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| The '''van 't Hoff equation''' in [[chemical thermodynamics]] relates the change in the [[equilibrium constant]], ''K<sub>eq</sub>'', of a chemical equilibrium to the change in [[temperature]], ''T'', given the [[Enthalpy of formation|standard enthalpy change]], ''ΔH<sup><s>o</s></sup>'', for the process. It was proposed by Dutch chemist [[Jacobus Henricus van't Hoff|J.H. van't Hoff]] in 1884.<ref>[http://nobelprize.org/nobel_prizes/chemistry/laureates/1901/hoff-bio.html Biography on Nobel prize website]. Nobelprize.org (1911-03-01). Retrieved on 2013-11-8.</ref>
| | == Mbt Paris I think it was past 9pm == |
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| The '''van't Hoff equation''' has been widely utilized to explore the changes in [[state functions]] in a [[thermodynamic system]]. The '''van't Hoff plot''', which is derived from this equation, is especially effective in estimating the change in [[enthalpy]], or total energy, and [[entropy]], or amount of disorder, of a [[chemical reaction]].
| | At the end of March, the coroner's court handed over copies of all the evidence gathered for the inquiry including copies of the three notes she left before her apparent suicide, a police report, toxicology results, a statement from the duty nurse who was the last person to see her alive as well as a letter from her GP which is expected to detail whether she [http://www.aquasky.fr/libraries/openid/Auth/Yadis/title.php Mbt Paris] was on medication at the . <br><br>I think it was past 9pm, "Ravi, you know Sania Mirza is upset with Bangaluru crowds. Keep the html/xhtml code clean and remove old code when not in use. I just dont know how you keep sane, you ae so incredibly strong and I admire [http://www.hotel-aragon-fitou.fr/wp-includes/Text/Diff/Renderer/cancle.php Sac Michael Kors] you both so much. At age 33, Liz got married for the first time and within six weeks she began to lose her hair in little peasize spots . <br><br>Actually, without sufficient info, a driver in Pennsylvania can end up paying unnecessarily high premiums on the wrong auto insurance policy. Apart from their lower testosterone levels which limit muscle size, avoiding very heavy weights means you'll end up sleek and sculptured rather than big and beefy. <br><br>MichaelJ's photos tell the story. It saves you a ton of time too !Related PostsLinking to different pages in your blog from every page is a great search engine optimization tactic.. Kylook also guarantees users a permanent access to their information due to the automatic security copies that are saved encrypted in [http://www.latuilliere.fr/libraries/joomla/base/editor.php Louis Vuitton Lunette] its servers... <br><br>The males were at 62 of deliveries; 70 provided emotional support at the [http://morphman59.free.fr/libraries/joomla/installer/files.php Chaussures Prada] time. Only in some games though. One of my early articles looked at Berkshire Hathaway's portfolio using my portfolio analysis software. FB has many private settings. It's the web pages that change drastically. <br><br>I checked my email [http://www.campingduvaljoyeux.fr/115/defines.php Tn Nike Pas Cher] and my best friend, Sara, had emailed me a link to what would get me tons of income, hours of stuff to do, and just pure fun! You see, this link is a like to DUCK TAPE duct tape brand's annual "Stuck at Prom" contest.. She is near sighted, so she can't see things that are far away, other than that she can see just fine.. <br><br>You may be offered the swine flu vaccine as well. Asparagus is a rich source of potassium, a mineral that regulates fluid balance; so the diuretic effects of asparagus can reduce bloating in the tummy area that sometimes occurs after eating a big meal.. <br><br>That's not to say that Apple didn't give us a whole heap of extremely random problems, or that I rush to install updates as soon as they're out, but most of the time there was no problem with updates, and when there was, it was /always/ . He given module is used to administer all core features of the program.<ul> |
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| | <li>[http://annuncianimali.altervista.org/index.php?page=item&id=133834 http://annuncianimali.altervista.org/index.php?page=item&id=133834]</li> |
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| | <li>[http://cerisier.info/spip.php?article25/ http://cerisier.info/spip.php?article25/]</li> |
