How to I find the equilibrium temperature in this problem?

From Castellan's *Physical Chemistry*, chapter 12 [1, p. 276]:



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> **12.18** At $\pu{25 °C}$ we have for rhombic sulfur: $ΔG\_\mathrm{f}^\circ = 0,$ $ΔS^\circ = \pu{31.88 ± 0.17 J K-1 mol-1};$ and for monoclinic sulfur: $ΔG\_\mathrm{f}^\circ = \pu{63 J mol-1},$ $ΔS^\circ = \pu{32.55 ± 0.25 J K-1 mol-1}.$ Assuming that the entropies do not vary with temperature, sketch the value of $μ$ versus $T$ for the two forms of sulfur. From the data determine the equilibrium temperature for the transformation of rhombic sulfur to monoclinic sulfur. Compare this temperature with the experimental value, $\pu{95.4 °C},$ noting the uncertainties in the values of $ΔS^\circ.$
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I have plotted the graph of $μ$ vs $T$ successfully, but unable to find the equilibrium temperature. The answer is showing 119 °C and possible range from 83 °C to 277 °C.


How do I find it mathematically? I have used the equation $\mathrm d\mu = -S\,\mathrm dT + V\,\mathrm dp,$ but lot of the things are unknown. Can anyone solve it completely with calculation?


![my worked out graph](https://i.stack.imgur.com/RNKAa.jpg)


### References


1. Castellan, G. W. Physical Chemistry, 3rd ed.; Addison-Wesley: Reading, Mass, 1983. ISBN 978-0-201-10386-1.


