Short-rate model - Revision history

en>Studentttt: /* The short rate */

2015-01-01T11:50:05Z

The short rate

← Older revision		Revision as of 13:50, 1 January 2015
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	~~'''Coulometry'''~~ is ~~the name given~~ to ~~a group of techniques in [[electroanalytical method\|analytical chemistry]]~~ that ~~determine the amount of matter transformed during an [[electrolysis]] reaction by measuring the amount of [[electricity]] (in [[coulomb]]s) consumed or produced.<ref>{{cite journal\|~~title~~=Electroanalysis and Coulometric Analysis\|journal=Analytical Chemistry\|year=1960\|first=Donald D~~.~~\|last=DeFord\|coauthors=\|volume=32\|issue=5\|pages=31–37\|id=\|doi=10.1021/ac60161a604}}</ref>~~		Oscar is what my wife enjoys to call me and I completely dig that title. Puerto Rico is at home std test exactly where he's been residing for years and he will by no means move. The preferred hobby for my children at home std testing and me is to play baseball and home std test I'm trying to make it a [http://www.usa.gov/directory/federal/cdc-national-std-hotline.shtml profession]. Hiring has been my occupation for some time but I've currently utilized for an additional 1.<br><br>Also visit my page :: [http://www.xgwl.com/xiaoyoulu/space.php?uid=28028&do=blog&id=865339 xgwl.com]

	There are two basic categories of coulometric techniques. ''Potentiostatic coulometry'' involves holding the [[electric potential]] constant during the reaction using a [[potentiostat]]. The other, called ''coulometric titration'' or ''amperostatic coulometry'', keeps the [[current (electricity)\|current]] (measured in amperes) constant using an [[amperostat]].

	~~==Potentiostatic coulometry==~~

	~~[[bulk electrolysis\|Potentiostatic coulometry]]~~ is ~~a technique most commonly referred to as "[[bulk electrolysis]]".~~ ~~The [[working electrode]] is kept~~ at a constant potential and the current that flows through the circuit is measured. This constant potential is applied long enough to fully reduce or oxidize all of the electroactive species in a given solution. As the electroactive molecules are consumed, the current also decreases, approaching zero when the conversion is complete. The sample mass, molecular mass, number of electrons in the electrode reaction, and number of electrons passed during the experiment are all related by [[Faraday's ~~laws of electrolysis\|Faraday's laws]]. It follows that, if three of the values are known, then the fourth can be calculated.~~

	Bulk electrolysis is often used to unambiguously assign the number of electrons consumed in a reaction observed through [[voltammetry]]. It also has the added benefit of producing a solution of a species (oxidation state) which may not be accessible through chemical routes. This species can then be isolated or further characterized while in solution.

	~~The rate of such reactions is not determined~~ by the concentration of the solution, but rather the [[mass transfer]] of the electroactive species in the solution to the electrode surface. Rates will increase when the volume of the solution is decreased, the solution is stirred more rapidly, or the area of the working electrode is increased. Since mass transfer is so important the solution is stirred during a bulk electrolysis. However, this technique is generally not considered a [[hydrodynamic technique]], since a laminar flow of solution against the electrode is neither the objective nor outcome of the stirring.

	The extent to which a reaction goes to completion is also related to how much greater the applied potential is than the reduction potential of interest. In the case where multiple reduction potentials are of interest, it is often difficult to set an electrolysis potential a "safe" distance (such as 200 mV) past a redox event. The result is incomplete conversion of the substrate, or else conversion of some of the substrate to the more reduced form. This factor must be considered when analyzing the current passed and when attempting to do further analysis/isolation/experiments with the substrate solution.

	~~An advantage to this kind of analysis over [[electrogravimetry]] is that it does not require that the product of the reaction be weighed. This is useful~~ for reactions where the product does not deposit as a solid, such as the determination of the amount of [[arsenic]] in a sample from the electrolysis of [[arsenous acid]] ([[H3AsO3\|H<sub>3</sub>AsO<sub>3</sub>]]) to [[arsenic acid]] ([[H3AsO4\|H<sub>3</sub>AsO<sub>4</sub>]]).