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| | <li>[http://verdamilio.info/org/spip.php?article573/ http://verdamilio.info/org/spip.php?article573/]</li> |
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| | </ul> |
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| ==Equation== | | == Tn Requin Pas Cher . == |
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| ===Under standard conditions===
| | It's one of the famous Indian website where you can find some of the best games of till date like the SpiderMan Mission Impossible. The TRT is a panel of concerned citizens who represent local counties, commercial businesses, and OHV recreationists.. <br><br>And around the world. It's not enough to insert your company name in the title tag though. Many of the Training practices have been part of the Scheme for successive years, and most of the Trainers hold the PGCert Ed qualification. Education 1960 1964 Rumbek Secondary School 1964 1968 University of Khartoum, Faculty of Liberal, graduating [http://www.campingduvaljoyeux.fr/115/defines.php Tn Requin Pas Cher] with honours degree in Literature Geography Employment and Work Experience 1968 1969 MP in National Assembly, Khartoum representing Constituency of 132 of Paliet area He taught in the following Hight Schools Kosti el Ghoz 1969 1970 Madina Arab Secondary School [http://francis.poulain.free.fr/plugins/user/user.php Mont Blanc Stylo] 1970 1971 Hantoub , . <br><br>Career Cannon made her screen debut in 1960 in The Rise and Fall of Legs Diamond however her . I'm not sure why I bothered, as I'd already checked in online. "I started a German course in the prison and one day while we were on break during one of our lessons I went back to my room and saw some strange people in the room and I turned back because I thought that I had entered a wrong room, but as I made steps to go back my room [http://www.aquasky.fr/libraries/openid/Auth/Yadis/title.php Mbt Chaussures] mate called me to come in that it was our room.. <br><br>She thanks her mother, Dianna Roberson (ne Goss), for introducing her to the world of letters, words, and books. The all natural herb seems to have the majority health components,Next follows bigger selection of Oakley solar shades,fredpreeypolo, while the inhibition in teeth cavities along with cavity enducing plaque, according to "stevia sweetener: natural Sweetener" near Rita Elkins... <br><br>Tips about information [http://www.hotel-aragon-fitou.fr/wp-includes/Text/Diff/Renderer/cancle.php Sac Michael Kors] on the easiest way partners should cherish his or her own spouses Exactly partners possibly may want to cherish their very own women "Will you put associated with written, to commitment, personal mortgages, promises, placing best wishes on the road to article simply freelance text is useful the email emailer and also also the wr to remember fondly the . <br><br>Our doctors really do value our opinions and it is great to be able to chat to them informally about the practice, tell them what we [http://www.odea-amcala.fr/wp-content/themes/itheme2/includes/pear.php Nike Shox Pas Cher] think, praise what we like and offer suggestions if we think something could be done better. The Little Library is an open source app that allows you to upload, store, and share creative commons licensed content across computers and digital devices, offline and in the cloud.<ul> |
| The van't Hoff equation is based on the assumption that the enthalpy and entropy are constant with temperature changes. In practice, the equation is experimentally approximate in that both enthalpy and entropy changes of a process (reaction) vary (each differently) with temperature.<ref>{{cite journal|last=Craig|first=Norman|title=Entropy Diagrams|journal=J. Chem. Educ.|year=1996|issue=73|page=710|doi=10.1021/ed073p710|url=http://pubs.acs.org/doi/abs/10.1021/ed073p710?journalCode=jceda8&quickLinkVolume=73&quickLinkPage=710&selectedTab=citation&volume=73}}</ref><ref>{{cite journal|last=Gutman|first=I.|coauthors=Djurdjevic|title=P.|journal=J. Chem. Educ|year=1988|issue=65|page=399|doi=10.1021/ed065p399|url=http://pubs.acs.org/doi/abs/10.1021/ed065p399?journalCode=jceda8&quickLinkVolume=65&quickLinkPage=399&selectedTab=citation&volume=65}}</ref> Its accuracy is determined in accounting for the curvature in the standard enthalpy changes over temperature. A major use of the equation is to estimate a new [[equilibrium constant]] at a new [[absolute temperature]] assuming a constant [[Standard enthalpy of reaction|standard enthalpy]] change over the temperature range.
