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In [[chemistry]], '''Le Chatelier's principle''', also called '''Chatelier's principle''' or "The Equilibrium Law", can be used to predict the effect of a change in conditions on a [[chemical equilibrium]]. The principle is named after [[Henry Louis Le Chatelier]] and sometimes [[Karl Ferdinand Braun]] who discovered it independently. It can be stated as: | |||
:If a chemical system at equilibrium experiences a change in [[concentration]], [[temperature]], [[volume]], or partial [[pressure]], then the equilibrium shifts to counteract the imposed change and a new equilibrium is established. | |||
This principle has a variety of names, depending upon the discipline using it. See, for example, [[homeostasis]]. It is common to take Le Chatelier's principle to be a more general observation,<ref name="Systemantics">{{cite book | quote = ''The System always kicks back'' | first = John | last = Gall | title = The Systems Bible | edition = 3<sup>rd</sup> | publisher = General Systemantics Press | year = 2002 | url = }}</ref> roughly stated: | |||
:''Any change in [[status quo]] prompts an opposing reaction in the responding system''. | |||
In [[chemistry]], the principle is used to manipulate the outcomes of reversible reactions, often to increase the [[Yield (chemistry)|yield]] of reactions. In [[pharmacology]], the binding of [[Ligand (biochemistry)|ligands]] to the receptor may shift the equilibrium according to Le Chatelier's principle, thereby explaining the diverse phenomena of receptor activation and desensitization.<ref name="Bio-balance">{{cite web|url=http://www.bio-balance.com/Graphics.htm|title=The Biophysical Basis for the Graphical Representations|accessdate=2009-05-04}}</ref> In [[economics]], the principle has been generalized to help explain the [[Economic equilibrium|price equilibrium]] of efficient economic systems. In simultaneous equilibrium systems, phenomena that are in apparent contradiction to Le Chatelier's principle can occur; these can be resolved by the theory of [[response reactions]]. | |||
==Status as a physical law== | |||
Le Chatelier's principle qualitatively describes systems of non-instantaneous change; the duration of adjustment depends on the strength of the [[negative feedback]] to the initial [[Shock (mechanics)|shock]]. Le Chatelier's principle also states that when there is an external constraint on a system, a behavioural shift in the system occurs so as to annul the effect of that change. Where a shock initially induces [[positive feedback]] (such as [[thermal runaway]]), the new equilibrium can be far from the old one, and can take a long time to reach. In [[Dynamical_systems_theory#Chaos_theory|some dynamic systems]], the end-state cannot be determined from the shock. The principle is typically used to describe closed negative-feedback systems, but applies, in general, to thermodynamically closed and isolated systems in nature, since the [[Second_law_of_thermodynamics#Energy_dispersal|second law of thermodynamics]] ensures that the [[disequilibrium]] caused by an instantaneous [[Shock (economics)|shock]] must have a finite [[Half-life#Half-life_in_non-exponential_decay|half-life]].<ref>{{cite book |chapter= Application of the Second Law of Thermodynamics and Le Chatelier's Principle to the Developing Ecosystem |quote= ''As systems are moved away from equilibrium, they will utilize all available avenues to counter the applied gradients''... Le Chatelier's principle is an example of this equilibrium seeking principle. |origyear= 1999 |first= J. J. |last= Kay |month= August |title= Handbook of Ecosystem Theories and Management |series= Environmental & Ecological (Math) Modeling |editor1-first= F. |editor1-last= Muller |publisher= CRC Press |date=February 2000 |isbn= 978-1-56670-253-9 }}<br/>'''''For full details, see''''': {{cite paper | id = {{citeseerx|10.1.1.11.856}} | title = Ecosystems as Self-organizing Holarchic Open Systems: Narratives and the Second Law of Thermodynamics | page = 5 }}</ref> The principle has analogs throughout the entire physical world. | |||
==Chemistry== | |||
===Effect of change in concentration=== | |||
Changing the concentration of an ingredient will shift the equilibrium to the side that would reduce that change in concentration. The chemical system will attempt to partially oppose the change affected to the original state of equilibrium. In turn, the rate of reaction, extent and yield of products will be altered corresponding to the impact on the system. | |||
This can be illustrated by the equilibrium of [[carbon monoxide]] and [[hydrogen]] gas, reacting to form [[methanol]]. | |||
:[[Carbon|C]][[Oxygen|O]] + 2 H<sub>2</sub> {{unicode|⇌}} CH<sub>3</sub>OH | |||
Suppose we were to increase the concentration of CO in the system. Using Le Chatelier's principle, we can predict that the amount of methanol will increase, decreasing the total change in CO. If we are to add a species to the overall reaction, the reaction will favor the side opposing the addition of the species. Likewise, the subtraction of a species would cause the reaction to fill the "gap" and favor the side where the species was reduced. This observation is supported by the [[collision theory]]. As the concentration of CO is increased, the frequency of successful collisions of that reactant would increase also, allowing for an increase in forward reaction, and generation of the product. Even if a desired product is not [[thermodynamic]]ally favored, the end-product can be obtained if it is continuously removed from the [[solution]]. | |||
===Effect of change in temperature=== | |||
The effect of changing the temperature in the equilibrium can be made clear by incorporating heat as either a reactant or a product. When the reaction is [[exothermic]] (ΔH is negative, puts energy out), we include heat as a product, and, when the reaction is [[endothermic]] (ΔH is positive, takes energy in), we include it as a reactant. Hence, we can determine whether increasing or decreasing the temperature would favour the forward or reverse reaction by applying the same principle as with concentration changes. | |||
Take, for example, the reaction of [[nitrogen]] gas with [[hydrogen]] gas. This is a [[reversible reaction]], in which the two gases react to form [[ammonia]]: | |||
:N<sub>2</sub> + 3 H<sub>2</sub> {{unicode|⇌}} 2 NH<sub>3</sub> ΔH = -92 [[kJ]] mol<sup>-1</sup> | |||
The product contains heat: | |||
:N<sub>2</sub> + 3 H<sub>2</sub> {{unicode|⇌}} 2 NH<sub>3</sub> + 92kJ | |||
This is an exothermic reaction (hence the minus sign) when producing [[ammonia]]. If we were to lower the temperature, the equilibrium would shift to produce more heat. Since making ammonia is exothermic, this would favour the production of more [[ammonia]]. In practice, in the [[Haber process]], the temperature is set at a compromise value, so [[ammonia]] is made quickly, even though less would be present at equilibrium. | |||
In [[exothermic reaction]]s, increase in temperature decreases the [[equilibrium constant]], K, whereas, in [[endothermic reaction]]s, increase in temperature increases the K value. | |||
