en>Barney Stratford: Change the reference to a pullback to refer to the categorical notion.

2013-05-14T20:50:02Z

Change the reference to a pullback to refer to the categorical notion.

← Older revision		Revision as of 22:50, 14 May 2013
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	~~She is understood by~~ the ~~category~~ of ~~[http~~://~~www~~.~~google~~.co.~~uk/search?hl~~=~~en&gl~~=~~us&tbm~~=~~nws&q~~=~~Maryjane~~+~~Lacroix&gs_l=news Maryjane Lacroix] but she never really liked that name. My wife we live~~ in ~~North Dakota. I used~~ to ~~be unemployed but now~~ i~~'m a librarian~~. ~~Her friends say it's not good for her but what she loves doing is creating and she's been doing it for a very long time. She's been working on her website for some time now. Give it a look here~~: ~~https~~://www.~~5goal~~.com/[~~https~~://~~www~~.~~5goal~~.~~com~~/~~โต๊ะบอล~~.~~html โต๊ะบอล~~]~~.html~~		'''Excess molar quantities''' are properties of mixtures which characterize the nonideal behaviour of real mixtures. They are the difference between the partial molar property of a component in a real mixture and that of the component in an ideal mixture. By definition, excess properties of a mixture are related to those of the pure substances in an ideal mixture by:

			:<math>z^E=z-\sum_i x_iz^{id}_i.</math>

			Here <math>*</math> denotes the pure substance, <math>E</math> the excess molar property, and <math>z</math> corresponds to the specific property under consideration. From the definition of partial molar properties,

			:<math>z=\sum_i x_i \bar{Z_i},</math>

			substitution yields:

			:<math>z^E=\sum_i x_i(\bar{Z_i}-z_i^{id}).</math>
			For volumes, internal energies and enthalpies the excess quantities are identical to the mixing quantities.

			==Examples==
			The volume of a mixture from the sum of the excess volumes of the components of a mixture is given by the formula:
			:<math>
			{V} = \sum_i V_i + \sum_i V_i^{E}
			</math>

			Deriving by temperature the thermal expansivities of the components in a mixture can be related to the expansivity of the mixture:
			:<math>\frac{\partial V}{\partial T} = \sum_i \frac{\partial V_i}{\partial T} + \sum_i \frac{\partial V_i^{E}}{\partial T}
			</math>
			Equivalently:
			<math>
			:\alpha_V V = \sum_i \alpha_{V,i} V_i + \sum_i \frac{\partial V_i^{E}}{\partial T}
			</math>

			Substituting the excess molar volume
			:<math>\frac{\partial \bar{V^E}_i}{\partial T} = R \frac{\partial (ln(\gamma_i))}{\partial P} +RT {\partial^2\over\partial T\partial P} ln(\gamma_i)</math>
			one can relate activity coefficients to thermal expansivity.

			==See also==
			*[[Apparent molar property]]
			*[[Heat of mixing]]

			==References==
			{{cite book \| last = Frenkel \| first = Daan \| authorlink = Daan Frenkel \| coauthors = Smit, Berend \| title = Understanding Molecular Simulation : from algorithms to applications \| publisher = [[Academic Press]] \| year = 2001 \| location = [[San Diego, California]] \| pages = \| url = \| doi = \| id = \| isbn = 0-12-267351-4 }}

			==External links==
			* [http://www.springerlink.com/content/c5h0r422j762k416/]
			* [http://scitation.aip.org/content/aip/journal/jcp/32/5/10.1063/1.1730921 excess quantities for electrolyte mixtures]
			[[Category:Physical quantities]]

en>Linas: /* References */ add ref

2012-09-01T23:50:38Z

References: add ref

New page

She is understood by the category of [http://www.google.co.uk/search?hl=en&gl=us&tbm=nws&q=Maryjane+Lacroix&gs_l=news Maryjane Lacroix] but she never really liked that name. My wife we live in North Dakota. I used to be unemployed but now i'm a librarian. Her friends say it's not good for her but what she loves doing is creating and she's been doing it for a very long time. She's been working on her website for some time now. Give it a look here: https://www.5goal.com/[https://www.5goal.com/โต๊ะบอล.html โต๊ะบอล].html

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en>Barney Stratford: Change the reference to a pullback to refer to the categorical notion.

en>Linas: /* References */ add ref