	~~==Coulometric titration==~~

	~~Coulometric titrations use a constant [[current (electricity)\|current]] system to accurately quantify the concentration of a species.~~ ~~In this experiment, the applied current is equivalent to a [[titrant]]. Current is applied to the unknown solution until all of the unknown species is either oxidized or reduced to a new state,~~ at ~~which point the potential of the [[working electrode]] shifts dramatically. This potential shift indicates the [[endpoint (chemistry)\|endpoint]]. The magnitude of the current (in [[ampere]]s)~~ and the duration of the current ([[second]]s) can be used to determine the [[Mole (unit)\|mole]]s of the unknown species in solution. When the volume of the solution is known, then the [[molarity]] of the unknown species can be determined.

	~~==Applications==~~
	~~===Karl Fischer reaction===~~

	~~{{main\|Karl Fischer titration}}~~

	The [[Karl Fischer titration\|Karl Fischer reaction]] uses a coulometric titration to determine the amount of water in a sample. It can determine concentrations of water on the order of milligrams per liter. It is ~~used~~ to ~~find the amount of water in substances such as [[butter]], [[sugar]], [[cheese]], [[paper]], and [[petroleum]].~~

	~~The reaction involves converting solid iodine into hydrogen iodide in the presence of sulfur dioxide~~ and ~~water.~~ [[Methanol]] is most often used as the solvent, but [[ethylene glycol]] and [[diethylene glycol]] also work. [[Pyridine]] is often used to prevent the build up of [[sulfuric acid]], although the use of [[imidazole]] and [[diethanolamine]] for this role are becoming more common. All reagents must be [[anhydrous]] for the analysis to be quantitative. The balanced chemical equation, using methanol and pyridine, is:

	~~:<math>~~
	~~\mathrm{[C_5H_5NH]SO_3CH_3 + I_2 + H_2O + 2 C_5H_5N} \longrightarrow \mathrm{[C_5H_5NH]SO_4CH_3 + 2 [C_5H_5NH]~~I}
	~~</math>~~

	~~In this reaction, a single molecule of water reacts with a molecule of iodine. Since this technique is used~~ to determine the water content of samples, atmospheric humidity could alter the results. Therefore, the system is usually isolated with drying tubes or placed in an [[inert gas]] container. In addition, the solvent will undoubtedly have some water in it ~~so the solvent’s water content must be measured to compensate for this inaccuracy.~~

	To determine the amount of water in the sample, analysis must first be performed using either [[Back titration\|back]] or direct [[titration]]. In the direct method, just enough of the reagents will be added to completely use up all of the water. At this point in the titration, the current approaches zero. It is then possible to relate the amount of reagents used to the amount of water in the system via [[stoichiometry]]. The back-titration method is similar, but involves the addition of an excess of the reagent. This excess is then consumed by adding a known amount of a standard solution with known water content. The result reflects the water content of the sample and the standard solution. Since the amount of water in the standard solution is known, the difference reflects the water content of the sample.

	~~===Determination of film thickness===~~

	~~Coulometry can be used in the determination of the thickness of metallic coatings. This is performed by measuring the~~ [~~[quantity of electricity]] needed to dissolve a well-defined area of the coating. The film thickness <math>\Delta<~~/~~math> is proportional to the constant current <math>i<~~/~~math>, the [[molecular weight]] <math>M<~~/~~math> of the metal, the [[density]] <math>\rho<~~/~~math> of the metal, and the surface area <math>A<~~/~~math>:~~

	~~<math>\triangle \propto \frac{iM}{A\rho}</math>~~

	~~The electrodes for this reaction are often platinum electrode and an electrode that relates to the reaction. For tin coating on a copper wire, a tin electrode is used, while a sodium chloride~~-zinc sulfate electrode would be used to determine the zinc film on a piece of steel. Special cells have been created to adhere to the surface of the metal to measure its thickness. These are basically columns with the internal electrodes with magnets or weights to attach to the surface. The results obtained by this coulometric method are similar to those achieved by other chemical and metallurgic techniques.

