Thermodynamics lecture 6 Flashcards
What is the fundamental equation? What condition does it have?
Via combing the first law of thermodynamics ( dU = dw +dq) and the second law of thermodynamics (dw(rev) = pdV and dq(rev) = TdS) we get our fundamental equation:
dU = TdS - pdV
However since dU is an exact function, it is independent of its path, so the same value of dU is obtained whether the change is brought reversibly or irreversibly
How can the Fundamental equation be rewritten?
The Fundamental equation tells us that in a closed system, the change that occurs to the internal energy is due to the change of either entropy or volume, (since dU is proportional to both dS and dV). Due to this, we can rewrite the infinitesimal change of U as a function of S and V where:
dU = (εU/εS)v dS + (εU/εV)s dV
where:
(εU/εS)v= T and (εU/εV)s = -p
What are all the Maxwell relations and their derivations?
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List out all of the fundamental equation
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What does the Gibbs Fundamental equation tell us?
The first term ( (εG/εT)p = -S ):
- because S > 0 for all substances, G decreases with the increase of temp.
- because (εG/εT)p becomes more negative as entropy increases (the slope gets sharper), the decreases in G with the increase in temp is most significant at larger entropy
(Therefore, the Gibbs energy of the gaseous phase of a sub-stance, which has a high molar entropy, is more sensitive to temperature than its liquid and solid phases)
The second term ( (εG/εp)T = V ):
-because V>0 for all substances, G increases with the increase of temp.
- because (εG/εp)T increases with the increase of V (the slope becomes sharper), the increase of G with the of P is most significant at large V.
(Because the molar volume of the gaseous phase of a substance is greater than that of its condensed phases, the molar Gibbs energy of a gas is more sensitive to pressure than its liquid and solid phases)
What is the derivation of the expression for the temperature variation of G/T?
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Because the equilibrium composition of a system depends on the Gibbs energy, to discuss the response of the composition to temperature it is necessary to know how G varies with temperature.
we do G/T, not G because G/T has a relation with the equilibrium constant which will be explained later
What is the variation of Gibbs energy with pressure under solid, liquid, and gas phase conditions?
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What is the relation between Gibbs’s energy and the reaction quotient? Include the scenario where the reaction is equilibrium.
∆rG = ∆rG° + RTlnQ, where ∆rG° is the standard Gibbs energy of the reaction, and Q is the reaction quotient (Pb/Pa) (note Pa and Pb are partial pressures)
When at equilibrium the ∆rG = 0 so then we can introduce a very important equation for standard Gibbs energy of reaction: ∆rG° = -RTlnQ.
how is the minimum value of Gibbs energy (∆rG = 0) deduced?
it is deduced by the mixing of two gases…NOTES
What does the equation relating Gibbs with the equilibrium reaction quotient tell us?
It tells us that when ∆rG° > 0 then, Q < 1 which means that there is more product than a reactant, and when ∆rG° < 0 then, Q > 1 which means that there is more reactant than product
What is the derivation of the Van’t Hoff equation? What does it imply?
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How does the Boltzmann distribution of molecules over the available energy levels show how the equilibrium changes?
As the temperature increases, the Boltzmann distribution adjusts and a change in the population occurs, the change corresponds to the increase of the population of higher energy states at the expense of the lower energy states.
Following this when the reaction is endothermic, an increase in temperature will cause an increase in the population of the energy states of the product and teh expense of the reactant states, therefore the equilibrium would lie more to the right
If the reaction is exothermic, then the increase in temp will cause an increase in the energy states of the reactants at the cost of the product states, therefore the equilibrium would lie more to the left
How can we use the Van’t Hoff equation to calculate the enthalpy?
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