How Do Stoichiometric Coefficients Affect Gibbs Free Energy Calculations?

[Puchinita5]

Homework Statement

For the reaction N2(g) + 3H2(g) <---> 2NH3(g)

I am supposed to determine the equilibrium constant at 298K and 1 bar. We have been given a table that states that

for NH3(g):
$\Delta_{r}G^{\Theta}= -16.45 kJ/mol$

I know that
$\Delta_{r}G^{\Theta}= \Sigma v G^{\Theta}_{product} - \Sigma v G^{\Theta}_{reactant}$

where v is the stoichiometric coefficient.

But what is confusing me is that you could also write the equation as

1/2 N2(g) + (3/2)(g) <----> NH3(g)

so in the first case, the answer would be

(2*-16.45 kJ/mol) - ((1*0)+(3*0)) = -32.90 kJ/mol

But in the second case, the answer would be

(-16.45 kJ/mol) - (1/2*0 + 3/2 *0) = -16.45 kJ/mol

Since both equations should be valid, what answer is correct? I don't understand which one I should choose because they both look like the should be right.

 

[Ygggdrasil]

In the two cases, the expression for the equilibrium constant will be different. In the first case K = [NH3]^2/[N2]

^3 whereas in the second case K = [NH3]/[N2]^(1/2)

^(3/2). This is why you always need to include a balanced reaction along with any equilibrium constant you provide.

 

[jtruth914]

Hey, I had the same concern. They are both right; it depends on the stoichiometry. The professor would have to specify which one he is looking for like he did last time.

 

[Puchinita5]

Thanks guys! Did he specify last time? I must not have understood him. This was really confusing me, good to know that both are right! I feel better now. :)