| | |
| | | <li>[http://verdamilio.net/tonio/spip.php?article1968/ http://verdamilio.net/tonio/spip.php?article1968/]</li> |
| Under [[Standard conditions for temperature and pressure|standard conditions]], the van't Hoff equation is<ref>{{Cite book |title=Physical chemistry |author=P.W. Atkins |publisher=Oxford University Press |year=1978 |isbn=0-198-55148-7}}</ref><ref>Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, ISBN 0-356-03736-3</ref>
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| | | <li>[http://ldsbee.com/index.php?page=item&id=4141343 http://ldsbee.com/index.php?page=item&id=4141343]</li> |
| {{Equation box 1
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| |indent =:
| | <li>[http://tonydog518.lauraonline.net/read.php?tid=2179084 http://tonydog518.lauraonline.net/read.php?tid=2179084]</li> |
| |equation = <math> \frac{d \ln K_{eq}}{dT} = \frac{\Delta H^\ominus}{RT^2},</math>
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| |border colour = #50C878
| | <li>[http://www.bbscan.com/news/html/?215714.html http://www.bbscan.com/news/html/?215714.html]</li> |
| |background colour = #ECFCF4}}
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| | | </ul> |
| where ''R'' is the [[gas constant]]. This can also be written as<ref name="Atkins2006">{{cite book |last1=Atkins |first1=Peter |last2=De Paula |first2=Julio |title=Physical Chemistry |page=212 |publisher=W.H. Freeman and Company |edition=8th |date=10 March 2006 |isbn=0-7167-8759-8}}</ref>
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| :<math> \frac{d \ln K_{eq}}{d {\frac{{1 }}{{T }}}} = -\frac{\Delta H^\ominus}{R}. </math>
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| Taking the definite integral of this differential equation between temperatures ''T<sub>1</sub>'' and ''T''<sub>2</sub> gives
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| :<math>\ln \left( {\frac{{K_2 }}{{K_1 }}} \right) = \frac{{\ - \Delta H^\ominus }}{R}\left( {\frac{1}{{T_2 }} - \frac{1}{{T_1 }}} \right).</math>
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| In this equation ''K''<sub>1</sub> is the equilibrium constant at absolute temperature ''T''<sub>1</sub>, and ''K''<sub>2</sub> is the equilibrium constant at absolute temperature ''T''<sub>2</sub>.
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| | |
| From the definition of [[Gibbs free energy]]
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| :<math> \Delta G^\ominus = \Delta H^\ominus - T\Delta S^\ominus </math>
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| where ''S'' is the [[entropy]] of the system, and from the Gibbs free energy isotherm equation<ref>Chemistry, Matter, and the Universe, R.E. Dickerson, I. Geis, W.A. Benjamin Inc. (USA), 1976, ISBN 0-19-855148-7</ref>
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| :<math>\Delta G^\ominus = -RT \ln K_{eq} </math>
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| the linear form of the van't Hoff equation can be obtained
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| :<math>\ln K_{eq} = - \frac{{\Delta H^\ominus}}{RT}+ \frac{{\Delta S^\ominus }}{R}. </math>
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| Therefore, when the range in temperature is small enough that the standard enthalpy change is essentially constant, a plot of the [[natural logarithm]] of the equilibrium constant versus the [[Multiplicative inverse|reciprocal]] temperature gives a straight line. The slope of the line is equal to minus the standard [[enthalpy]] change divided by the [[gas constant]], -Δ''H''<sup><s>o</s></sup>/''R'', and the intercept is equal to the standard [[entropy]] change divided by the gas constant, Δ''S''<sup><s>o</s></sup>/''R''. Differentiation of this expression with respect to the variable (1/T) yields the van't Hoff equation.
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| ===Van't Hoff isotherm===
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| The [[Gibbs free energy]] can change with the change of the temperature and pressure of the [[thermodynamic system]]. The '''van't Hoff [[isothermal process|isotherm]]''' can be used to determine the Gibbs free energy for non-standard state reactions at a constant temperature:<ref>{{cite book|last=Monk|first=Paul|title=Physical Chemistry: Understanding our Chemical World|year=2004|publisher=Wiley|isbn=978-0471491811|page=162}}</ref>
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| <math>\left(\frac {dG}{d\xi}\right)_{T,p} = \Delta_rG + RT \ln Q_r~</math>
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| | |
| where <math>\Delta_rG</math> is the Gibbs free energy for the reaction, and <math>Q_r~</math> is the [[reaction quotient]]. When a reaction is at [[Chemical equilibrium|equilibrium]], <math>Q_r~=K_{eq}</math>. The van't Hoff isotherm can help estimate the equilibrium reaction shift. When <math>\Delta_rG<0</math>, the reaction moves in the forward direction. When <math>\Delta_rG>0</math>, the reaction moves in the backwards directions. See [[Chemical equilibrium]].
| |
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| ==Van't Hoff plot==
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| For a [[reversible reaction]], the equilibrium constant can be measured at a variety of temperatures. This data can be plotted on a graph with <math>\ln K_{eq}</math> on the Y-axis and <math>1/T</math> on the X-axis. The data should have a linear relationship, the equation for which can be found by fitting the data using the linear form of the van't Hoff equation
| |
| :<math>\ln K_{eq} = - \frac{{\Delta H^\ominus}}{RT}+ \frac{{\Delta S^\ominus }}{R}. </math>
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| This graph is called the '''van't Hoff plot''' and is widely used to estimate the [[enthalpy]] and [[entropy]] of a [[chemical reaction]]. From this plot, <math>-\frac{\Delta H}{R}</math> is the slope and <math>\frac{\Delta S}{R}</math> is the intercept of the linear fit.
