What percentage of N2O4 decomposes at 370K ?

[RJLiberator]

Homework Statement

Dinitrogen tetroxide decomposes to nitrogen dioxide:
N2O4(g)→2NO2(g) ΔHorxn=55.3kJ
At 298 K, a reaction vessel initially contains 0.100 atm of N2O4. When equilibrium is reached, 58% of the N2O4 has decomposed to NO2.

What percentage of N2O4 decomposes at 370K ? Assume that the initial pressure of N2O4 is the same (0.100 atm).

How is this problem done?
We know:
Delta H of reaction = 55.3 kJ
Equilibrium means Delta G = 0 AT 298 K and 58% decomposition.

We need to find what percentage of N2O4 decomposes at 370K.

I'm not entirely sure what equations I should be using. We are talking about Gibbs Free Energy. This is a mast. chem. problem and the last of the 40-50 I have left.

If someone could guide me towards a correct equation, I can work this out.

 

[Chestermiller]

You need to first determine the equilibrium constant at 370 K. Do you know how to do that from the data provided? If you knew the equilibrium constant at 370 K, how would you then proceed to solve the problem?

Chet