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Lecture

34- Gibbs Energy and Equilibrium.docx

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School
Department
Chemistry
Course
CHEM 204
Professor
Christopher Barrett
Semester
Winter

Description
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 -58 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 3 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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