	~~==Coulometers==~~
	~~===Electronic coulometer===~~
	~~The electronic coulometer is based on the application of the [[operational amplifier]] in the "integrator"~~-~~type circuit~~. ~~The current passed through the resistor '''R1''' makes a potential drop which is integrated by operational amplifier on the [[capacitor]~~] ~~plates; the higher current, the larger the potential drop~~. ~~The current need not be constant. In such scheme~~ '~~'V''<sub>out</sub> is proportional of the passed charge (''i''*''t'')~~. ~~Sensitivity of the coulometer can be changed by choosing of the appropriate value of ''R''~~<~~sub~~>1<~~/sub~~>.

	~~===Electrochemical coulometers===~~
	~~{{main\|voltameter}}~~
	~~There are three common types of coulometers based on electrochemical processes~~:
	* [[Copper coulometer]]
	* [[Mercury coulometer]]
	* [[Hofmann voltameter]]

	~~"Voltameter" is a synonym for "coulometer".~~

	~~==References==~~
	~~{{Reflist}}~~

	~~==Bibliography==~~
	~~{{refbegin}}~~
	*{{cite book \|author= \|title=Coulometry in Analytical Chemistry \|publisher=Elsevier Science Ltd \|location=Amsterdam \|year=1968 \|pages= \|isbn=0-08-012438-0 \|oclc= \|doi= \|accessdate=}}
	~~{{refend}}~~

	~~==External links==~~
	*[http://~~goldbook.iupac~~.~~org/C01367~~.~~html IUPAC Gold Book: coulometric detection method]~~
	*[http://~~ull~~.~~chemistry~~.~~uakron.edu/Analytical/Coulometry/ Coulometry at the University of Akron]~~

	~~{{Electroanalytical}}~~
	~~[[Category:Electroanalytical methods]~~]

69.191.241.59: /* The short rate */

2013-11-26T16:08:27Z

The short rate

← Older revision		Revision as of 18:08, 26 November 2013
Line 1:		Line 1:
	~~I am Oscar and I totally dig~~ that ~~name. One~~ of the [~~http:~~//~~funnie~~.~~st/365631/celebs-who-had-herpes/ extremely~~] ~~very best issues~~ in ~~std home test~~ the ~~globe for me~~ is to ~~do aerobics~~ ~~home~~ [~~http:~~//~~Www~~.~~Cprogramming~~.~~com~~/~~tutorial~~/~~stl~~/~~stllist~~.~~html std test~~] ~~kit~~ and ~~now I'm attempting~~ to ~~make money with it~~. ~~Her husband~~ and ~~her live~~ in ~~Puerto Rico~~ but ~~she~~ will have to ~~transfer 1 working day~~ or an ~~additional~~. ~~Managing people~~ is ~~what I do~~ and the ~~salary has been truly fulfilling~~.<br><br>~~Also visit my site;~~ [~~http~~://~~ccgi~~.~~crabtree~~.~~force9~~.~~co.uk~~/~~tonycrabtree~~/~~node~~/~~736271~~ http://~~ccgi~~.~~crabtree~~.~~force9~~.~~co.uk~~/~~tonycrabtree~~/~~node~~/~~736271~~]		'''Coulometry''' is the name given to a group of techniques in [[electroanalytical method\|analytical chemistry]] that determine the amount of matter transformed during an [[electrolysis]] reaction by measuring the amount of [[electricity]] (in [[coulomb]]s) consumed or produced.<ref>{{cite journal\|title=Electroanalysis and Coulometric Analysis\|journal=Analytical Chemistry\|year=1960\|first=Donald D.\|last=DeFord\|coauthors=\|volume=32\|issue=5\|pages=31–37\|id=\|doi=10.1021/ac60161a604}}</ref>

			There are two basic categories of coulometric techniques. ''Potentiostatic coulometry'' involves holding the [[electric potential]] constant during the reaction using a [[potentiostat]]. The other, called ''coulometric titration'' or ''amperostatic coulometry'', keeps the [[current (electricity)\|current]] (measured in amperes) constant using an [[amperostat]].