[[File:NO2-N2O4.jpg|thumb|left|alt=Alternative text|The value of K changes with temperature. In the endothermic reaction N<sub>2</sub>O<sub>4</sub>(g) {{unicode|⇌}} 2NO<sub>2</sub>(g), the equilibrium position can be shifted by changing the temperature. When heat is added and the temperature increases, the reaction shifts to the right and the flask turns reddish brown due to an increase in NO<sub>2</sub>. When heat is removed and the temperature decreases, the reaction shifts to the left and flask turns colorless due to an increase in N<sub>2</sub>O<sub>4</sub>. This demonstrates Le Chatelier’s Principle because the equilibrium shifts in the direction that consumes energy.]] | |||
===Effect of change in pressure=== | |||
Changes in pressure are attributable to changes in volume. The equilibrium concentrations of the products and reactants do not directly depend on the pressure subjected to the system. However, a change in pressure due to a change in volume of the system will shift the equilibrium. | |||
Considering the reaction of nitrogen gas with hydrogen gas to form ammonia: | |||
:N<sub>2</sub> + 3 H<sub>2</sub> {{unicode|⇌}} 2 NH<sub>3</sub> ΔH = -92kJ mol<sup>-1</sup> | |||
:4 volumes {{unicode|⇌}} 2 volumes | |||
Note the number of [[mole (unit)|moles]] of gas on the left-hand side and the number of moles of gas on the right-hand side. When the volume of the system is changed, the partial pressures of the gases change. If we were to decrease pressure by increasing volume, the equilibrium of the above reaction will shift to the left, because the reactant side has greater number of moles than does the product side. The system tries to counteract the decrease in partial pressure of gas molecules by shifting to the side that exerts greater pressure. Similarly, if we were to increase pressure by decreasing volume, the equilibrium shifts to the right, counteracting the pressure increase by shifting to the side with fewer moles of gas that exert less pressure. If the volume is increased because there are more moles of gas on the reactant side, this change is more significant in the denominator of the [[equilibrium constant]] expression, causing a shift in equilibrium. | |||
<!-- If we take the above reaction at [[standard conditions for temperature and pressure]] (STP), <math>K_c</math> would be as follow: | |||
:<math>K_c=\frac{{[NH_3]} ^2} {{[N_2]}^1 {[H_2]}^3}</math> | |||
::<math>=\frac{{(12)} ^2} {{(4)}^1 {(2)}^3}</math> | |||
::<math>=1.125</math> | |||
If we double the pressure of the above situation, then the volume of both sides would be half the current values. Then <math>K_c</math> would now be as follow: | |||
:<math>K_c=\frac{{[NH_3]} ^2} {{[N_2]}^1 {[H_2]}^3}</math> | |||
::<math>=\frac{{(6)} ^2} {{(2)}^1 {(1)}^3}</math> | |||
::<math>=18</math> --> | |||
Thus, an increase in system pressure due to decreasing volume causes the reaction to shift to the side with the fewer moles of gas.<ref name=Atkins-1993-p114>{{harvnb|Atkins1993|p=114}}</ref> A decrease in pressure due to increasing volume causes the reaction to shift to the side with more moles of gas. There is no effect on a reaction where the number of moles of gas is the same on each side of the chemical equation. | |||
===Effect of adding an inert gas=== | |||
An [[inert]] gas (or [[noble gas]]) such as [[helium]] is one that does not react with other elements or compounds. Adding an inert gas into a gas-phase equilibrium at constant volume does not result in a shift.<ref name=Atkins-1993-p114/> This is because the addition of a non-reactive gas does not change the [[partial pressures]] of the other gases in the container. While it is true that the total pressure of the system increases, the total pressure does not have any effect on the equilibrium constant; rather, it is a change in partial pressures that will cause a shift in the equilibrium. If, however, the volume is allowed to increase in the process, the partial pressures of all gases would be decreased resulting in a shift towards the side with the greater number of moles of gas. | |||
There is a short form to remember this: LBMF (little boy married fiona); L stands for less pressure, B—backward reaction, M—more pressure, and F—forward reaction. Note that this mnemonic ONLY applies for a reaction resulting in a greater number of gas molecules on the products side, than the reactants (does not apply if the reverse is true). | |||
===Effect of a catalyst=== | |||
A catalyst has no effect on equilibrium. It speeds up both forward and backward reactions equally. | |||
E.g.: N<sub>2</sub> + 3 H<sub>2</sub> → 2 NH<sub>3</sub> | |||
Here Iron (Fe) and Molybdenum (Mo) are catalysts, but the two catalysts do not affect the state of equilibrium. | |||
Hence a catalyst has no effect on equilibrium state. | |||
==Applications in economics== | |||
In economics, a similar concept also named after Le Chatelier was introduced by U.S. economist [[Paul Samuelson]] in 1947. There the generalized Le Chatelier principle is for a maximum condition of [[economic equilibrium]]: Where all unknowns of a function are independently variable, [[Constraint (mathematics)|auxiliary constraints]]—"just-binding" in leaving initial equilibrium unchanged—reduce the response to a parameter change. Thus, factor-demand and commodity-supply [[Elasticity (economics)|elasticities]] are hypothesized to be lower in the short run than in the long run because of the fixed-cost constraint in the short run.<ref name="PaulS">{{cite book|last=Samuelson|first=Paul A|title=Foundations of Economic Analysis|publisher=Harvard University Press|year=1983|isbn=0-674-31301-1}}</ref> | |||
==See also== | |||
*[[Homeostasis]] | |||
*[[Common-ion effect]] | |||
*[[Response reactions]] | |||
==References== | |||
{{reflist}} | |||
{{refbegin}} | |||
{{refend}} | |||
==Bibliography== | |||
* {{cite book | first = P.W. | last = Atkins | title = The Elements of Physical Chemistry | edition = 3<sup>rd</sup> | publisher = Oxford University Press | year = 1993 | ref = harv }} | |||
* Le Chatelier, H. and [[Octave Leopold Boudouard|Boudouard O]]. (1898), "Limits of Flammability of Gaseous Mixtures", ''[[Bulletin de la Société Chimique de France]]'' (Paris), v. 19, pp. 483–488. | |||
* Hatta, Tatsuo (1987), "Le Châtelier principle," ''The [[New Palgrave: A Dictionary of Economics]]'', v. 3, pp. 155–57. | |||
* Samuelson, Paul A. (1947, Enlarged ed. 1983). ''[[Foundations of Economic Analysis]]'', Harvard University Press. ISBN 0-674-31301-1 | |||
* D.J. Evans, D.J. Searles and E. Mittag (2001), "[[Fluctuation theorem]] for Hamiltonian systems—Le Châtelier's principle", ''Physical Review E'', 63, 051105(4). | |||
* Also refer to Brown Lemay Bursten. 10th or 11e edition for this principle. | |||
==External links== | |||
* [http://www.youtube.com/watch?v=YMqyG9QG6oc&feature=related YouTube video of Le Chatelier's principle and pressure] | |||
[[Category:Equilibrium chemistry]] | |||
[[Category:Homeostasis]] | |||
Revision as of 05:52, 19 November 2013
In chemistry, Le Chatelier's principle, also called Chatelier's principle or "The Equilibrium Law", can be used to predict the effect of a change in conditions on a chemical equilibrium. The principle is named after Henry Louis Le Chatelier and sometimes Karl Ferdinand Braun who discovered it independently. It can be stated as:
- If a chemical system at equilibrium experiences a change in concentration, temperature, volume, or partial pressure, then the equilibrium shifts to counteract the imposed change and a new equilibrium is established.
