Thermodynamics lecture 5

Question 1

what are Gibbs and Helmholtz energies?

Answer 1

Gibbs — G = H - TS

Helmholtz — A = U - TS

Question 2

what are the new criteria for spontaneity (based on Gibbs and Helmholtz energies)? How did we conclude that?

Answer 2

before we explain new criteria we need to define some concepts:

The definition of entropy of the surroundings is very simply given by qsur/T, and Clausius inequality is given by dS >= q/t (TdS >= q)

First new criteria:
At constant volume, the heat released (qv) is equal to the internal energy of the system, applying the Clausius inequality we see that TdS >= dU (where at constant volume and internal energy the entropy increases with a spontaneous change dSu,v >= 0). Using Helmholtz equation (A = dU - TdS) and our predefined Clauius inequality we redefine the criteria for spontaneity as dAt,v <= 0

Second new criteria:
When heat is transferred at constant pressure and there is no other work other than expansion work we re-define our Clausius inequality as TdS >= dH as dpv = dH (This states that at constant pressure and constant enthalpy the entropy change increases in a spontaneous reaction dSh,p >= 0). Using Gibbs energy (G = dH - TdS) and our re-defined Clausius inequality our new criteria for spontaneity is as defined dGt,p <= 0

Question 3

At equilibrium how is Helmotz and Gibb’s energy represented?

Answer 3

dA = 0
dG = 0

Question 4

What is the relation between the change in Helmholtz energy and the maximum work?

Answer 4

Notessss

Question 5

what two possible seniors can happen to achieve the maximum work done?

Answer 5

1. The entropy of the system is negative (TS < 0) meaning that enough heat needs to be released into the surroundings to increase the entropy of surrounding enough for the reaction to be spontaneous. This means that the maximum work done is less than the internal energy(U)
2. the entropy of the system is positive(TS > 0) meaning that some energy will be taken from the surroundings into the system with the caution that the entropy of the system remains more positive than the entropy of the surroundings making the reaction spontaneous. This means that the work done is more than the internal energy

note: U is a negative value and the expression is Wmax = U - TS

Question 6

What is the relation between the change in Gibbs’s energy and the maximum non-expansion work?

Answer 6

Notessssss

Question 7

What is the standard Gibbs energy of reaction?

Answer 7

∆rG = ∆rH - T∆rS

Question 8

What is the standard Gibbs energy of formation?

Answer 8

it is the standard Gibbs energy of reaction for the formation of a compound from its elements in their reference states

Question 9

What is H^+(aq) Gibbs energy of formation?

Answer 9

It is set at zero, as it is not possible to form Cation without their anions so this would adjust all the actual Gibbs energy of formations for all ions.

Question 10

how can we find the Gibbs energy of formation for an ion?

Answer 10

By setting up a born-haber cycle and solving for its formation ( note this only gives an approximation)

Question 11

What is the relation between Gibbs’s energy of reaction and electrical cell potential?

Answer 11

We know that Gibbs energy is equal to the maximum change of non-expansion works, which in terms of a circuit is equal tp Wel,

so we can define ∆rG = Wel = - EFV

therefore

E = - ∆rG/FV

Question 12

How do we derive the Nernst equation?

Answer 12

Notesss

Question 13

What is the expression of Gibbs’s energy with partial pressure derived from entropy?

Answer 13

Notessss