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

 

[Blueshift5]

Calculating the triple point of benzene requires using the Clausius-Clapeyron equation, which relates the temperature and pressure at which a substance can exist in different phases. In this case, we are interested in the triple point, which is the temperature and pressure at which benzene can exist simultaneously as a solid, liquid, and gas.

To use the Clausius-Clapeyron equation, we need to know the heat of fusion, vaporization, and sublimation for benzene, as well as its melting point and densities for the solid and liquid phases. From this information, we can construct a phase diagram and locate the triple point.

To calculate the triple point mathematically, we can set the heat of fusion, vaporization, and sublimation equal to each other and solve for the temperature and pressure at which this occurs. This will give us the coordinates of the triple point on the phase diagram.

It is important to note that the Clausius-Clapeyron equation is an approximation and may not give an exact value for the triple point. However, it is a useful tool for estimating the triple point based on experimental data.

In summary, to calculate the triple point of benzene, you will need to use the Clausius-Clapeyron equation and the given data on heat of fusion, vaporization, sublimation, melting point, and densities. Good luck!