This principle has a variety of names, depending upon the discipline using it. See, for example, homeostasis. It is common to take Le Chatelier's principle to be a more general observation,[1] roughly stated:
- Any change in status quo prompts an opposing reaction in the responding system.
In chemistry, the principle is used to manipulate the outcomes of reversible reactions, often to increase the yield of reactions. In pharmacology, the binding of ligands to the receptor may shift the equilibrium according to Le Chatelier's principle, thereby explaining the diverse phenomena of receptor activation and desensitization.[2] In economics, the principle has been generalized to help explain the price equilibrium of efficient economic systems. In simultaneous equilibrium systems, phenomena that are in apparent contradiction to Le Chatelier's principle can occur; these can be resolved by the theory of response reactions.
Status as a physical law
Le Chatelier's principle qualitatively describes systems of non-instantaneous change; the duration of adjustment depends on the strength of the negative feedback to the initial shock. Le Chatelier's principle also states that when there is an external constraint on a system, a behavioural shift in the system occurs so as to annul the effect of that change. Where a shock initially induces positive feedback (such as thermal runaway), the new equilibrium can be far from the old one, and can take a long time to reach. In some dynamic systems, the end-state cannot be determined from the shock. The principle is typically used to describe closed negative-feedback systems, but applies, in general, to thermodynamically closed and isolated systems in nature, since the second law of thermodynamics ensures that the disequilibrium caused by an instantaneous shock must have a finite half-life.[3] The principle has analogs throughout the entire physical world.
Chemistry
Effect of change in concentration
Changing the concentration of an ingredient will shift the equilibrium to the side that would reduce that change in concentration. The chemical system will attempt to partially oppose the change affected to the original state of equilibrium. In turn, the rate of reaction, extent and yield of products will be altered corresponding to the impact on the system.
This can be illustrated by the equilibrium of carbon monoxide and hydrogen gas, reacting to form methanol.
- CO + 2 H2 PROPERTY builders did not have the simplest year, what with the cooling measures imposed in January and the loan curbs in June, but some still managed to do effectively while others made their first foray abroad.
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Suppose we were to increase the concentration of CO in the system. Using Le Chatelier's principle, we can predict that the amount of methanol will increase, decreasing the total change in CO. If we are to add a species to the overall reaction, the reaction will favor the side opposing the addition of the species. Likewise, the subtraction of a species would cause the reaction to fill the "gap" and favor the side where the species was reduced. This observation is supported by the collision theory. As the concentration of CO is increased, the frequency of successful collisions of that reactant would increase also, allowing for an increase in forward reaction, and generation of the product. Even if a desired product is not thermodynamically favored, the end-product can be obtained if it is continuously removed from the solution.
Effect of change in temperature
The effect of changing the temperature in the equilibrium can be made clear by incorporating heat as either a reactant or a product. When the reaction is exothermic (ΔH is negative, puts energy out), we include heat as a product, and, when the reaction is endothermic (ΔH is positive, takes energy in), we include it as a reactant. Hence, we can determine whether increasing or decreasing the temperature would favour the forward or reverse reaction by applying the same principle as with concentration changes.
Take, for example, the reaction of nitrogen gas with hydrogen gas. This is a reversible reaction, in which the two gases react to form ammonia:
- N2 + 3 H2 PROPERTY builders did not have the simplest year, what with the cooling measures imposed in January and the loan curbs in June, but some still managed to do effectively while others made their first foray abroad.
As a public-listed company and a pioneer in the improvement of landed properties in Singapore, we have now been constructing some of Singapore's nicely-recognized, established residential estates for over 50 years. Our many developments in Singapore are an affidavit of our steady want to create not just high quality houses however communities for you and your family members Hotel Properties Limited (HPL) was listed on the Inventory Trade of Singapore in 1982. Beginning with simply the Hilton Lodge in Singapore, HPL has expanded rapidly through the years. As we speak HPL has pursuits in 19 resorts with almost 4000 rooms in 8 countries. An Choice or Settlement/Contract for the Buy of a Home or Flat will be formedin many ways e.g. A gaggle of persons, whether in partnership or otherwise
Certainly one of Asia's premier property firms, Keppel Land is recognised for its sterling portfolio of award-profitable residential developments and funding-grade business properties as well as excessive requirements of company governance and transparency. Keppel Land is without doubt one of the largest listed property corporations by total assets on the Singapore Change. The Group's total assets amounted to about $13.eight billion as at 31 March 2014. Additionally it is a component of a number of stock indices including the FTSE ST Real Property Index, FTSE ST China Prime Index, FTSE All-World Index, FTSE Asia Pacific ex-Japan Index, FTSE EPRA/NAREIT World Real Estate Index and EPRA/NAREIT Index. WOODSVALE PERSONAL CONDOMINIUM CONDOMINIUM WOODSVALE CLOSE, SINGAPORE (DISTRICT thirteen) Industrial
LINCOLN RESIDENCES, THE NON-PUBLIC CONDOMINIUM APARTMENT SURREY STREET, SINGAPORE (DISTRICT eleven) LUCIDA NON-PUBLIC CONDOMINIUM APARTMENT SUFFOLK ROAD, SINGAPORE (DISTRICT 11) LUMOS, THE PRIVATE CONDOMINIUM APARTMENT LEONIE HILL, SINGAPORE (DISTRICT 09) LUXURIE, THE PRIVATE CONDOMINIUM CONDOMINIUM COMPASSVALE BOW, SINGAPORE (DISTRICT 19) M66 NON-PUBLIC CONDOMINIUM RESIDENCE MOONSTONE LANE, SINGAPORE (DISTRICT 12) MARINA BAY SUITES PRIVATE CONDOMINIUM CONDOMINIUM CENTRAL BOULEVARD, SINGAPORE (DISTRICT 01) MEIER SUITES PERSONAL CONDOMINIUM house in singapore MARGATE STREET, SINGAPORE (DISTRICT 15) MKZ, THE NON-PUBLIC CONDOMINIUM CONDO MACKENZIE STREET, SINGAPORE (DISTRICT 09) MONTCLAIR @ WHITLEY CLUSTER STRATA HOUSE WHITLEY HIGHWAY, SINGAPORE (DISTRICT 11) Condominiums by District
The Singapore Property Awards recognise excellence in actual estate development initiatives or individual properties in terms of design, aesthetics, functionality, contribution to the constructed atmosphere and neighborhood at massive. It represents an outstanding achievement which developers, professionals and property house owners aspire to achieve. It bestows upon the winner the correct to use the coveted award emblem recognised extensively throughout the FIABCI network.
