SIMPLE algorithm: Difference between revisions

Revision as of 14:59, 10 December 2013

An osmotic coefficient φ is a quantity which characterises the deviation of a solvent from ideal behaviour, referenced to Raoult's law. The osmotic coefficient based on molality b is defined by:

φ = \frac{μ_{A}^{*} - μ_{A}}{R T M_{A} \sum_{i} b_{i}}

and on an amount fraction basis by:

φ = - \frac{μ_{A}^{*} - μ_{A}}{R T \ln x_{A}}

where $μ_{A}^{*}$ is the chemical potential of the pure solvent and $μ_{A}$ is the chemical potential of the solvent in a solution, M_A is its molar mass, x_A its amount fraction, R the gas constant and T the temperature in kelvins.^[1] The latter osmotic coefficient is sometimes called the rational osmotic coefficient. The values for the two definitions are different, but since

\ln x_{A} = - \ln (1 + M_{A} \sum_{i} b_{i}) \approx - M_{A} \sum_{i} b_{i},

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 Gibbs free energy $G_{e x}$ by the relations:

R T b (1 - φ) = G_{e x} - b \frac{d G_{e x}}{d b}

R T \ln γ = \frac{d G_{e x}}{d b}

and there is thus a differential relationship between them (temperature and pressure held constant):

d ((φ - 1) b) = b d \ln γ

In ionic solutions, Debye-Hückel theory implies that $(φ - 1) \sum_{i} b_{i}$ is asymptotic to $- \frac{2}{3} A I^{3 / 2}$ , 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 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^[2] or TCPC model.^[3]^[4]^[5]^[6]

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

↑ Template:Cite web
↑ I. Grenthe and H. Wanner, Guidelines for the extrapolation to zero ionic strength, http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf
↑ 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
↑ 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
↑ 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
↑ 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

[1] Template:Cite web

[davies-2] I. Grenthe and H. Wanner, Guidelines for the extrapolation to zero ionic strength, http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf

[3] 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

[4] 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

[5] 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

[6] 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

[1]

[2]

[3]

[4]

[5]

[6]

@@ Line 1: / Line 1: @@
-Surely the second option would be more beneficial for any website. It is very easy to customize plugins according to the needs of a particular business. The Word - Press Dashboard : an administrative management tool that supports FTP content upload  2.  For more information about [http://www.anjomanma.cloudsite.ir/S80P wordpress backup] review our own web-page. If you are using videos on your site then this is the plugin to use. It's as simple as hiring a Wordpress plugin developer or learning how to create what is needed. <br><br>Right starting from social media support to search engine optimization, such plugins are easily available within the Word - Press open source platform. After all, Word - Press is free, many of the enhancements for Word - Press like themes and plugins are also free, and there is plenty of free information online about how to use Word - Press. There are number of web services that offer Word press development across the world. These four plugins will make this effort easier and the sites run effectively as well as make other widgets added to a site easier to configure. W3C compliant HTML and a good open source powered by Word - Press CMS site is regarded as the prime minister. <br><br>Your Word - Press blog or site will also require a domain name which many hosting companies can also provide. The following piece of content is meant to make your choice easier and reassure you that the decision to go ahead with this conversion is requited with rich benefits:. Whether or not it's an viewers on your web page, your social media pages, or your web page, those who have a present and effective viewers of "fans" are best best for provide provides, reductions, and deals to help re-invigorate their viewers and add to their main point here. Nonetheless, with stylish Facebook themes obtainable on the Globe Broad Internet, half of your enterprise is done previously. Article Source:  Stevens works in Internet and Network Marketing. <br><br>You can add keywords but it is best to leave this alone. High Quality Services: These companies help you in creating high quality Word - Press websites. One of the great features of Wordpress is its ability to integrate SEO into your site. Contact Infertility Clinic Providing One stop Fertility Solutions at:. Fortunately, Word - Press Customization Service is available these days, right from custom theme design, to plugin customization and modifying your website, you can take any bespoke service for your Word - Press development project. <br><br>A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. If you operate a website that's been built on HTML then you might have to witness traffic losses because such a site isn't competent enough in grabbing the attention of potential consumers. You can select color of your choice, graphics of your favorite, skins, photos, pages, etc. Word - Press is an open source content management system which is easy to use and offers many user friendly features. Article Source:  Hostgator discount coupons for your Wordpress site here.
+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>
+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]]

SIMPLE algorithm: Difference between revisions

Revision as of 14:59, 10 December 2013

See also

References

Navigation menu

Search