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| By measuring the [[equilibrium constant]], ''K<sub>eq</sub>'', at different temperatures, the van't Hoff plot can be used to assess a reaction when temperature changes.<ref>{{cite journal|last=Kim|first=Tae Woo|title=Dynamic [2]Catenation of Pd(II) Self-assembled Macrocycles in Water|journal=Chem. Lett.|year=2012|issue=41|page=70|doi=10.1246/cl.2012.70}}</ref><ref>{{cite journal|last=Ichikawa|first=Takayuki|title=Thermodynamic properties of metal amides determined by ammonia pressure-composition isotherms|journal=J. Chem. Thermodynamics|year=2010|issue=42|page=140|doi=10.1016/j.jct.2009.07.024}}</ref> Knowing the slope and intercept from the van't Hoff plot, the enthalpy and entropy of a reaction can be easily obtained using
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| <math>\Delta H = - R * slope,</math>
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| <math>\Delta S = R * interception.</math>
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| The van't Hoff plot can be used to quickly determine the enthalpy of a chemical reaction both qualitatively and quantitatively. Change in enthalpy can be positive or negative, leading to two major forms of the van't Hoff plot.
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| ===Endothermic reactions===
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| [[File:Endothermic Reaction van't Hoff Plot.png|thumb|right|x285px|Endothermic Reaction van't Hoff Plot]]
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| For an [[endothermic reaction]], heat is absorbed, making the net enthalpy change positive. Thus, according to the definition of the slope:
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| <math>Slope= -\frac{\Delta H}{R}</math> | |
| | |
| for an [[endothermic]] reaction,
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| <math>\Delta H > 0</math> and R is the [[gas constant]]
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| So
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| | |
| <math>Slope= -\frac{\Delta H}{R} < 0</math>
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| Thus, for an endothermic reaction, the van't Hoff plot should always have a negative slope.
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| ===Exothermic reactions===
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| [[File:Exothermic Reaction van't Hoff Plot.png|thumb|right|x285px|Exothermic Reaction van't Hoff Plot]]
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| For an [[exothermic reaction]], heat is released, making the net enthalpy change negative. Thus, according to the definition of the slope:
| |
| | |
| <math>Slope= -\frac{\Delta H}{R}</math>
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| | |
| from an [[exothermic]] reaction,
| |
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| <math>\Delta H < 0</math> and R is the [[gas constant]]
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| | |
| So
| |
| | |
| <math>Slope= -\frac{\Delta H}{R} > 0</math>
| |
| | |
| Thus, for an exothermic reaction, the van't Hoff plot should always have a positive slope.
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| | |
| ===Temperature dependence of the equilibrium constant===
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| By analyzing the van't Hoff plots for endothermic and exothermic reactions, it is possible to determine how the equilibrium constant is affected by changes in temperature. On a van't Hoff plot, temperature is plotted as 1/T. Because of this, the left side of the plot represents higher temperatures. Looking at a plot of an endothermic reaction, it can be determined that as temperature increases, the equilibrium constant also increases. This leads to a greater amount of product formation as temperature increases.
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| Conversely, it can be seen on the exothermic reaction plot that as temperature increases, the equilibrium constant decreases. This leads to less product formation as temperature increases.
| |
| | |
| ==Applications of the van't Hoff plot==
| |
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| ===Van't Hoff analysis===
| |
| [[File:Van't Hoff analysis.png|thumb|right|x275px|Van't Hoff analysis]]
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| In biological research, the van't Hoff plot is also called van't Hoff analysis.<ref>{{cite web|title=Van't Hoff Analysis|url=http://enzyme.ucd.ie/main/index.php/Van't_Hoff_Analysis|publisher=Protein Analysis and Design Group}}</ref> It's most effective in determining the favored product in a reaction.
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| | |
| Assume two products B and C form in a reaction:
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| <math>\mathrm{a\ A + d\ D \longrightarrow b\ B}</math>
| |
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| <math>\mathrm{a\ A + d\ D \longrightarrow c\ C}</math>
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| In this case, <math>K_{eq}</math> can be defined as ratio of B to C rather than the equilibrium constant.
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| When <math>\frac {B}{C} >1 </math>, B is the favored product, and the data on the van't Hoff plot will be in the positive region.
