Calculating the triple point of benzene

[Physter]

Homework Statement

We're given various temperature and pressure values for benzene as well as its melting point and densities for when it's a solid and when it's a liquid. We're asked to construct a phase diagram based on the given data and locate the triple point - graphically and mathematically for an additional bonus mark.

Homework Equations

N/A.

The Attempt at a Solution

I've made my phase diagram and it looks quite dandy but the only thing I don't know how to do is calculate the triple point mathematically.

I'm inclined to setting my values of heat of fusion, vaporization and sublimation equal to each other but I'm unsure as to which equation I use. Would it be the http://upload.wikimedia.org/math/2/5/a/25af58f66f466bb2a5abc84306631456.png" or is there something else more suitable? Or is my way of approaching the problem not the right one at all?

Any pointers would be greatly appreciated. Thanks.

 

[eli64]

I think you have a good plan but I think you only need 2 equations (so choose 2 of the heats) since you want to know 2 variables P and T