L 14,15,16

# L 14,15,16 - "Gibbs and Helmholtz Energies Prof Gianluigi...

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“Gibbs and Helmholtz Energies” Prof. GianluigiVeglia

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So far we have discussed thermal equilibrium (equalization of temperature) and mechanical equilibrium (equalization of forces, i.e. pressures). What about material equilibrium? (i.e. the most stable distribution of stuff in a system). Example: Sublimation of dry ice: CO 2(s) CO 2(g)
Another example is the equilibrium of N 2 , H 2 , and NH 3 over an ammonia synthesis catalyst: To analyze such situations, we will need to introduce two new state functions: N 2(g) H 2(g) NH 3(g) TS U A = TS H G = Helmholtz Function Gibbs Function

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Imagine that I have a system far from material equilibrium. It might be the situation that arises immediately after mixing an acid and a base: Acid and base H + H + H + H + H + OH - OH - OH - OH - OH - OH - H + H + H 2 O H 2 O Far from equilibrium Equilibrium
How can I establish the criteria that must be met for me to know when the equilibrium has been attained? Consider first an isolated system. We know that dS ≥0, where the inequality corresponds to a situation for which all change is reversible. At the equilibrium, all change is reversible, even chemical change, e.g.: Let’s see how to interpret this graphically. liq aq aq O H OH H 2 + +

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Since the forward and the reverse reactions are balanced. So if I were to start a system far from equilibrium, I could monitor its progress toward the equilibrium by measuring the entropy as a function of time: We cannot predict how long it will take to reach equilibrium. But we will know when we arrive. Since the above discussion applies only to isolated systems, it is of limited use. However, the universe as a whole constitutes an isolated system, so we could say that at equilibrium: 0 = + gs surroundin system dS dS
The above equation is still of limited usefulness, because it requires that we keep track of the system and the surroundings: that is not very practical. Can we develop criteria for the equilibrium expressed only in terms of state function? Yes! Let’s see how… In the past lectures, we showed that where the equality applies at the equilibrium. Taking into account the first law We can write: T q dS δ w q dU δ+ = q TdS

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Or if we combine the two formulas: For PV work only at the equilibrium. Now, we have a prescription for equilibrium that is expressed purely in terms of the state function of the system: it tells us that the equilibrium is obtained when U stops changing with time under conditions of constant volume and constant entropy. PdV TdS dU w TdS dU TdS w dU TdS q + δ
Are we done? No yet! The expression is still of limited use because it is not easy to design a system in which the entropy is a fixed quantity. So we slog along: We now add –SdT-TdS to both sides: PdV TdS dU TdS SdT PdV TdS TdS SdT dU SdT PdV TS d dU ) ( ( ) SdT PdV TS U d

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Now, we have something! Since U, T and S are state functions, so is U-TS. What the above expression tells us is
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L 14,15,16 - "Gibbs and Helmholtz Energies Prof Gianluigi...

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