Chemistry
posted by Kelsey on .
Consider the decomposition of a metal oxide to its elements, where M represents a generic metal.
M203(s)> 2M(s) + 3/2 O2(g)
info given for Gf(kJ/mol):
M203= 10.60
M(s)=0
O2(g)= 0
1.) what is the standard change in Gibbs energy for rxn as written in forward direction? (kJ/mol)
2.) What is the equilibrium constant (K) of this rxn, as written in forward direction at 298K?
3.) What is the equilibrium pressure of O2(g) over M(s) at 298K? (atm)
For 1.) I got 10.6 kJ/mol and this is correct
For 2.) I got K= 4.28 and it marked me wrong. Now I got an answer of .01387. Is this correct???
For 3.) I got PO2= 0.0016 atm and it marked me wrong......I don't know how it is wrong.
Could you please check #2 and #3 and tell me what I did wrong and what are the answers thanks.

I agree with your answer to #2.
For #3, if we do
0.01378 = pO2^{3/2}
and I evaluate that as 0.05748 atm but that has too many s.f. and I would round to 0.0575 atm. I tried 0.05748^1.5 and that = 0.01378. Check that carefully. 
Yes it is correct! Thanks! :) I see my mistake!

hello mon amie

Bonjour mon ami... Ca va? La chemie est un excellent science n'estce pas? Alors je vais partir maintenant, aie une bonne vie!

@DrBob222 , can you explain how exactly you evaluated to get that number because im confused howd you got there

I see what asker did wrong too, because she left it incomplete at first.
Since Kelsey found #1, 10.6, I'll leave it at that.
Part 2: (Gibbs energy)= RTln(K)
> 10.6 kJ/mol= (8.314 J/molxK)(298K)ln(K)
> 10.6 x 10^3 (J/mol) = (2477.6 J/mol)ln(K)
> Divide "RT" (which is 2477.6 J/mol) from both sides
> 4.278 = ln(K)
> e^(4.278) = K (because e and ln cancels out)
> 0.0139
From what I see...
Part 3: pO2 is (pO2)^(3/2) because of the 3/2 moles in M203(s)> 2M(s) + 3/2 O2(g). So...
>(pO2)= 0.0139
> [(pO2)^(3/2)]^(2/3)= (0.0139)^(2/3)
> pO2= 0.0578 
Sorry, for part three, it is not only because of 3/2 moles from O2(g). Part 3 is asking for "equilibrium pressure of O2(g) over M(s) at 298K? (atm)." Although it is 3/2 nevertheless, because M(s) also has 1 mole, it is due to O2(g)/M(s) so (3/2)/(1) =3/2. Please correct me if my thinking is wrong.

Oh, how embarrassing for the spam, but what I stated earlier, just above, was a work of negligence. Because I quickly looked at the problem, I mistook M203 for M(s). If only there was an editing button...I'll just leave my work up in the open, as I was trying to follow DrBob222's reasoning.

.11789 because K^1/2= PO2 .0139^1/2 gives you .11789 which was right for me