Inverse Gaussian distribution - Revision history

en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB

2014-06-01T08:43:16Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB

← Older revision		Revision as of 10:43, 1 June 2014
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	I~~'m Yoshiko Oquendo. My job is a manufacturing and distribution officer~~ and I~~'m performing fairly~~ great ~~financially~~. ~~Bottle tops gathering~~ is ~~the only pastime his wife doesn't approve of~~. My home is ~~now in Kansas~~.<br><br>~~Stop by~~ my ~~blog post:~~ [~~http~~://~~Chilevisual~~.~~net/index~~.~~php?mod=users&action=view&id=7096 Chilevisual~~.~~net~~]		Hi there, I am Alyson Pomerleau and I think it seems quite great when you say it. Doing ballet is some thing she would by no means give up. Mississippi is exactly where her home is but her husband wants them to move. She works as a travel agent but quickly she'll be on her own.<br><br>Here is my webpage; clairvoyant psychic ([https://www.machlitim.org.il/subdomain/megila/end/node/12300 linked web site])

en>AnomieBOT: Dating maintenance tags: {{Deadlink}}

2014-02-19T21:50:22Z

Dating maintenance tags: {{Deadlink}}

← Older revision		Revision as of 23:50, 19 February 2014
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	'~~''Heat of formation group additivity''' methods in [[thermochemistry]] enable the calculation and prediction of [[heat of formation]] of [[organic compound]]s based on [[Chemical additive\|additivity]]~~. This method was pioneered by S. W. Benson.<ref>''Estimation of heats of formation of organic compounds by additivity methods'' N. Cohen, S. W. Benson [[Chem. Rev.]]; '''1993'''; 93(7); 2419-2438 [http://pubs.acs.org/cgi-bin/abstract.cgi/chreay/1993/93/i07/f-pdf/f_cr00023a005.pdf Abstract]</ref>		I'm Yoshiko Oquendo. My job is a manufacturing and distribution officer and I'm performing fairly great financially. Bottle tops gathering is the only pastime his wife doesn't approve of. My home is now in Kansas.<br><br>Stop by my blog post: [http://Chilevisual.net/index.php?mod=users&action=view&id=7096 Chilevisual.net]

	~~== Benson model ==~~
	~~{{Main\|Benson group increment theory}}~~
	~~Starting with simple linear and branched [[alkane]]s and [[alkene]]s the method works by collecting~~ a ~~large number of experimental heat of formation data (see: [[Standard enthalpy change of formation (data table)\|Heat of Formation table]])~~ and ~~then divide each molecule up into distinct groups each consisting of a central atom with multiple ligands:~~

	~~: X-(A)i(B)j(C)k(D)l~~

	~~To each group is then assigned an empirical incremental value which is independent on its position inside the molecule~~ and ~~independent of the nature of its neighbors:~~

	* P primary C-(C)(H)3 '''~~-10~~.~~00'''~~
	* S secondary C-(C)2(H)2 '''-5.00'''
	* T tertiary C-(C)3(H) '''-2.40'''
	* Q quaternary C-(C)4 '''-0.10'''
	* [[Gauche (stereochemistry)\|gauche]] correction '''+0.80'''
	* 1,5 [[pentane interference]] correction '''+1.60 '''
	~~: in kcal/mol and 298 K~~

	~~The following example illustrates how these values can be derived.~~

	~~The experimental heat of formation of [[ethane]]~~ is -20.03 kcal/mol and ethane consists of 2 P groups. Likewise [[propane]] (-25.02 kcal/mol) can be written as 2P+S, [[isobutane]] (-32.07) as 3P+T and [[neopentane]] (-40.18 kcal/mol) as 4P+Q. These four equations and 4 unknowns work out to estimations for P (-10.01 kcal/mol), S (-4.99 kcal/mol), T (-2.03 kcal/mol) and Q (-0.12 kcal/mol). Of course the ~~accuracy will increase when the dataset increases.~~

