Gibbs free energy: Difference between revisions
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1800s, Josiah Willard Gibbs, (1839-1903) submitted scientific papers which mathematically combined both enthalpy and entropy (the measure of energy release and disorder in a system respectively) that also incorporates the second law of thermodynamics: | 1800s, [[Josiah Willard Gibbs|Josiah Willard Gibbs]], (1839-1903) submitted scientific papers which mathematically combined both enthalpy and entropy (the measure of energy release and disorder in a system respectively) that also incorporates the second law of thermodynamics: | ||
<blockquote>'''Entropy can never decrease, only increase for a reaction to take place.''' </blockquote> | <blockquote>'''Entropy can never decrease, only increase for a reaction to take place.''' </blockquote> | ||
in order to measure the amount of free enerfy present within any given system.<ref name="Hmolpedia">Sadi, Carnot. (2013). Willard Gibbs. Available: http://www.eoht.info/page/Willard+Gibbs. Last accessed 28th Nov 2013.</ref> | in order to measure the amount of free enerfy present within any given system.<ref name="Hmolpedia">Sadi, Carnot. (2013). Willard Gibbs. Available: http://www.eoht.info/page/Willard+Gibbs. Last accessed 28th Nov 2013.</ref> | ||
=== Why doesn't free energy = enthalpy - entropy? === | |||
==== Reasoning behind Gibbs equation ==== | |||
<blockquote>'''X= U - S''' </blockquote><blockquote>(where X = Function, U = Enthalpy, S = Entropy) <ref>Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp; Sons, Inc.. p84-90.</ref></blockquote> | |||
The signs for enthalpy and entropy must be opposites to each other, "because one function tends to a maximum and the other tends to a minimum." <ref name="Concise Physical Chemistry">Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp;amp;amp; Sons, Inc.. p84-90.</ref>As a consequence the one equation proposed for this "unknown energy function"<ref>Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp;amp; Sons, Inc.. p84-90.</ref> could be: ==== | |||
<blockquote>'''X= U - S''' </blockquote><blockquote>(where X = Function, U = Enthalpy, S = Entropy) <ref>Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp;amp; Sons, Inc.. p84-90.</ref></blockquote> | |||
Although this must be carried out under standard conditions, so U must be substituted for an H to demonstrate a constant pressure. (of 1atm) In addition to this, the units are wrong in our current equation; as we know, enthalpy is measure in joules ('''J''') of energy, entropy on the other hand is measured in joules per kelvin. ('''J K<sup>-1</sup>''') Thus, we must also multiply entropy ('''S''') by temperature in Kelvin. ('''T''') Giving us the following equation when delta symbols are incorporate to represent that this function is for free energy changes: | Although this must be carried out under standard conditions, so U must be substituted for an H to demonstrate a constant pressure. (of 1atm) In addition to this, the units are wrong in our current equation; as we know, enthalpy is measure in joules ('''J''') of energy, entropy on the other hand is measured in joules per kelvin. ('''J K<sup>-1</sup>''') Thus, we must also multiply entropy ('''S''') by temperature in Kelvin. ('''T''') Giving us the following equation when delta symbols are incorporate to represent that this function is for free energy changes: | ||
<blockquote>'''dG = dH - dTS''' </blockquote><blockquote>(where G = Free energy, H = Enthalpy, S = Entropy, T = Temperature, d = Change in associated function) <ref>Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp; Sons, Inc.. p84-90.</ref></blockquote> | <blockquote>'''dG = dH - dTS''' </blockquote><blockquote>(where G = Free energy, H = Enthalpy, S = Entropy, T = Temperature, d = Change in associated function) <ref>Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp;amp; Sons, Inc.. p84-90.</ref></blockquote> | ||
'''<u> | ==== '''<u></u>'''Application'''<u></u>''' ==== | ||
< | We can now determine each individual component of this equation, enthalpy change being determined via "calorimetric measurment" <ref>Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp;amp; Sons, Inc.. p84-90.</ref> to give us our value for '''dH; '''entropy can then be found if '''dG''' and temperature are known, the opposite can be said for determining '''dG''' itself with '''dS '''being our known value instead. For a reaction to be possible, it has been stated that the entropy of the universe is always increased. Consequently for a reaction to take place, '''dG '''must always be negative, with '''dS''' in the the equation for free energy exceeding that of the enthalpy change '''dH'''. | ||
=== References === | |||
<references /> | <references /><br> | ||
Revision as of 03:02, 29 November 2013
1800s, Josiah Willard Gibbs, (1839-1903) submitted scientific papers which mathematically combined both enthalpy and entropy (the measure of energy release and disorder in a system respectively) that also incorporates the second law of thermodynamics:
Entropy can never decrease, only increase for a reaction to take place.
in order to measure the amount of free enerfy present within any given system.[1]
Why doesn't free energy = enthalpy - entropy?
Reasoning behind Gibbs equation
The signs for enthalpy and entropy must be opposites to each other, "because one function tends to a maximum and the other tends to a minimum." [2]As a consequence the one equation proposed for this "unknown energy function"[3] could be: ====
X= U - S
(where X = Function, U = Enthalpy, S = Entropy) [4]
Although this must be carried out under standard conditions, so U must be substituted for an H to demonstrate a constant pressure. (of 1atm) In addition to this, the units are wrong in our current equation; as we know, enthalpy is measure in joules (J) of energy, entropy on the other hand is measured in joules per kelvin. (J K-1) Thus, we must also multiply entropy (S) by temperature in Kelvin. (T) Giving us the following equation when delta symbols are incorporate to represent that this function is for free energy changes:
dG = dH - dTS
(where G = Free energy, H = Enthalpy, S = Entropy, T = Temperature, d = Change in associated function) [5]
Application
We can now determine each individual component of this equation, enthalpy change being determined via "calorimetric measurment" [6] to give us our value for dH; entropy can then be found if dG and temperature are known, the opposite can be said for determining dG itself with dS being our known value instead. For a reaction to be possible, it has been stated that the entropy of the universe is always increased. Consequently for a reaction to take place, dG must always be negative, with dS in the the equation for free energy exceeding that of the enthalpy change dH.
References
- ↑ Sadi, Carnot. (2013). Willard Gibbs. Available: http://www.eoht.info/page/Willard+Gibbs. Last accessed 28th Nov 2013.
- ↑ Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp;amp; Sons, Inc.. p84-90.
- ↑ Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp; Sons, Inc.. p84-90.
- ↑ Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp; Sons, Inc.. p84-90.
- ↑ Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp; Sons, Inc.. p84-90.
- ↑ Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley &amp;amp; Sons, Inc.. p84-90.