ADRIA NON-PUBLIC CONDOMINIUM CONDOMINIUM DERBYSHIRE HIGHWAY, THOMSON ROAD, SINGAPORE (DISTRICT eleven) AMBER RESIDENCES (PREPARED HOUSES) PRIVATE CONDOMINIUM RESIDENCE AMBER STREET, SINGAPORE (DISTRICT 15) ARC AT TAMPINES GOVERNMENT CONDOMINIUM APARTMENT TAMPINES AVENUE 8, SINGAPORE (DISTRICT 18) ARDMORE RESIDENCE NON-PUBLIC CONDOMINIUM CONDO ARDMORE PARK, SINGAPORE (DISTRICT 10) ARISTO @ AMBER , THE PRIVATE CONDOMINIUM CONDOMINIUM AMBER STREET, SINGAPORE (DISTRICT 15) ASPEN LINQ NON-PUBLIC CONDOMINIUM RESIDENCE INSTITUTION HILL, SINGAPORE (DISTRICT 09) BARTLEY RESIDENCES NON-PUBLIC CONDOMINIUM HOUSE BARTLEY HIGHWAY, SINGAPORE (DISTRICT 19) BEACON HEIGHTS PERSONAL CONDOMINIUM CONDO MAR THOMA STREET, SINGAPORE (DISTRCT 12) title searches and authorized requisitions on the property; and
Hongkong Land is a number one property funding, administration and growth group with a serious portfolio in Hong Kong and different property pursuits in Asia. As considered one of Singapore's largest property gamers, Singapore Land (SingLand) is synonymous with premier property developments in both prime and suburban areas. YHS made its first foray into property improvement with Tivoli Gardens, a 59-unit landed estate in District 19. This was adopted by the launch of The Sterling, a freehold condominium in Bukit Timah, and landed projects resembling Tai Keng Villas, Parry Inexperienced, Chuan Villas and Princeton Vale. Its newest growth is JARDIN, an exclusive property nestled alongside Bukit Timah/Dunearn Highway Learn More Can Singapore safely deflate its property market?
GPS Funding Sales operates like an entrepreneur group drawing on wealth of experiences with in depth insight locally and having a global perspective. We are in a position to provide investment methods that tailor-made to the clients profile. Our purchasers starting from Wealth Fund managers, Multinational Companies, Small Medium Enterprise companies, Property Developers and Ultra Networth Individual. En-bloc Sales Department Sustainability, property growth, sustainability initiatives, tripple backside line, measuring sustainability, reporting, metrics and benchmarks When you've loved what you've got read thus far why not sign up for our FREE property alert and online journal PropertyWire Confidential. District 23, ninety nine years Leasehold condominium BUILD TO ALTER 2 NH3 ΔH = -92 kJ mol-1
The product contains heat:
- N2 + 3 H2 PROPERTY builders did not have the simplest year, what with the cooling measures imposed in January and the loan curbs in June, but some still managed to do effectively while others made their first foray abroad.
As a public-listed company and a pioneer in the improvement of landed properties in Singapore, we have now been constructing some of Singapore's nicely-recognized, established residential estates for over 50 years. Our many developments in Singapore are an affidavit of our steady want to create not just high quality houses however communities for you and your family members Hotel Properties Limited (HPL) was listed on the Inventory Trade of Singapore in 1982. Beginning with simply the Hilton Lodge in Singapore, HPL has expanded rapidly through the years. As we speak HPL has pursuits in 19 resorts with almost 4000 rooms in 8 countries. An Choice or Settlement/Contract for the Buy of a Home or Flat will be formedin many ways e.g. A gaggle of persons, whether in partnership or otherwise
Certainly one of Asia's premier property firms, Keppel Land is recognised for its sterling portfolio of award-profitable residential developments and funding-grade business properties as well as excessive requirements of company governance and transparency. Keppel Land is without doubt one of the largest listed property corporations by total assets on the Singapore Change. The Group's total assets amounted to about $13.eight billion as at 31 March 2014. Additionally it is a component of a number of stock indices including the FTSE ST Real Property Index, FTSE ST China Prime Index, FTSE All-World Index, FTSE Asia Pacific ex-Japan Index, FTSE EPRA/NAREIT World Real Estate Index and EPRA/NAREIT Index. WOODSVALE PERSONAL CONDOMINIUM CONDOMINIUM WOODSVALE CLOSE, SINGAPORE (DISTRICT thirteen) Industrial
LINCOLN RESIDENCES, THE NON-PUBLIC CONDOMINIUM APARTMENT SURREY STREET, SINGAPORE (DISTRICT eleven) LUCIDA NON-PUBLIC CONDOMINIUM APARTMENT SUFFOLK ROAD, SINGAPORE (DISTRICT 11) LUMOS, THE PRIVATE CONDOMINIUM APARTMENT LEONIE HILL, SINGAPORE (DISTRICT 09) LUXURIE, THE PRIVATE CONDOMINIUM CONDOMINIUM COMPASSVALE BOW, SINGAPORE (DISTRICT 19) M66 NON-PUBLIC CONDOMINIUM RESIDENCE MOONSTONE LANE, SINGAPORE (DISTRICT 12) MARINA BAY SUITES PRIVATE CONDOMINIUM CONDOMINIUM CENTRAL BOULEVARD, SINGAPORE (DISTRICT 01) MEIER SUITES PERSONAL CONDOMINIUM house in singapore MARGATE STREET, SINGAPORE (DISTRICT 15) MKZ, THE NON-PUBLIC CONDOMINIUM CONDO MACKENZIE STREET, SINGAPORE (DISTRICT 09) MONTCLAIR @ WHITLEY CLUSTER STRATA HOUSE WHITLEY HIGHWAY, SINGAPORE (DISTRICT 11) Condominiums by District
The Singapore Property Awards recognise excellence in actual estate development initiatives or individual properties in terms of design, aesthetics, functionality, contribution to the constructed atmosphere and neighborhood at massive. It represents an outstanding achievement which developers, professionals and property house owners aspire to achieve. It bestows upon the winner the correct to use the coveted award emblem recognised extensively throughout the FIABCI network.