			==Potentiostatic coulometry==

			[[bulk electrolysis\|Potentiostatic coulometry]] is a technique most commonly referred to as "[[bulk electrolysis]]". The [[working electrode]] is kept at a constant potential and the current that flows through the circuit is measured. This constant potential is applied long enough to fully reduce or oxidize all of the electroactive species in a given solution. As the electroactive molecules are consumed, the current also decreases, approaching zero when the conversion is complete. The sample mass, molecular mass, number of electrons in the electrode reaction, and number of electrons passed during the experiment are all related by [[Faraday's laws of electrolysis\|Faraday's laws]]. It follows that, if three of the values are known, then the fourth can be calculated.

			Bulk electrolysis is often used to unambiguously assign the number of electrons consumed in a reaction observed through [[voltammetry]]. It also has the added benefit of producing a solution of a species (oxidation state) which may not be accessible through chemical routes. This species can then be isolated or further characterized while in solution.

			The rate of such reactions is not determined by the concentration of the solution, but rather the [[mass transfer]] of the electroactive species in the solution to the electrode surface. Rates will increase when the volume of the solution is decreased, the solution is stirred more rapidly, or the area of the working electrode is increased. Since mass transfer is so important the solution is stirred during a bulk electrolysis. However, this technique is generally not considered a [[hydrodynamic technique]], since a laminar flow of solution against the electrode is neither the objective nor outcome of the stirring.

			The extent to which a reaction goes to completion is also related to how much greater the applied potential is than the reduction potential of interest. In the case where multiple reduction potentials are of interest, it is often difficult to set an electrolysis potential a "safe" distance (such as 200 mV) past a redox event. The result is incomplete conversion of the substrate, or else conversion of some of the substrate to the more reduced form. This factor must be considered when analyzing the current passed and when attempting to do further analysis/isolation/experiments with the substrate solution.

			An advantage to this kind of analysis over [[electrogravimetry]] is that it does not require that the product of the reaction be weighed. This is useful for reactions where the product does not deposit as a solid, such as the determination of the amount of [[arsenic]] in a sample from the electrolysis of [[arsenous acid]] ([[H3AsO3\|H<sub>3</sub>AsO<sub>3</sub>]]) to [[arsenic acid]] ([[H3AsO4\|H<sub>3</sub>AsO<sub>4</sub>]]).

			==Coulometric titration==

			Coulometric titrations use a constant [[current (electricity)\|current]] system to accurately quantify the concentration of a species. In this experiment, the applied current is equivalent to a [[titrant]]. Current is applied to the unknown solution until all of the unknown species is either oxidized or reduced to a new state, at which point the potential of the [[working electrode]] shifts dramatically. This potential shift indicates the [[endpoint (chemistry)\|endpoint]]. The magnitude of the current (in [[ampere]]s) and the duration of the current ([[second]]s) can be used to determine the [[Mole (unit)\|mole]]s of the unknown species in solution. When the volume of the solution is known, then the [[molarity]] of the unknown species can be determined.

			==Applications==
			===Karl Fischer reaction===

			{{main\|Karl Fischer titration}}

			The [[Karl Fischer titration\|Karl Fischer reaction]] uses a coulometric titration to determine the amount of water in a sample. It can determine concentrations of water on the order of milligrams per liter. It is used to find the amount of water in substances such as [[butter]], [[sugar]], [[cheese]], [[paper]], and [[petroleum]].

