An osmotic coefficient
is a quantity which characterises the deviation of a
solvent
A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
from
ideal behaviour, referenced to
Raoult's law. It can be also applied to solutes. Its definition depends on the ways of expressing
chemical composition
A chemical composition specifies the identity, arrangement, and ratio of the elements making up a compound.
Chemical formulas can be used to describe the relative amounts of elements present in a compound. For example, the chemical formula for ...
of mixtures.
The osmotic coefficient based on
molality
Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution.
A commonly used unit for molali ...
''m'' is defined by:
and on a
mole fraction
In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This ex ...
basis by:
where
is the
chemical potential
In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
of the pure solvent and
is the
chemical potential
In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
of the solvent in a solution, ''M''
A is its
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, p ...
, ''x''
A its
mole fraction
In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This ex ...
, ''R'' the
gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
and ''T'' the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
in
Kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...
. The latter osmotic
coefficient is sometimes called the rational osmotic coefficient. The values for the two definitions are different, but since
the two definitions are similar, and in fact both approach 1 as the concentration goes to zero.
Applications
For liquid solutions, the osmotic coefficient is often used to calculate the salt
activity coefficient
In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same (or ...
from the solvent activity, or vice versa. For example,
freezing point depression
Freezing-point depression is a drop in the minimum temperature at which a substance freezing, freezes, caused when a smaller amount of another, non-Volatility (chemistry), volatile substance is added. Examples include adding salt into water (u ...
measurements, or measurements of deviations from ideality for other
colligative properties
In chemistry, colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the chemical species present. The number ...
, allows calculation of the salt activity coefficient through the osmotic coefficient.
Relation to other quantities
In a single solute solution, the (molality based) osmotic coefficient and the solute activity coefficient
are related to the
excess Gibbs free energy by the relations:
:
:
and there is thus a differential relationship between them (temperature and pressure held constant):
:
Liquid electrolyte solutions
For a single salt solute with molal activitiy (
), the osmotic coefficient can be written as
where
is the stochiometric number of salt and
the activity of the solvent.
can be calculated from the salt activity coefficient via:
:
Moreover, the activity coefficient of the salt
can be calculated from:
:
According to
Debye–Hückel theory
The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas.
It is a linearized Poisson–Boltzmann model, which assumes an extrem ...
, which is accurate only at low concentrations,
is
asymptotic
In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates tends to infinity. In projective geometry and related contexts, ...
to
, where ''I'' is
ionic strength
The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as ...
and ''A'' is the Debye–Hückel constant (equal to about 1.17 for water at 25 °C). This means that, at least at low concentrations, the vapor pressure of the solvent will be greater than that predicted by Raoult's law. For instance, for solutions of
magnesium chloride
Magnesium chloride is the family of inorganic compounds with the formula , where x can range from 0 to 12. These salts are colorless or white solids that are highly soluble in water. These compounds and their solutions, both of which occur in natu ...
, the
vapor pressure
Vapor pressure (or vapour pressure in English-speaking countries other than the US; see spelling differences) or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases ...
is slightly greater than that predicted by Raoult's law up to a concentration of 0.7 mol/kg, after which the vapor pressure is lower than Raoult's law predicts. For aqueous solutions, the osmotic coefficients can be calculated theoretically by
Pitzer equations
Pitzer equations are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. They were first described by physical chemist Kenneth Pitzer. The parameters of the Pitzer equations are ...
[I. Grenthe and H. Wanner, ''Guidelines for the extrapolation to zero ionic strength'', http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf] or TCPC model.
See also
*
Bromley equation
The Bromley equation was developed in 1973 by Leroy A. Bromley with the objective of calculating activity coefficients for aqueous electrolyte solutions whose concentrations are above the range of validity of the Debye–Hückel equation. This equ ...
*
Pitzer equation
Pitzer equations are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. They were first described by physical chemist Kenneth Pitzer. The parameters of the Pitzer equations are ...
*
Davies equation
The Davies equation is an empirical extension of Debye–Hückel theory which can be used to calculate activity coefficients of electrolyte solutions at relatively high concentrations at 25 °C. The equation, originally published in 1938, was ...
*
van 't Hoff factor
The van 't Hoff factor (named after Dutch chemist Jacobus Henricus van 't Hoff) is a measure of the effect of a solute on colligative properties such as osmotic pressure, relative lowering in vapor pressure, boiling-point elevation and freez ...
*
Law of dilution Wilhelm Ostwald’s dilution law is a relationship proposed in 1888 between the dissociation constant ' and the degree of dissociation ' of a weak electrolyte. The law takes the form
:K_d = \cfrac = \frac \cdot c_0
Where the square brackets deno ...
*
Thermodynamic activity
In chemical thermodynamics, activity (symbol ) is a measure of the "effective concentration" of a species in a mixture, in the sense that the species' chemical potential depends on the activity of a real solution in the same way that it would depen ...
*
Ion transport number
References
{{reflist
Physical chemistry