# Entropy and equilibriuum

1. Jan 14, 2012

### jsmith613

Given that at equilibrium total entropy change = 0
how does the following equation make sense
ΔS(total) = R*lnK
if ΔS(total) is 0???
thanks

2. Jan 14, 2012

### Staff: Mentor

Units don't match, so it doesn't make sense. Units of entropy are JK-1, units of ideal gas constant are JK-1mol-1.

3. Jan 14, 2012

### jsmith613

no units of entropy are J K-1 mol-1

4. Jan 14, 2012

### jsmith613

oh Standard entropy = R lnK

nonetheless how can a standard entropy change of zero have an equation R*lnK

5. Jan 14, 2012

### Mike H

Questions to ask yourself:

1.) What is K in your equation?

2.) What does K equal when the system is at equilibrium?

If you do this, the answer will fall right into your lap.

6. Jan 14, 2012

### jsmith613

1) K is the equilibrium constant
2) when the system is at equilibrium K = 1

...so your saying that ONLY at the point of equilibrium does total entropy change = zero
....i am still confused
sorry :(

7. Jan 14, 2012

### jsmith613

in fact K does NOT nessecaryily = 1 at equilibrium
...therefore how can the two be related

8. Jan 14, 2012

### jsmith613

9. Jan 14, 2012

### Mike H

I have to say I've never seen this particular twist in presentation of thermo before, which is why my earlier "shot-from-the-hip" answer isn't right. And I should probably read more carefully....

It's as if your text/reference material is trying to rework what is normally seen via Gibbs free energy statements in terms of entropy for whatever inexplicable reason - if you'll remember, we have the well-known equality

ΔG = ΔG° + RT*ln(Q)

where ΔG = 0 at equilibrium, and as Q → K at equilibrium, we have

ΔG° = -RT*ln(K).

It seems as if your text is trying to do something similar in terms of ΔS and ΔS° for whatever reason, such that

ΔS = ΔS° - R*ln(K),

so when ΔS = 0,

ΔS° = R*ln(K).

I suppose it's valid, although I've never seen it presented this particular way, at least that I can recall.

10. Jan 15, 2012

### jsmith613

what is the difference between ΔS° and ΔS
and are they both calculated in the same way