en>Yangshuai: The relation name should be uppercase.

2013-05-15T10:44:43Z

The relation name should be uppercase.

← Older revision		Revision as of 12:44, 15 May 2013
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	~~They contact me Emilia~~. ~~Bookkeeping~~ is ~~her working day occupation now. Years in~~ the ~~past we moved~~ to ~~North Dakota~~. ~~The favorite hobby for my children~~ and ~~me is to perform baseball but I haven~~'~~t made a dime with it~~.<br><br>~~Feel free to surf to my website~~ - [~~http:~~//~~facehack~~.ir/~~index.php?do~~=/~~blog~~/20/~~what~~-~~you~~-~~have~~-to-do-~~facing-candida~~/ ~~home std test~~]		In chemistry, a '''regular solution''' is a solution that diverges from the behavior of an [[ideal solution]] only moderately.<ref>Simon & McQuarrie Physical Chemistry: A molecular approach</ref> Its [[entropy of mixing]] is equal to that of an ideal solution with the same composition, due to random mixing without strong specific interactions.<ref>P. Atkins and J. de Paula, ''Atkins' Physical Chemistry'' (8th ed. W.H. Freeman 2006) p.149</ref><ref>P.A. Rock, ''Chemical Thermodynamics. Principles and Applications'' (Macmillan 1969) p.263</ref> For two components

			:<math>\Delta S_m = -nR(x_1\ln x_1 + x_2\ln x_2)\,</math>

			where <math>R\,</math> is the [[gas constant]], <math>n\,</math> the total number of [[mole (unit)\|moles]] and <math>x_i\,</math> the [[mole fraction]] of each component. The [[enthalpy]] of mixing is non-zero, unlike for an ideal solution.

			A regular solution can also be described by [[Raoult's law]] modified with a [[Margules function]] with only one parameter A:

			:<math>\ P_1= x_1P^*_1f_{1,M}\,</math>
			:<math>\ P_2= x_2P^*_2f_{2,M}\,</math>

			Where the Margules function is

			:<math>\ f_{1,M}= exp(Ax_2^2)\,</math>
			:<math>\ f_{2,M}= exp(Ax_1^2)\,</math>

			Notice that the Margules function for each component contains the mole fraction of the other component. It can also be shown using the [[Gibbs-Duhem relation]] that if the first Margules expression holds, then the other one must have the same shape.

			The value of α can be interpreted as W/RT, where W = 2U<sub>12</sub> - U<sub>11</sub> - U<sub>22</sub> represents the difference in interaction energy between like and unlike neighbors.

			In contrast to the case of ideal solutions, regular solutions do possess a non-zero enthalpy of mixing, due to the W term. If the unlike interactions are more unfavorable than the like ones, we get competition between an entropy of mixing term that produces a minimum in the Gibbs free energy at x<sub>1</sub>= 0.5 and the enthalpy term that has a maximum there. At high temperatures the entropy wins and the system is fully miscible, but at lower temperatures the G curve will have two minima and a maximum in between. This results in phase separation. In general there will be a temperature where the three extremes coalesce and the system becomes fully miscible. This point is known as the [[upper critical solution temperature]] or the upper consolute temperature.

			In contrast to ideal solutions, the volumes in the case of regular solutions are no longer strictly additive but must be calculated from the [[partial molar volume]]s that are a function of x<sub>1</sub>.

			The term was introduced in 1927 by the American physical chemist [[Joel Henry Hildebrand]].<ref>[http://www.nature.com/nature/journal/v168/n4281/abs/168868a0.html The Term 'Regular Solution'] Nature, v.168, p.868 (1951)</ref>
			==See also==
			[[solid solution]]
			==References==
			{{Reflist}}
			[[Category:Thermodynamics]]
			[[Category:Chemical thermodynamics]]

en>Mild Bill Hiccup: /* Improved version */ spelling

2011-05-20T10:55:39Z

Improved version: spelling

New page

They contact me Emilia. Bookkeeping is her working day occupation now. Years in the past we moved to North Dakota. The favorite hobby for my children and me is to perform baseball but I haven't made a dime with it.<br><br>Feel free to surf to my website - [http://facehack.ir/index.php?do=/blog/20/what-you-have-to-do-facing-candida/ home std test]

Nested loop join - Revision history

en>Yangshuai: The relation name should be uppercase.

en>Mild Bill Hiccup: /* Improved version */ spelling