	~~the data allow the calculation~~ of ~~heat of formation for isomers. For example the pentanes:~~
	* n-pentane = 2P + 3S = -35 (exp. -35 kcal/mol)
	* isopentane = 3P + S + T + 1 gauche correction = -36.6 (exp. -36.7 kcal/mol)
	* neopentane = 4P + Q = 40.1 (exp. 40.1 kcal/mol)

	~~The group additivities for alkenes are:~~
	* Cd-(H2) '''+6.27'''
	* Cd-(C)(D) '''+8.55'''
	* Cd-(C)2 '''+10.19'''
	* Cd-(Cd)(H) '''+6.78'''
	* Cd-(Cd)(C) '''+8.76'''
	* C-(Cd)(H)3 '''-10.00'''
	* C-(Cd)(C)(H)2 '''-4.80'''
	* C-(Cd)(C)2(H) '''-1.~~67'''~~
	* C-(Cd)(C)3 '''+1.77'''
	* C-(Cd)2(H)2 '''-4.30'''
	* [[cis isomer\|cis]] correction '''+1.10'''
	* alkene gauche correction '''+0.80'''

	~~In alkenes the cis isomer~~ is ~~always less stable than the trans isomer by 1~~.~~10 kcal/mol.~~

	~~More group additivity tables exist for a wide range of functional groups.~~

	~~==Gronert model==~~
	~~An alternative model has been developed by S. Gronert based not on breaking molecules into fragments but based on 1,2 and 1,3 interactions~~ <~~ref~~>~~''An Alternative Interpretation of the C-H Bond Strengths of Alkanes'' Scott Gronert [[J. Org. Chem.]]; '''2006'''; 71(3) pp 1209 - 1219;~~ [http://~~dx.doi~~.~~org~~/10.1021/jo052363t Abstract]</ref><ref>''An Alternative Interpretation of the C-H Bond Strengths of Alkanes'' Scott Gronert [[J. Org. Chem.]]; '''2006'''; 71(25) pp 9560 - 9560; (Addition/Correction) {{DOI\|10.1021/jo062078p}}.</ref>

	~~The Gronert equation reads:~~
	~~<math>\ \Delta H_f~~ = ~~-146.0n_{C-C} -124.2n_{C-H} - 66.2n_{C~~=~~C} + 10.2n_{C-C-C}~~
	~~+ 9.3n_{C-C-H} + 6.6n_{H-C-H} + f(C,H)</math>~~

	~~<math>\ f(C,H)~~ = ~~(231~~.~~3n_{C} + 52.1n_{H})</math>~~

	~~The pentanes are now calculated as:~~
	* n-pentane = 4CC + 12CH + 9HCH + 18HCC + 3CCC + (5C + 12H) = - 35.1 kcal/mol
	* isopentane = 4CC + 12CH + 10HCH + 16HCC + 4CCC + (5C + 12H) = - 36.7 kcal/mol
	* neopentane = 4CC + 12CH + 12HCH + 12HCC + 6CCC + (5C + 12H) = -40.1 kcal/mol

	Key in this treatment is the introduction of 1,3-repulsive and destabilizing interactions and this type of [[steric hindrance]] should exist considering the [[molecular geometry]] of simple alkanes. In [[methane]] the distance between the hydrogen atoms is 1.8 [[angstrom]] but the combined [[Van der Waals radius\|van der Waals radii]] of hydrogen are 2.4 angstrom implying steric hindrance. Also in propane the methyl to methyl distance is 2.5 angstrom whereas the combined van der Waals radii are much larger (4 angstrom).

	In the Gronert model these repulsive 1,3 interactions account for trends in [[bond dissociation energy\|bond dissociation energies]] which for example decrease going from methane to ethane to isopropane to neopentane. In this model the [[homolysis (chemistry)\|homolysis]] of a C-H bond releases [[strain energy]] in the alkane. In traditional bonding models the driving force is the ability of alkyl groups to donate electrons to the newly formed [[free radical]] carbon.

