Standard Gibbs of a reaction

[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. :)

 

[DeeNos]

The correct answer will depend on the convention being used for the standard Gibbs free energy of formation. In the first case, the equation is written using the convention where the standard Gibbs free energy of formation of elements in their standard state is taken to be zero. In this case, the answer of -32.90 kJ/mol is correct.

In the second case, the equation is written using the convention where the standard Gibbs free energy of formation of elements in their most stable form at the specified temperature and pressure is taken to be zero. In this case, the answer of -16.45 kJ/mol is correct.

Both conventions are commonly used and either answer is acceptable as long as the correct convention is specified. It is important to be consistent in using the same convention throughout your calculations.