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An '''osmotic coefficient''' ''φ'' is a quantity which characterises the deviation of a [[solvent]] from [[ideal solution|ideal behaviour]], referenced to [[Raoult's law]]. The osmotic coefficient based on [[molality]] ''b'' is defined by:
: <math>\varphi=\frac{\mu_A^*-\mu_A}{RTM_A\sum_i b_i}\,</math>


and on an [[amount fraction]] basis by:


:<math>\varphi=-\frac{\mu_A^*-\mu_A}{RT \ln x_A}\,</math>
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where <math>\mu_A^*</math> is the [[chemical potential]] of the pure solvent and <math>\mu_A</math> is the [[chemical potential]] of the solvent in a solution, ''M''<sub>A</sub> is its [[molar mass]], ''x''<sub>A</sub> its [[amount fraction]], ''R'' the [[gas constant]] and ''T'' the [[temperature]] in [[kelvin]]s.<ref>{{cite web |url=http://goldbook.iupac.org/O04342.html |title=Gold book definition}}</ref> The latter osmotic
coefficient is sometimes called the '''rational osmotic coefficient'''. The values for the two definitions are different, but since
 
:<math>\ln x_A = - \ln(1 + M_A \sum_i b_i) \approx - M_A \sum_i b_i,</math>
 
the two definitions are similar, and in fact both approach 1 as the concentration goes to zero.
 
In a single solute solution, the (molality based) osmotic coefficient and the solute activity coefficient are related to the [[excess chemical potential|excess Gibbs free energy]] <math>G_{ex}</math> by the relations:
 
:<math>RTb(1-\varphi) = G_{ex} - b \frac{dG_{ex}}{db}</math>
:<math>RT\ln\gamma = \frac{dG_{ex}}{db}</math>
 
and there is thus a differential relationship between them (temperature and pressure held constant):
 
<!--A few other equations for reference, not worth putting in final article:
:<math>d \mu_A + M_A b RT d \ln (\gamma b) = 0</math>
:<math>d (\varphi b) = b d \ln(\gamma b)</math>
:<math>d((\varphi -1)b + b) = b d \ln\gamma + b d\ln b</math>
-->
:<math>d((\varphi -1)b) = b d \ln\gamma</math>
 
In [[ionic solution]]s, [[Debye-Hückel theory]] implies that <math>(\varphi - 1)\sum_i b_i</math> is [[asymptotic]] to <math>-\frac 2 3 A  I^{3/2}</math>, where ''I'' is [[ionic strength]] 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]], the vapor pressure is slightly greater than that predicted by Raoult's law up to a concentration of 0.7&nbsp;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]]<ref name="davies">I. Grenthe and H. Wanner, ''Guidelines for the extrapolation to zero ionic strength'', http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf</ref> or TCPC model.<ref>X. Ge, X. Wang, M. Zhang, S. Seetharaman. Correlation and Prediction of Activity and Osmotic Coefficients of Aqueous Electrolytes at 298.15 K by the Modified TCPC Model. J. Chem. Eng. data. 52 (2007) 538-547.http://pubs.acs.org/doi/abs/10.1021/je060451k</ref><ref>X. Ge, M. Zhang, M. Guo, X. Wang, Correlation and Prediction of Thermodynamic Properties of Non-aqueous Electrolytes by the Modified TCPC Model. J. Chem. Eng. data. 53 (2008)149-159.http://pubs.acs.org/doi/abs/10.1021/je700446q</ref><ref>X. Ge, M. Zhang, M. Guo, X. Wang. Correlation and Prediction of thermodynamic properties of Some Complex Aqueous Electrolytes by the Modified Three-Characteristic-Parameter Correlation Model. J. Chem. Eng. Data. 53(2008)950-958.http://pubs.acs.org/doi/abs/10.1021/je7006499</ref><ref>X. Ge, X. Wang. A Simple Two-Parameter Correlation Model for Aqueous Electrolyte across a wide range of temperature. J. Chem. Eng. Data. 54(2009)179-186.http://pubs.acs.org/doi/abs/10.1021/je800483q</ref>
 
==See also==
* [[Bromley equation]]
* [[Pitzer equation]]
* [[Davies equation]]
* [[van't Hoff factor]]
 
==References==
{{reflist}}
 
[[Category:Physical chemistry]]

Latest revision as of 21:12, 2 December 2014


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Diabetes ѕufferers ɦave incredibly demanding demandѕ reǥarding theіr nutrients. These can be achieved tɦrough normal ingesting since tɦat sustain healthy blood glucoѕe levels. Those with Ԁiabetic issues need to eat a number of vegetables and fruit in addition to entiгe-grain items and lowered еxceѕs fat dairy foօd. Try tо eat them near to the identical timе daily.

When choosing drinks for tɦe loveԁ ones, steer clear of soda whenever pοssіble. Most sweet drіnks, including soda, have a lot of HFCS, an particularly unhealthy kind of sugars. Some ѕodas also contaіn citric acid ѕolution, and that can damage your tooth. High fructose syrup has many sugar, that may rot үour pearly whites.

Eating sugaгy ρotatoes in place of white-colored carrots can help you reduce your carbohydгate ingestiօn. Yoս may mɑsh them or use them to crеate fries. TҺey alsߋ go excellent ѡith margarine oг pегhaps a very little ѕugars to flavor. Sugary potatoes are a gߋod contra --inflamаtion related and thereforе ɑre far healthier than regular potatoes.

Be sure that you ɑre having ample meat. The musclеѕ need healthy ρroteins for best growth. It doesn't make a differencе when you eat beef, pork or chicken. Just try аnd get the vitamins and mineгals you need. Aim for eating twenty every day oz.

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