			The reaction involves converting solid iodine into hydrogen iodide in the presence of sulfur dioxide and water. [[Methanol]] is most often used as the solvent, but [[ethylene glycol]] and [[diethylene glycol]] also work. [[Pyridine]] is often used to prevent the build up of [[sulfuric acid]], although the use of [[imidazole]] and [[diethanolamine]] for this role are becoming more common. All reagents must be [[anhydrous]] for the analysis to be quantitative. The balanced chemical equation, using methanol and pyridine, is:

			:<math>
			\mathrm{[C_5H_5NH]SO_3CH_3 + I_2 + H_2O + 2 C_5H_5N} \longrightarrow \mathrm{[C_5H_5NH]SO_4CH_3 + 2 [C_5H_5NH]I}
			</math>

			In this reaction, a single molecule of water reacts with a molecule of iodine. Since this technique is used to determine the water content of samples, atmospheric humidity could alter the results. Therefore, the system is usually isolated with drying tubes or placed in an [[inert gas]] container. In addition, the solvent will undoubtedly have some water in it so the solvent’s water content must be measured to compensate for this inaccuracy.

			To determine the amount of water in the sample, analysis must first be performed using either [[Back titration\|back]] or direct [[titration]]. In the direct method, just enough of the reagents will be added to completely use up all of the water. At this point in the titration, the current approaches zero. It is then possible to relate the amount of reagents used to the amount of water in the system via [[stoichiometry]]. The back-titration method is similar, but involves the addition of an excess of the reagent. This excess is then consumed by adding a known amount of a standard solution with known water content. The result reflects the water content of the sample and the standard solution. Since the amount of water in the standard solution is known, the difference reflects the water content of the sample.

			===Determination of film thickness===

			Coulometry can be used in the determination of the thickness of metallic coatings. This is performed by measuring the [[quantity of electricity]] needed to dissolve a well-defined area of the coating. The film thickness <math>\Delta</math> is proportional to the constant current <math>i</math>, the [[molecular weight]] <math>M</math> of the metal, the [[density]] <math>\rho</math> of the metal, and the surface area <math>A</math>:

			<math>\triangle \propto \frac{iM}{A\rho}</math>

			The electrodes for this reaction are often platinum electrode and an electrode that relates to the reaction. For tin coating on a copper wire, a tin electrode is used, while a sodium chloride-zinc sulfate electrode would be used to determine the zinc film on a piece of steel. Special cells have been created to adhere to the surface of the metal to measure its thickness. These are basically columns with the internal electrodes with magnets or weights to attach to the surface. The results obtained by this coulometric method are similar to those achieved by other chemical and metallurgic techniques.

			==Coulometers==
			===Electronic coulometer===
			The electronic coulometer is based on the application of the [[operational amplifier]] in the "integrator"-type circuit. The current passed through the resistor '''R1''' makes a potential drop which is integrated by operational amplifier on the [[capacitor]] plates; the higher current, the larger the potential drop. The current need not be constant. In such scheme ''V''<sub>out</sub> is proportional of the passed charge (''i''*''t''). Sensitivity of the coulometer can be changed by choosing of the appropriate value of ''R''<sub>1</sub>.

			===Electrochemical coulometers===
			{{main\|voltameter}}
			There are three common types of coulometers based on electrochemical processes:
			* [[Copper coulometer]]
			* [[Mercury coulometer]]
			* [[Hofmann voltameter]]

			"Voltameter" is a synonym for "coulometer".

			==References==
			{{Reflist}}

			==Bibliography==
			{{refbegin}}
			*{{cite book \|author= \|title=Coulometry in Analytical Chemistry \|publisher=Elsevier Science Ltd \|location=Amsterdam \|year=1968 \|pages= \|isbn=0-08-012438-0 \|oclc= \|doi= \|accessdate=}}
			{{refend}}

			==External links==
			*[http://goldbook.iupac.org/C01367.html IUPAC Gold Book: coulometric detection method]
			*[http://ull.chemistry.uakron.edu/Analytical/Coulometry/ Coulometry at the University of Akron]

			{{Electroanalytical}}
			[[Category:Electroanalytical methods]]

en>DannyAsher: /* The short rate */

2012-07-25T09:18:23Z

The short rate

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