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| When <math>\frac {B}{C} <1 </math>, C is the favored product, and the data on the van't Hoff plot will be in the negative region.
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| Using this information, a van't Hoff analysis can help determine the most suitable temperature for a favored product.
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| Recently, a van't Hoff analysis was used to determine whether water preferentially forms a [[hydrogen bond]] with the [[C-terminus]] or the [[N-terminus]] of the [[amino acid]] proline.<ref>{{cite journal|last=Prell|first=James|coauthors=Williams E|title=Entropy Drives an Attached Water Molecule from the C- to N-Terminus on Protonated Proline|journal=J. Am. Chem. Soc.|year=2010|volume=132|issue=42|pages=14733|doi=10.1021/ja106167d}}</ref> The equilibrium constant for each reaction was found at a variety of temperatures, and a van't Hoff plot was created. This analysis showed that enthalpically, the water preferred to hydrogen bond to the C-terminus, but entropically it was more favorable to hydrogen bond with the N-terminus. Specifically, they found that C-terminus hydrogen bonding was favored by 4.2-6.4 kJ/mol. The N-terminus hydrogen bonding was favored by 31-43 J/(mol K).
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| This data alone could not conclude which site water will preferentially hydrogen bond to, so additional experiments were used. It was determined that at lower temperatures, the enthalpically favored species, the water hydrogen bonded to the C-terminus, was preferred. At higher temperatures, the entropically favored species, the water hydrogen bonded to the N-terminus, was preferred.
| |
| | |
| ===Mechanistic studies===
| |
| [[File:Van't Hoff plot in Mechanism study.png|thumb|right|x275px|Van't Hoff plot in Mechanism study]] | |
| | |
| A chemical reaction may undergo different reaction mechanisms under different temperatures.<ref>{{cite journal|last=Chatake|first=Toshiyuki|journal=Cryst. Growth Des.|year=2010|volume=10|page=1090|doi=10.1021/cg9007075}}</ref>
| |
| | |
| In this case, a van't Hoff plot with two or more linear fits may be exploited. Each linear fit has a different slope and intercept which indicates different changes in enthalpy and entropy for each distinct mechanisms. The van't Hoff plot can be used to find the enthalpy and entropy change for each mechanism and the favored mechanism under different temperatures.
| |
| | |
| <math>\Delta H_1 = - R * slope_1,</math>
| |
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| <math>\Delta S_1 = R * interception_1;</math> | |
| | |
| <math>\Delta H_2 = - R * slope_2,</math>
| |
| | |
| <math>\Delta S_2 = R * interception_2;</math> | |
| | |
| In the example figure, the reaction undergoes mechanism 1 at high temperature and mechanism 2 at low temperature.
| |
| | |
| ===Temperature dependence===
| |
| [[File:Temperature dependence van't Hoff plot.png|thumb|right|x275px|Temperature dependent van't Hoff plot]] | |
| The van't Hoff plot is linear based on the assumption that the enthalpy and entropy are almost constant with temperature changes. However, in some cases the enthalpy and entropy do change dramatically with temperature. In this case, an additional term, <math>\frac {1}{T^2} </math>, can be added to the van't Hoff equations. A polynomial fit can then be used to analyze the data.:<ref>{{cite journal|last=David|first=Victor|title=Deviation from van't Hoff dependence in RP-LC induced by tautomeric interconversion observed for four compounds|journal=Journal of Separation Science|date=28 April 2011|volume=34|issue=12|page=1423|doi=10.1002/jssc.201100029}}</ref>
| |
| | |
| <math>ln K_{eq} = a+ \frac {b}{T} + \frac {c}{T^2} ,</math>
| |
| | |
| where
| |
| | |
| <math>\Delta H = - R * (b+2\frac {c}{T}),</math>
| |
| | |
| <math>\Delta S = R * (a-\frac {c}{T^2}).</math>
| |
| | |
| Thus, the enthalpy and entropy of a reaction can still be determined at specific temperatures even when a temperature dependence exists.
| |
| | |
| ==See also==
| |
| *[[Clausius-Clapeyron relation]]
| |
| *[[Van 't Hoff factor]] (i)
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| *[[Gibbs-Helmholtz equation]]
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| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| {{use dmy dates|date=January 2012}}
| |
| | |
| [[Category:Equilibrium chemistry]]
| |
| [[Category:Thermochemistry]]
| |
| [[Category:Equations]]
| |
Mbt Paris I think it was past 9pm
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Tn Requin Pas Cher .
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