ADRIA NON-PUBLIC CONDOMINIUM CONDOMINIUM DERBYSHIRE HIGHWAY, THOMSON ROAD, SINGAPORE (DISTRICT eleven) AMBER RESIDENCES (PREPARED HOUSES) PRIVATE CONDOMINIUM RESIDENCE AMBER STREET, SINGAPORE (DISTRICT 15) ARC AT TAMPINES GOVERNMENT CONDOMINIUM APARTMENT TAMPINES AVENUE 8, SINGAPORE (DISTRICT 18) ARDMORE RESIDENCE NON-PUBLIC CONDOMINIUM CONDO ARDMORE PARK, SINGAPORE (DISTRICT 10) ARISTO @ AMBER , THE PRIVATE CONDOMINIUM CONDOMINIUM AMBER STREET, SINGAPORE (DISTRICT 15) ASPEN LINQ NON-PUBLIC CONDOMINIUM RESIDENCE INSTITUTION HILL, SINGAPORE (DISTRICT 09) BARTLEY RESIDENCES NON-PUBLIC CONDOMINIUM HOUSE BARTLEY HIGHWAY, SINGAPORE (DISTRICT 19) BEACON HEIGHTS PERSONAL CONDOMINIUM CONDO MAR THOMA STREET, SINGAPORE (DISTRCT 12) title searches and authorized requisitions on the property; and
Hongkong Land is a number one property funding, administration and growth group with a serious portfolio in Hong Kong and different property pursuits in Asia. As considered one of Singapore's largest property gamers, Singapore Land (SingLand) is synonymous with premier property developments in both prime and suburban areas. YHS made its first foray into property improvement with Tivoli Gardens, a 59-unit landed estate in District 19. This was adopted by the launch of The Sterling, a freehold condominium in Bukit Timah, and landed projects resembling Tai Keng Villas, Parry Inexperienced, Chuan Villas and Princeton Vale. Its newest growth is JARDIN, an exclusive property nestled alongside Bukit Timah/Dunearn Highway Learn More Can Singapore safely deflate its property market?
GPS Funding Sales operates like an entrepreneur group drawing on wealth of experiences with in depth insight locally and having a global perspective. We are in a position to provide investment methods that tailor-made to the clients profile. Our purchasers starting from Wealth Fund managers, Multinational Companies, Small Medium Enterprise companies, Property Developers and Ultra Networth Individual. En-bloc Sales Department Sustainability, property growth, sustainability initiatives, tripple backside line, measuring sustainability, reporting, metrics and benchmarks When you've loved what you've got read thus far why not sign up for our FREE property alert and online journal PropertyWire Confidential. District 23, ninety nine years Leasehold condominium BUILD TO ALTER 2 NH3 + 92kJ
This is an exothermic reaction (hence the minus sign) when producing ammonia. If we were to lower the temperature, the equilibrium would shift to produce more heat. Since making ammonia is exothermic, this would favour the production of more ammonia. In practice, in the Haber process, the temperature is set at a compromise value, so ammonia is made quickly, even though less would be present at equilibrium.
In exothermic reactions, increase in temperature decreases the equilibrium constant, K, whereas, in endothermic reactions, increase in temperature increases the K value.
As a public-listed company and a pioneer in the improvement of landed properties in Singapore, we have now been constructing some of Singapore's nicely-recognized, established residential estates for over 50 years. Our many developments in Singapore are an affidavit of our steady want to create not just high quality houses however communities for you and your family members Hotel Properties Limited (HPL) was listed on the Inventory Trade of Singapore in 1982. Beginning with simply the Hilton Lodge in Singapore, HPL has expanded rapidly through the years. As we speak HPL has pursuits in 19 resorts with almost 4000 rooms in 8 countries. An Choice or Settlement/Contract for the Buy of a Home or Flat will be formedin many ways e.g. A gaggle of persons, whether in partnership or otherwise
Certainly one of Asia's premier property firms, Keppel Land is recognised for its sterling portfolio of award-profitable residential developments and funding-grade business properties as well as excessive requirements of company governance and transparency. Keppel Land is without doubt one of the largest listed property corporations by total assets on the Singapore Change. The Group's total assets amounted to about $13.eight billion as at 31 March 2014. Additionally it is a component of a number of stock indices including the FTSE ST Real Property Index, FTSE ST China Prime Index, FTSE All-World Index, FTSE Asia Pacific ex-Japan Index, FTSE EPRA/NAREIT World Real Estate Index and EPRA/NAREIT Index. WOODSVALE PERSONAL CONDOMINIUM CONDOMINIUM WOODSVALE CLOSE, SINGAPORE (DISTRICT thirteen) Industrial
LINCOLN RESIDENCES, THE NON-PUBLIC CONDOMINIUM APARTMENT SURREY STREET, SINGAPORE (DISTRICT eleven) LUCIDA NON-PUBLIC CONDOMINIUM APARTMENT SUFFOLK ROAD, SINGAPORE (DISTRICT 11) LUMOS, THE PRIVATE CONDOMINIUM APARTMENT LEONIE HILL, SINGAPORE (DISTRICT 09) LUXURIE, THE PRIVATE CONDOMINIUM CONDOMINIUM COMPASSVALE BOW, SINGAPORE (DISTRICT 19) M66 NON-PUBLIC CONDOMINIUM RESIDENCE MOONSTONE LANE, SINGAPORE (DISTRICT 12) MARINA BAY SUITES PRIVATE CONDOMINIUM CONDOMINIUM CENTRAL BOULEVARD, SINGAPORE (DISTRICT 01) MEIER SUITES PERSONAL CONDOMINIUM house in singapore MARGATE STREET, SINGAPORE (DISTRICT 15) MKZ, THE NON-PUBLIC CONDOMINIUM CONDO MACKENZIE STREET, SINGAPORE (DISTRICT 09) MONTCLAIR @ WHITLEY CLUSTER STRATA HOUSE WHITLEY HIGHWAY, SINGAPORE (DISTRICT 11) Condominiums by District
The Singapore Property Awards recognise excellence in actual estate development initiatives or individual properties in terms of design, aesthetics, functionality, contribution to the constructed atmosphere and neighborhood at massive. It represents an outstanding achievement which developers, professionals and property house owners aspire to achieve. It bestows upon the winner the correct to use the coveted award emblem recognised extensively throughout the FIABCI network.
