For very dilute solutions, the activities of the substances in the solution closely approach the formal concentration what the calculated concentration should be based on how much substance was measured out. As solutions get more concentrated, the activities of all of the species tend to be smaller than the formal concentration.
The decrease in activity as concentration increases is much more pronounced for ions than it is for neutral solutes. Activities are actually unitless ratios that compare an effective pressure or an effective concentration to a standard state pressure or concentration the correct term for the effective pressure is fugacity. There are several ways to define standard states for the different components of a solution, but a common system is. Thus, when we discuss the activity of a gas, we actually are discussing the ratio of the effective pressure to the standard state pressure:.
For all solids, the activity is a ratio of the concentration of a pure solid to the concentration of that same pure solid. For all liquids, the activity is a ratio of the concentration of a pure liquid to the concentration of that same pure liquid:.
For most experimental situations, solutions are assumed to be dilute with respect to the solvent. This assumption implies the solvent can be approximated with pure liquid.
According to Raoult's Law , the vapor pressure of the solvent in a solution is equal to the mole fraction of the solvent in the solution times the vapor pressure of the pure solvent:. The mole fraction of solvent in a dilute solution is approximately 1, so the vapor pressure of the solution is essentially identical to the vapor pressure of the pure solvent.
This means that the activity of a solvent in dilute solution will always has a value of 1, with no units. Activity indicates how many particles "appear" to be present in the solution, which is different from how many actually are present.
Hence, activity is a "fudge factor" to ideal solutions that correct the true concentration. The activity coefficient for a nonvolatile, neutral solute is often estimated by non-linear curve fitting, taking into account the molality of the solute and the activity of the solvent usually its vapor pressure.
In most situations, it is more practical to look up the values of the activity coefficient for a given solute than it is to carry out the curve fitting. Estimating the activity coefficient of electrolytes solutes that dissolve or react with the solvent to form ions depends upon the number of ions formed by the dissociation of the solute in solution or the reaction of the solute with the solution, because each ion formed is dealt with individually.
In a theoretical, infinitely dilute ideal solution, an electrolyte would dissociate or react completely to form an integer number of independent ions.
In reality, it is found that electrolytes almost always act as if they contain fewer moles of ions than expected based on the formal concentration. An activity coefficient incorporates the particle interactions into a single term that modifies the formal concentration to give an estimate of the effective concentration, or activity, of each ion.
This means that the same limiting mean ionic activity coefficient is found for sodium chloride and potassium chloride and that also the values for the and salts sodium sulfate and calcium chloride are identical. At higher electrolyte concentrations though, these values change very strongly and are usually modeled using empirical parameters regressed to the experimental data. Electrolytes almost always act as if they contain fewer moles of ions than expected based on the formal concentration.
This equation takes into account the solution environment as well as the individual characteristics of the specific ion of interest.
It is not difficult to calculate single ion activity coefficients, but tables of these activity coefficients for many common ions in solutions of various concentrations are available e. Repeat the calculation for a solution of 0. In the case of 0. For a salt, such as NaCl, ionic strength and molar concentration are identical. This creates a contradiction. In place of concentrations, we define the true thermodynamic equilibrium constant using activities. Unless otherwise specified, the equilibrium constants in the appendices are thermodynamic equilibrium constants.
For a gas the proper terms are fugacity and fugacity coefficient, instead of activity and activity coefficient. For a reaction that involves only these species, the difference between activity and concentration is negligible.
The effective radius is greater for smaller, more highly charged ions than it is for larger, less highly charged ions. Source: Kielland, J. Second, an activity coefficient is smaller, and the effect of activity is more important, for an ion with a higher charge and a smaller effective radius.
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