	~~== See also ==~~
	* [[Joback method]]

	~~== References ==~~
	~~<references/>~~

	~~[[Category:Thermochemistry]]~~
	~~[[Category:Thermodynamic models]~~]

en>BeyondNormality: /* External links */

2013-12-10T03:53:23Z

External links

← Older revision		Revision as of 05:53, 10 December 2013
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	~~Andrew Simcox~~ is the ~~title his parents gave him~~ and ~~he totally loves this title~~. ~~Distributing manufacturing~~ is ~~how he tends~~ to ~~make a living~~. ~~Some time ago he selected to live in North Carolina~~ and ~~he doesn~~'~~t plan on changing it~~. ~~What me and my family adore~~ is ~~performing ballet~~ but I'~~ve been using on new issues lately~~.<br><br>~~my homepage~~ - ~~tarot card readings~~ (~~[http:~~//~~isaworld~~.pe.kr/~~?document_srl~~=~~392088 http~~://~~isaworld~~.pe.kr/])		'''Heat of formation group additivity''' methods in [[thermochemistry]] enable the calculation and prediction of [[heat of formation]] of [[organic compound]]s based on [[Chemical additive\|additivity]]. This method was pioneered by S. W. Benson.<ref>''Estimation of heats of formation of organic compounds by additivity methods'' N. Cohen, S. W. Benson [[Chem. Rev.]]; '''1993'''; 93(7); 2419-2438 [http://pubs.acs.org/cgi-bin/abstract.cgi/chreay/1993/93/i07/f-pdf/f_cr00023a005.pdf Abstract]</ref>

			== Benson model ==
			{{Main\|Benson group increment theory}}
			Starting with simple linear and branched [[alkane]]s and [[alkene]]s the method works by collecting a large number of experimental heat of formation data (see: [[Standard enthalpy change of formation (data table)\|Heat of Formation table]]) and then divide each molecule up into distinct groups each consisting of a central atom with multiple ligands:

			: X-(A)i(B)j(C)k(D)l

			To each group is then assigned an empirical incremental value which is independent on its position inside the molecule and independent of the nature of its neighbors:

			* P primary C-(C)(H)3 '''-10.00'''
			* S secondary C-(C)2(H)2 '''-5.00'''
			* T tertiary C-(C)3(H) '''-2.40'''
			* Q quaternary C-(C)4 '''-0.10'''
			* [[Gauche (stereochemistry)\|gauche]] correction '''+0.80'''
			* 1,5 [[pentane interference]] correction '''+1.60 '''
			: in kcal/mol and 298 K

			The following example illustrates how these values can be derived.

			The experimental heat of formation of [[ethane]] is -20.03 kcal/mol and ethane consists of 2 P groups. Likewise [[propane]] (-25.02 kcal/mol) can be written as 2P+S, [[isobutane]] (-32.07) as 3P+T and [[neopentane]] (-40.18 kcal/mol) as 4P+Q. These four equations and 4 unknowns work out to estimations for P (-10.01 kcal/mol), S (-4.99 kcal/mol), T (-2.03 kcal/mol) and Q (-0.12 kcal/mol). Of course the accuracy will increase when the dataset increases.

			the data allow the calculation of heat of formation for isomers. For example the pentanes:
			* n-pentane = 2P + 3S = -35 (exp. -35 kcal/mol)
			* isopentane = 3P + S + T + 1 gauche correction = -36.6 (exp. -36.7 kcal/mol)
			* neopentane = 4P + Q = 40.1 (exp. 40.1 kcal/mol)

			The group additivities for alkenes are:
			* Cd-(H2) '''+6.27'''
			* Cd-(C)(D) '''+8.55'''
			* Cd-(C)2 '''+10.19'''
			* Cd-(Cd)(H) '''+6.78'''
			* Cd-(Cd)(C) '''+8.76'''
			* C-(Cd)(H)3 '''-10.00'''
			* C-(Cd)(C)(H)2 '''-4.80'''
			* C-(Cd)(C)2(H) '''-1.67'''
			* C-(Cd)(C)3 '''+1.77'''
			* C-(Cd)2(H)2 '''-4.30'''
			* [[cis isomer\|cis]] correction '''+1.10'''
			* alkene gauche correction '''+0.80'''

			In alkenes the cis isomer is always less stable than the trans isomer by 1.10 kcal/mol.

