## Four Cases

$\Delta G^{\circ}= \Delta H^{\circ} - T \Delta S^{\circ}$

$\Delta G^{\circ}= -RT\ln K$

$\Delta G^{\circ}= \sum \Delta G_{f}^{\circ}(products) - \sum \Delta G_{f}^{\circ}(reactants)$

Abigail Volk 1F
Posts: 52
Joined: Fri Sep 29, 2017 7:07 am
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### Four Cases

What are the four cases of spontaneity on ΔS and ΔH for a system at constant T and P? Whats an easy way to memorize these?

Hannah Guo 3D
Posts: 56
Joined: Fri Sep 29, 2017 7:06 am

### Re: Four Cases

One way to look at this problem is to plug numbers into the formula ΔG=ΔH-TΔS and try to get the answer through comparing the results.
When 1. ΔS +, ΔH - : (T is always >0) thus ΔG<0 -----> spontaneous at all T
2. ΔS +, ΔH + : if TΔS > ΔH, then ΔG<0; so T needs to be large -----> spontaneous at high T
3. ΔS -, ΔH- : -TΔS > 0, so we need to make -TΔS as small as possible, so -TΔS doesn't cancel out the ΔH -; if TΔS < ΔH, then ΔG<0; so T needs to be small -----> spontaneous at low T
4. ΔS -, ΔH+ : -TΔS > 0, ΔH > 0, thus ΔG > 0 -----> not spontaneous at any T

Hope it helps!

Jingyi Li 2C
Posts: 56
Joined: Fri Sep 29, 2017 7:06 am

### Re: Four Cases

1. ΔS>0, ΔH>0, spontaneous at high T (TΔS>ΔH)
2. ΔS>0, ΔH<0, spontaneous at all T
3. ΔS<0, ΔH>0, non-spontaneous at all T (reverse rxn. is spontaneous)
4. ΔS<0, ΔH<0, spontaneous at low T

My approach is to remember the formula ΔG=ΔH-TΔS and see how can I get a negative ΔG.