ADRIA NON-PUBLIC CONDOMINIUM CONDOMINIUM DERBYSHIRE HIGHWAY, THOMSON ROAD, SINGAPORE (DISTRICT eleven) AMBER RESIDENCES (PREPARED HOUSES) PRIVATE CONDOMINIUM RESIDENCE AMBER STREET, SINGAPORE (DISTRICT 15) ARC AT TAMPINES GOVERNMENT CONDOMINIUM APARTMENT TAMPINES AVENUE 8, SINGAPORE (DISTRICT 18) ARDMORE RESIDENCE NON-PUBLIC CONDOMINIUM CONDO ARDMORE PARK, SINGAPORE (DISTRICT 10) ARISTO @ AMBER , THE PRIVATE CONDOMINIUM CONDOMINIUM AMBER STREET, SINGAPORE (DISTRICT 15) ASPEN LINQ NON-PUBLIC CONDOMINIUM RESIDENCE INSTITUTION HILL, SINGAPORE (DISTRICT 09) BARTLEY RESIDENCES NON-PUBLIC CONDOMINIUM HOUSE BARTLEY HIGHWAY, SINGAPORE (DISTRICT 19) BEACON HEIGHTS PERSONAL CONDOMINIUM CONDO MAR THOMA STREET, SINGAPORE (DISTRCT 12) title searches and authorized requisitions on the property; and
Hongkong Land is a number one property funding, administration and growth group with a serious portfolio in Hong Kong and different property pursuits in Asia. As considered one of Singapore's largest property gamers, Singapore Land (SingLand) is synonymous with premier property developments in both prime and suburban areas. YHS made its first foray into property improvement with Tivoli Gardens, a 59-unit landed estate in District 19. This was adopted by the launch of The Sterling, a freehold condominium in Bukit Timah, and landed projects resembling Tai Keng Villas, Parry Inexperienced, Chuan Villas and Princeton Vale. Its newest growth is JARDIN, an exclusive property nestled alongside Bukit Timah/Dunearn Highway Learn More Can Singapore safely deflate its property market?
GPS Funding Sales operates like an entrepreneur group drawing on wealth of experiences with in depth insight locally and having a global perspective. We are in a position to provide investment methods that tailor-made to the clients profile. Our purchasers starting from Wealth Fund managers, Multinational Companies, Small Medium Enterprise companies, Property Developers and Ultra Networth Individual. En-bloc Sales Department Sustainability, property growth, sustainability initiatives, tripple backside line, measuring sustainability, reporting, metrics and benchmarks When you've loved what you've got read thus far why not sign up for our FREE property alert and online journal PropertyWire Confidential. District 23, ninety nine years Leasehold condominium BUILD TO ALTER 2NO2(g), the equilibrium position can be shifted by changing the temperature. When heat is added and the temperature increases, the reaction shifts to the right and the flask turns reddish brown due to an increase in NO2. When heat is removed and the temperature decreases, the reaction shifts to the left and flask turns colorless due to an increase in N2O4. This demonstrates Le Chatelier’s Principle because the equilibrium shifts in the direction that consumes energy.
Effect of change in pressure
Changes in pressure are attributable to changes in volume. The equilibrium concentrations of the products and reactants do not directly depend on the pressure subjected to the system. However, a change in pressure due to a change in volume of the system will shift the equilibrium.
Considering the reaction of nitrogen gas with hydrogen gas to form ammonia:
- N2 + 3 H2 PROPERTY builders did not have the simplest year, what with the cooling measures imposed in January and the loan curbs in June, but some still managed to do effectively while others made their first foray abroad.
As a public-listed company and a pioneer in the improvement of landed properties in Singapore, we have now been constructing some of Singapore's nicely-recognized, established residential estates for over 50 years. Our many developments in Singapore are an affidavit of our steady want to create not just high quality houses however communities for you and your family members Hotel Properties Limited (HPL) was listed on the Inventory Trade of Singapore in 1982. Beginning with simply the Hilton Lodge in Singapore, HPL has expanded rapidly through the years. As we speak HPL has pursuits in 19 resorts with almost 4000 rooms in 8 countries. An Choice or Settlement/Contract for the Buy of a Home or Flat will be formedin many ways e.g. A gaggle of persons, whether in partnership or otherwise
Certainly one of Asia's premier property firms, Keppel Land is recognised for its sterling portfolio of award-profitable residential developments and funding-grade business properties as well as excessive requirements of company governance and transparency. Keppel Land is without doubt one of the largest listed property corporations by total assets on the Singapore Change. The Group's total assets amounted to about $13.eight billion as at 31 March 2014. Additionally it is a component of a number of stock indices including the FTSE ST Real Property Index, FTSE ST China Prime Index, FTSE All-World Index, FTSE Asia Pacific ex-Japan Index, FTSE EPRA/NAREIT World Real Estate Index and EPRA/NAREIT Index. WOODSVALE PERSONAL CONDOMINIUM CONDOMINIUM WOODSVALE CLOSE, SINGAPORE (DISTRICT thirteen) Industrial
LINCOLN RESIDENCES, THE NON-PUBLIC CONDOMINIUM APARTMENT SURREY STREET, SINGAPORE (DISTRICT eleven) LUCIDA NON-PUBLIC CONDOMINIUM APARTMENT SUFFOLK ROAD, SINGAPORE (DISTRICT 11) LUMOS, THE PRIVATE CONDOMINIUM APARTMENT LEONIE HILL, SINGAPORE (DISTRICT 09) LUXURIE, THE PRIVATE CONDOMINIUM CONDOMINIUM COMPASSVALE BOW, SINGAPORE (DISTRICT 19) M66 NON-PUBLIC CONDOMINIUM RESIDENCE MOONSTONE LANE, SINGAPORE (DISTRICT 12) MARINA BAY SUITES PRIVATE CONDOMINIUM CONDOMINIUM CENTRAL BOULEVARD, SINGAPORE (DISTRICT 01) MEIER SUITES PERSONAL CONDOMINIUM house in singapore MARGATE STREET, SINGAPORE (DISTRICT 15) MKZ, THE NON-PUBLIC CONDOMINIUM CONDO MACKENZIE STREET, SINGAPORE (DISTRICT 09) MONTCLAIR @ WHITLEY CLUSTER STRATA HOUSE WHITLEY HIGHWAY, SINGAPORE (DISTRICT 11) Condominiums by District
The Singapore Property Awards recognise excellence in actual estate development initiatives or individual properties in terms of design, aesthetics, functionality, contribution to the constructed atmosphere and neighborhood at massive. It represents an outstanding achievement which developers, professionals and property house owners aspire to achieve. It bestows upon the winner the correct to use the coveted award emblem recognised extensively throughout the FIABCI network.