			More group additivity tables exist for a wide range of functional groups.

			==Gronert model==
			An alternative model has been developed by S. Gronert based not on breaking molecules into fragments but based on 1,2 and 1,3 interactions <ref>''An Alternative Interpretation of the C-H Bond Strengths of Alkanes'' Scott Gronert [[J. Org. Chem.]]; '''2006'''; 71(3) pp 1209 - 1219; [http://dx.doi.org/10.1021/jo052363t Abstract]</ref><ref>''An Alternative Interpretation of the C-H Bond Strengths of Alkanes'' Scott Gronert [[J. Org. Chem.]]; '''2006'''; 71(25) pp 9560 - 9560; (Addition/Correction) {{DOI\|10.1021/jo062078p}}.</ref>

			The Gronert equation reads:
			<math>\ \Delta H_f = -146.0n_{C-C} -124.2n_{C-H} - 66.2n_{C=C} + 10.2n_{C-C-C}
			+ 9.3n_{C-C-H} + 6.6n_{H-C-H} + f(C,H)</math>

			<math>\ f(C,H) = (231.3n_{C} + 52.1n_{H})</math>

			The pentanes are now calculated as:
			* n-pentane = 4CC + 12CH + 9HCH + 18HCC + 3CCC + (5C + 12H) = - 35.1 kcal/mol
			* isopentane = 4CC + 12CH + 10HCH + 16HCC + 4CCC + (5C + 12H) = - 36.7 kcal/mol
			* neopentane = 4CC + 12CH + 12HCH + 12HCC + 6CCC + (5C + 12H) = -40.1 kcal/mol

			Key in this treatment is the introduction of 1,3-repulsive and destabilizing interactions and this type of [[steric hindrance]] should exist considering the [[molecular geometry]] of simple alkanes. In [[methane]] the distance between the hydrogen atoms is 1.8 [[angstrom]] but the combined [[Van der Waals radius\|van der Waals radii]] of hydrogen are 2.4 angstrom implying steric hindrance. Also in propane the methyl to methyl distance is 2.5 angstrom whereas the combined van der Waals radii are much larger (4 angstrom).

			In the Gronert model these repulsive 1,3 interactions account for trends in [[bond dissociation energy\|bond dissociation energies]] which for example decrease going from methane to ethane to isopropane to neopentane. In this model the [[homolysis (chemistry)\|homolysis]] of a C-H bond releases [[strain energy]] in the alkane. In traditional bonding models the driving force is the ability of alkyl groups to donate electrons to the newly formed [[free radical]] carbon.

			== See also ==
			* [[Joback method]]

			== References ==
			<references/>

			[[Category:Thermochemistry]]
			[[Category:Thermodynamic models]]

en>Braincricket: Typo fixing, typos fixed: Schrodinger → Schrödinger using AWB (8062)

2012-06-29T00:05:17Z

Typo fixing, typos fixed: Schrodinger → Schrödinger using AWB (8062)

New page

Andrew Simcox is the title his parents gave him and he totally loves this title. Distributing manufacturing is how he tends to make a living. Some time ago he selected to live in North Carolina and he doesn't plan on changing it. What me and my family adore is performing ballet but I've been using on new issues lately.<br><br>my homepage - tarot card readings ([http://isaworld.pe.kr/?document_srl=392088 http://isaworld.pe.kr/])