Question

1. Indicate based on signs of enthalpy and entropy changes how temperature will affect spontaneity and/or calculate temperature at which spontaneity changes. (give example)

2. Explain how sign of ΔG, sign of E, and value of K indicate spontaneity from standard conditions.

Answer 1

Q1

In order to compare equilibirum vs. spontaneous/nonspontaneous reactions, we better use a criteria.

Recall that if dSuniverse > 0, this is spontaneous, if dSuniverse = 0, this is inequilbirium and if dSuniverse < 0 this is never possible.

Then, recall that

dSuniverse = dSsurroundings + dSsystem

dSsystem = Sproducts - Sreactants

dSsurroundings = Qsurroundings/T = -dHsystem/T

therefore

dSystem =  -dHsystem/T + dSsystem

If we multiply by -T

dGrxn = dHrxn - T*dSrxn

Now, analysis of dG value... which is the "free energy" available for a process to follow

if dG <0 , this will be spontaneous

if dG = 0 , this is in equilibrium

if dG > 0, this will not be spontaneous

Now...

dG = dH - T*dS

Possible values are, dH = +/- and dS = +/-; T is always positive ( absolute value)

Analysis of cases:

Case 1.

if dH is positive (-) and dS is positive (+) --> this favours always a negative value of dG; spontaneous

Case 2.

if dH is positive (+) and dS is positive (-) --> this favours always a positive value of dG; not spontaneous

Case 3.

if dH is positive (+) and dS is positive (+) --> dG = dH - T*dS --> analysis must be done

if T is very low... then dH > T*dS; then this will be Positive value in dG; i.e. not spontaneous

if T is very high... then  dH < T*dS; then this will be Negative value in dG; i.e. spontaneous

Case 4.

if dH is positive (-) and dS is positive (-) --> dG = dH - T*dS --> analysis must be done

if T is very low... then dH > T*dS; then this will be Negative value in dG; i.e. spontaneous

if T is very high... then  dH < T*dS; then this will be Positive value in dG; i.e. non spontaneous

Q2

dG = -n*F*E°cell

dG = -RT*ln(K)

then, for spontaneous process:

dG < 0, K > 1, E°cell > 0

then, for non-spontaneous process:

dG > 0, K < 1, E°cell < 0