of species in solution. In general, the accurate measurement of chemical activities is experimentally exacting. In this chapter, we consider some of the basic concepts involved. We focus primarily on molecular solvents and solutes; that is, neutral molecules that exist as such in solution. We introduce a simplified model, called the ideal solution model, which is often a useful approximation, particularly for dilute solutions. In Sections 16.16-16.18, we touch on the special issues that arise when we consider the activities of dissolved ions.
- 16.1: Solutions Whose Components are in Equilibrium with Their Own Gases
- One way to find activities is to find the composition and pressure of the gas phase that is in equilibrium with the solution. If the gases are not ideal, we also need experimental data on the partial molar volumes of the components in the gas phase. Collecting such data is feasible for solutions of volatile molecular liquids. For solutions of electrolytes or other non-volatile components, other methods are required.
- 16.2: Raoult's Law and Ideal Solutions
- An ideal solution is a homogeneous liquid solution that is at equilibrium with an ideal-gas solution in which the vapor pressure of each component satisfies Raoult’s law that asserts a relationship among the gas- and solution-phase mole fractions of the solute, the vapor pressure of the pure liquid, and the pressure of the system.
- 16.8: When the Solute Obeys Henry's Law, the Solvent Obeys Raoult's Law
- When the solute obeys Henry’s law and the solvent behaves as an ideal gas in the gas phase above its solution, the solvent obeys Raoult’s law.
- 16.9: Properties of Ideal Solutions
- We have found the chemical potential of any component in an ideal solution. Now let us find some other thermodynamic properties of an ideal solution. The value of an extensive thermodynamic property of the solution will be the sum of the values of that property for the separate pure components plus the change that occurs when these components are mixed.
- 16.11: Colligative Properties - Freezing-point Depression
- The freezing point of a pure solvent, at a specified pressure, is the temperature at which the chemical potential of the pure-solid solvent is equal to the chemical potential of the pure-liquid solvent. The freezing point of a solution is the temperature at which the chemical potential of the pure-solid solvent is equal to the chemical potential of the solution-phase solvent. The freezing point of the solution is less than the freezing point of the pure solvent; this difference is the freezing-p
- 16.12: Colligative Properties - Osmotic Pressure
- The phenomena of boiling-point elevation and freezing-point depression involve relationships between composition and equilibrium temperature—at constant system pressure. We turn now to a phenomenon, osmotic pressure, which involves a relationship between composition and equilibrium pressure—at constant system temperature.
- 16.13: Colligative Properties - Solubility of a Solute in an Ideal Solution
- Although the result has few practical applications, we can also use these ideas to calculate the solubility of a solid solute in an ideal solution. The arguments are similar to those we used to estimate the freezing-point depression of a solution. The freezing point of a solution is the temperature at which the solution is in equilibrium with its pure-solid solvent. The solubility of a solute is the mole fraction of the solute in a solution that is at equilibrium with pure-solid solute.
- 16.14: Colligative Properties - Solubility of a Gas
- That the solubilities of gases generally decrease with increasing temperature is a well-known experimental observation. It stands in contrast to the observation that the solubilities of liquid or solid—at P and T —substances generally increase with increasing temperature. Our analysis of gas solubility provides a satisfying theoretical interpretation for an experimental observation which otherwise appears to be counterintuitive.
- 16.17: Activities of Electrolytes - The Mean Activity Coefficient
- we cannot determine the activity or activity coefficient for an individual ion experimentally. The mean activity coefficient can be determined experimentally as a function of molality, but the individual activity coefficients cannot. It is common to present the results of activity measurements on electrolytic solutions as a table or a graph that shows the mean activity coefficient as a function of the salt molality. Debyend Hückel developed such a theory.
- 16.18: Activities of Electrolytes - The Debye-Hückel Theory
- The Debye-Hückel theory leads to an equation for the activity coefficient of an ion in solution. The theory gives accurate values for the activity of an ion in very dilute solutions. As salt concentrations become greater, the accuracy of the Debye-Hückel model decreases. As a rough rule of thumb, the theory gives useful values for the activity coefficients of dissolved ions in solutions whose total salt concentrations are less than about 0.01 molal. The theory is based on an electrostatic model.
Thumbnail: The Effect of Solution Formation on Entropy. (CC BY-SA-NC; anonymous by request)