ADRIA NON-PUBLIC CONDOMINIUM CONDOMINIUM DERBYSHIRE HIGHWAY, THOMSON ROAD, SINGAPORE (DISTRICT eleven) AMBER RESIDENCES (PREPARED HOUSES) PRIVATE CONDOMINIUM RESIDENCE AMBER STREET, SINGAPORE (DISTRICT 15) ARC AT TAMPINES GOVERNMENT CONDOMINIUM APARTMENT TAMPINES AVENUE 8, SINGAPORE (DISTRICT 18) ARDMORE RESIDENCE NON-PUBLIC CONDOMINIUM CONDO ARDMORE PARK, SINGAPORE (DISTRICT 10) ARISTO @ AMBER , THE PRIVATE CONDOMINIUM CONDOMINIUM AMBER STREET, SINGAPORE (DISTRICT 15) ASPEN LINQ NON-PUBLIC CONDOMINIUM RESIDENCE INSTITUTION HILL, SINGAPORE (DISTRICT 09) BARTLEY RESIDENCES NON-PUBLIC CONDOMINIUM HOUSE BARTLEY HIGHWAY, SINGAPORE (DISTRICT 19) BEACON HEIGHTS PERSONAL CONDOMINIUM CONDO MAR THOMA STREET, SINGAPORE (DISTRCT 12) title searches and authorized requisitions on the property; and
Hongkong Land is a number one property funding, administration and growth group with a serious portfolio in Hong Kong and different property pursuits in Asia. As considered one of Singapore's largest property gamers, Singapore Land (SingLand) is synonymous with premier property developments in both prime and suburban areas. YHS made its first foray into property improvement with Tivoli Gardens, a 59-unit landed estate in District 19. This was adopted by the launch of The Sterling, a freehold condominium in Bukit Timah, and landed projects resembling Tai Keng Villas, Parry Inexperienced, Chuan Villas and Princeton Vale. Its newest growth is JARDIN, an exclusive property nestled alongside Bukit Timah/Dunearn Highway Learn More Can Singapore safely deflate its property market?
GPS Funding Sales operates like an entrepreneur group drawing on wealth of experiences with in depth insight locally and having a global perspective. We are in a position to provide investment methods that tailor-made to the clients profile. Our purchasers starting from Wealth Fund managers, Multinational Companies, Small Medium Enterprise companies, Property Developers and Ultra Networth Individual. En-bloc Sales Department Sustainability, property growth, sustainability initiatives, tripple backside line, measuring sustainability, reporting, metrics and benchmarks When you've loved what you've got read thus far why not sign up for our FREE property alert and online journal PropertyWire Confidential. District 23, ninety nine years Leasehold condominium BUILD TO ALTER 2 NH3 ΔH = -92kJ mol-1 - 4 volumes PROPERTY builders did not have the simplest year, what with the cooling measures imposed in January and the loan curbs in June, but some still managed to do effectively while others made their first foray abroad.
As a public-listed company and a pioneer in the improvement of landed properties in Singapore, we have now been constructing some of Singapore's nicely-recognized, established residential estates for over 50 years. Our many developments in Singapore are an affidavit of our steady want to create not just high quality houses however communities for you and your family members Hotel Properties Limited (HPL) was listed on the Inventory Trade of Singapore in 1982. Beginning with simply the Hilton Lodge in Singapore, HPL has expanded rapidly through the years. As we speak HPL has pursuits in 19 resorts with almost 4000 rooms in 8 countries. An Choice or Settlement/Contract for the Buy of a Home or Flat will be formedin many ways e.g. A gaggle of persons, whether in partnership or otherwise
Certainly one of Asia's premier property firms, Keppel Land is recognised for its sterling portfolio of award-profitable residential developments and funding-grade business properties as well as excessive requirements of company governance and transparency. Keppel Land is without doubt one of the largest listed property corporations by total assets on the Singapore Change. The Group's total assets amounted to about $13.eight billion as at 31 March 2014. Additionally it is a component of a number of stock indices including the FTSE ST Real Property Index, FTSE ST China Prime Index, FTSE All-World Index, FTSE Asia Pacific ex-Japan Index, FTSE EPRA/NAREIT World Real Estate Index and EPRA/NAREIT Index. WOODSVALE PERSONAL CONDOMINIUM CONDOMINIUM WOODSVALE CLOSE, SINGAPORE (DISTRICT thirteen) Industrial
LINCOLN RESIDENCES, THE NON-PUBLIC CONDOMINIUM APARTMENT SURREY STREET, SINGAPORE (DISTRICT eleven) LUCIDA NON-PUBLIC CONDOMINIUM APARTMENT SUFFOLK ROAD, SINGAPORE (DISTRICT 11) LUMOS, THE PRIVATE CONDOMINIUM APARTMENT LEONIE HILL, SINGAPORE (DISTRICT 09) LUXURIE, THE PRIVATE CONDOMINIUM CONDOMINIUM COMPASSVALE BOW, SINGAPORE (DISTRICT 19) M66 NON-PUBLIC CONDOMINIUM RESIDENCE MOONSTONE LANE, SINGAPORE (DISTRICT 12) MARINA BAY SUITES PRIVATE CONDOMINIUM CONDOMINIUM CENTRAL BOULEVARD, SINGAPORE (DISTRICT 01) MEIER SUITES PERSONAL CONDOMINIUM house in singapore MARGATE STREET, SINGAPORE (DISTRICT 15) MKZ, THE NON-PUBLIC CONDOMINIUM CONDO MACKENZIE STREET, SINGAPORE (DISTRICT 09) MONTCLAIR @ WHITLEY CLUSTER STRATA HOUSE WHITLEY HIGHWAY, SINGAPORE (DISTRICT 11) Condominiums by District
The Singapore Property Awards recognise excellence in actual estate development initiatives or individual properties in terms of design, aesthetics, functionality, contribution to the constructed atmosphere and neighborhood at massive. It represents an outstanding achievement which developers, professionals and property house owners aspire to achieve. It bestows upon the winner the correct to use the coveted award emblem recognised extensively throughout the FIABCI network.
