# Homework Help: Thermodynamics of mixing

1. Oct 17, 2009

### higherme

1. The problem statement, all variables and given/known data
at 25C & 1 atm, absolute entropy of methane and ethane are 186.19 J/K/mol and 229.49 J/K/mol in gas phase. Find absolute 3rd law entropy of a solution containing 1 mol of each gas in ideal behavior.

2. Relevant equations
I think this is the equation to use:
dSmix= -nR(x1lnx1 + x2lnx2)
where x1 and x2 i can find from 1 mole of each gas (mole fractions)

if i use this equation, then the absolute entropy of methane and ethane woud be useless in this equation. or is there another way of solving it with the absolute entropies?

2. Oct 17, 2009

### Mapes

What do you mean by "the absolute entropy of methane and ethane woud be useless in this equation"? (Note that the term represents an additional term to augment the sum of the unmixed entropies.)

3. Oct 18, 2009

### higherme

I mean the values 186.19 J/K/mol and 229.49 J/K/mol for methane and ethane given in the question. If i use the equation i said above, then these values would not be needed; so I was thinking there might be another way to do this...

"Note that the term represents an additional term to augment the sum of the unmixed entropies." - I don't get what you mean... which term are you referring to? the absolute entropies?

4. Oct 18, 2009

### Mapes

The total entropy of A and B, unmixed, is $S_A+S_B$.
The total entropy of A and B, mixed, is $S_A+S_B+\Delta S_\mathrm{mixing}$. Does this help?

5. Oct 18, 2009

### higherme

i don't really get why the entropies are summed if they are ummixed.

6. Oct 18, 2009

### Mapes

Entropy is an extensive quantity. If one container has entropy $S_A$ and the other has entropy $S_B$, then the total amount of entropy is $S_A+S_B$ before mixing.

7. Oct 18, 2009

thanks!