CHEM 204
04/05/2013 Lecture 34
Martin M. PHGY Tutor
Gibbs Energy and Equilibrium
How are Δ R and Δ G°Rrelated? We have to use the reaction quotients Q and K.
Where Q = [C][D]/[A][B] = P P / C PD A B (for gasses using partial pressures). This gives us
the result thatRΔ G = ΔRG° + RT lnQ.
At equilibrium this Q becomes the equilibrium constant, K. At equilibrium R G° = – RT ln K.
This simple equation can be used to predict the equilibrium of anything with a Gibbs energy.
Practical example:
What is the vapour pressure of water at 25°C?
the ΔVAPG° of water is ΔG°(g) – ΔG° (l) = 8.5 kJ/mol
( )( )
This is the vapour pressure at 25°C, 0.032 bar or 3.2% humidity. Everything in the weather is
relative to this 3.2% humidity. So when you say 100% humidity, you really mean 3.2% absolute.
This formulae predicts that everything, liquid or solid, evaporates! And this is completely true. If
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we take gold, which has a ΔG°(sublime) = +326kJ/mol and find K, we find that K = 4.7 10 .
This number is so small that it is irrelevant. We can apply this formula better by finding the
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vapour pressures of different substances. Let's assume we have a room of 100m , meaning 4000
moles of an ideal gas.
Substance K Amount in air
Water 0.032 2.3 kg
Benzene 0.13 41.3 kg
Hg 0.0000022 1.8 g
The equilibrium constant, K = e –ΔG°/R, will always be reached no matter what side we approach
from. If we add more A to the mixture, we get driven to B and vice versa.
The number of molecules is not fixed, but the ratio is. We can add or subtract molecules from a
reaction and the system will re-establish the equilibrium with Le Chatelier's principle. Let's take
an example:
A (liq) B (liq) 100 mol of pure A is placed in a container at 310K, and the
reaction is allowed to proceed to equilibrium. The ΔG° = –2830 J/mol. Solving for lnK,
Or ln(B/A), we get 3.0. This means there is always 3 times as much B as A in equilibrium. CHEM 204
04/05/2013 Lecture 34
Martin M. PHGY Tutor
The fraction and ratio of A will always be the same!
Moles added Ratio? Moles of B Moles of A
100 3.0 75 25
+20 (120) 3.0 90 30
-40 (80) 3.0 60 20
Adding some reactant

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