ADRIA NON-PUBLIC CONDOMINIUM CONDOMINIUM DERBYSHIRE HIGHWAY, THOMSON ROAD, SINGAPORE (DISTRICT eleven) AMBER RESIDENCES (PREPARED HOUSES) PRIVATE CONDOMINIUM RESIDENCE AMBER STREET, SINGAPORE (DISTRICT 15) ARC AT TAMPINES GOVERNMENT CONDOMINIUM APARTMENT TAMPINES AVENUE 8, SINGAPORE (DISTRICT 18) ARDMORE RESIDENCE NON-PUBLIC CONDOMINIUM CONDO ARDMORE PARK, SINGAPORE (DISTRICT 10) ARISTO @ AMBER , THE PRIVATE CONDOMINIUM CONDOMINIUM AMBER STREET, SINGAPORE (DISTRICT 15) ASPEN LINQ NON-PUBLIC CONDOMINIUM RESIDENCE INSTITUTION HILL, SINGAPORE (DISTRICT 09) BARTLEY RESIDENCES NON-PUBLIC CONDOMINIUM HOUSE BARTLEY HIGHWAY, SINGAPORE (DISTRICT 19) BEACON HEIGHTS PERSONAL CONDOMINIUM CONDO MAR THOMA STREET, SINGAPORE (DISTRCT 12) title searches and authorized requisitions on the property; and
Hongkong Land is a number one property funding, administration and growth group with a serious portfolio in Hong Kong and different property pursuits in Asia. As considered one of Singapore's largest property gamers, Singapore Land (SingLand) is synonymous with premier property developments in both prime and suburban areas. YHS made its first foray into property improvement with Tivoli Gardens, a 59-unit landed estate in District 19. This was adopted by the launch of The Sterling, a freehold condominium in Bukit Timah, and landed projects resembling Tai Keng Villas, Parry Inexperienced, Chuan Villas and Princeton Vale. Its newest growth is JARDIN, an exclusive property nestled alongside Bukit Timah/Dunearn Highway Learn More Can Singapore safely deflate its property market?
GPS Funding Sales operates like an entrepreneur group drawing on wealth of experiences with in depth insight locally and having a global perspective. We are in a position to provide investment methods that tailor-made to the clients profile. Our purchasers starting from Wealth Fund managers, Multinational Companies, Small Medium Enterprise companies, Property Developers and Ultra Networth Individual. En-bloc Sales Department Sustainability, property growth, sustainability initiatives, tripple backside line, measuring sustainability, reporting, metrics and benchmarks When you've loved what you've got read thus far why not sign up for our FREE property alert and online journal PropertyWire Confidential. District 23, ninety nine years Leasehold condominium BUILD TO ALTER 2 volumes
Note the number of moles of gas on the left-hand side and the number of moles of gas on the right-hand side. When the volume of the system is changed, the partial pressures of the gases change. If we were to decrease pressure by increasing volume, the equilibrium of the above reaction will shift to the left, because the reactant side has greater number of moles than does the product side. The system tries to counteract the decrease in partial pressure of gas molecules by shifting to the side that exerts greater pressure. Similarly, if we were to increase pressure by decreasing volume, the equilibrium shifts to the right, counteracting the pressure increase by shifting to the side with fewer moles of gas that exert less pressure. If the volume is increased because there are more moles of gas on the reactant side, this change is more significant in the denominator of the equilibrium constant expression, causing a shift in equilibrium.
Thus, an increase in system pressure due to decreasing volume causes the reaction to shift to the side with the fewer moles of gas.[4] A decrease in pressure due to increasing volume causes the reaction to shift to the side with more moles of gas. There is no effect on a reaction where the number of moles of gas is the same on each side of the chemical equation.
Effect of adding an inert gas
An inert gas (or noble gas) such as helium is one that does not react with other elements or compounds. Adding an inert gas into a gas-phase equilibrium at constant volume does not result in a shift.[4] This is because the addition of a non-reactive gas does not change the partial pressures of the other gases in the container. While it is true that the total pressure of the system increases, the total pressure does not have any effect on the equilibrium constant; rather, it is a change in partial pressures that will cause a shift in the equilibrium. If, however, the volume is allowed to increase in the process, the partial pressures of all gases would be decreased resulting in a shift towards the side with the greater number of moles of gas. There is a short form to remember this: LBMF (little boy married fiona); L stands for less pressure, B—backward reaction, M—more pressure, and F—forward reaction. Note that this mnemonic ONLY applies for a reaction resulting in a greater number of gas molecules on the products side, than the reactants (does not apply if the reverse is true).
Effect of a catalyst
A catalyst has no effect on equilibrium. It speeds up both forward and backward reactions equally.
E.g.: N2 + 3 H2 → 2 NH3
Here Iron (Fe) and Molybdenum (Mo) are catalysts, but the two catalysts do not affect the state of equilibrium.
Hence a catalyst has no effect on equilibrium state.
Applications in economics
In economics, a similar concept also named after Le Chatelier was introduced by U.S. economist Paul Samuelson in 1947. There the generalized Le Chatelier principle is for a maximum condition of economic equilibrium: Where all unknowns of a function are independently variable, auxiliary constraints—"just-binding" in leaving initial equilibrium unchanged—reduce the response to a parameter change. Thus, factor-demand and commodity-supply elasticities are hypothesized to be lower in the short run than in the long run because of the fixed-cost constraint in the short run.[5]
See also
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro. Template:Refbegin Template:Refend
Bibliography
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - Le Chatelier, H. and Boudouard O. (1898), "Limits of Flammability of Gaseous Mixtures", Bulletin de la Société Chimique de France (Paris), v. 19, pp. 483–488.
- Hatta, Tatsuo (1987), "Le Châtelier principle," The New Palgrave: A Dictionary of Economics, v. 3, pp. 155–57.
- Samuelson, Paul A. (1947, Enlarged ed. 1983). Foundations of Economic Analysis, Harvard University Press. ISBN 0-674-31301-1
- D.J. Evans, D.J. Searles and E. Mittag (2001), "Fluctuation theorem for Hamiltonian systems—Le Châtelier's principle", Physical Review E, 63, 051105(4).
- Also refer to Brown Lemay Bursten. 10th or 11e edition for this principle.
External links
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Template:Cite web
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
For full details, see: Template:Cite paper - ↑ 4.0 4.1 Template:Harvnb
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534