[ropy]

what will be the entropy of mixing if two same compounds of same concentrations are mixed ?
say the compound is N2 at 1 atm 300 K.

[Babcock_Hall]

You must show your attempt to answer, according to forum rules.

[ropy]

ok. If we take formula S=-nRΣxlnx , then as nitrogen is single compound , mole fraction x=1 and S should be zero. But due to mixing isn't the randomness increases ? is there any other formula I should use ?

[curiouscat]

It's a tricky question. Have you done Stat. Mech. yet?

[Babcock_Hall]

I would expect that if you mixed nitrogen and argon gases, for example, that the entropy would increase.  I am not so sure that it would when you mix two identical substances.  Proving it, one way or another, is above my pay grade.

[curiouscat]

I would expect that if you mixed nitrogen and argon gases, for example, that the entropy would increase.  I am not so sure that it would when you mix two identical substances.  Proving it, one way or another, is above my pay grade.

I'll try:

If the two substances are identical and with each entropy S the entropy of the mixture has to be 2×S since entropy is an extensive quantity and the final mix is at the same state of T, P etc.

e.g. If 2 kgs of stuff have to have twice the entropy of 1 kg of stuff assuming the only difference is quantity.

Does that make sense?

The catch lies in reconciling this with:

But due to mixing isn't the randomness increases ?

This I feel rests upon whether or not you consider molecules as distinguishable or indistinguishable. Now that is also above my pay grade. 

[Jorriss]

I would expect that if you mixed nitrogen and argon gases, for example, that the entropy would increase.  I am not so sure that it would when you mix two identical substances.  Proving it, one way or another, is above my pay grade.

Check out the Gibbs Paradox (it's not really a paradox though).

[ropy]

It's a tricky question. Have you done Stat. Mech. yet?

yep. I did .

[ropy]

check out the Gibbs Paradox (it's not really a paradox though).

thank u ! that was really helpful .

[adianadiadi]

Since molecules are same and the concentrations too, I expect there is not change in entropy per unit mass.