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The vapor pressure of zinc varies with temperature as

$$\log P(\pu{mm Hg}) = -6850/T - 0.755\log T + 11.24 \label{eqn:1}\tag{1}$$

and that of liquid zinc as

$$\log P(\pu{mm Hg}) = -6620/T - 1.255\log T + 12.34 \label{eqn:2}\tag{2}$$

Calculate:

a) boiling point of $\ce{Zn};$
b) triple point;
c) heat of evaporation at boiling point;
d) heat of fusion;
e) the difference in $C_p$ of solid and liquid zinc.

I have found out the boiling point by substituting pressure as $\pu{760 mm Hg}$ on first equation \eqref{eqn:1}, from here boiling point $T$ can be found out as $\pu{1181 K}.$

I have also found out triple point by equating the two equations because at triple point both the pressure of the two phases must be equal.

I have also found out heat of vaporization by using the equation

$$\frac{\mathrm d\ln p}{\mathrm dT} = \frac{H_\mathrm{vap}}{RT^2}.$$

But to find the heat of fusion I must know the heat of sublimation, but the heat of sublimation is not provided here. Is there any other way to know the heat of fusion (melting)?

Also, how to find the $C_p$ of both the phases and the difference of $C_p?$

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Use the equation for the vapor pressure of the solid to get the heat of sublimation. The heat capacity of the vapor minus the heat capacity of the liquid is equal to the derivative of the heat of vaporization with respect to temperature. The heat capacity of the vapor minus the heat capacity of the solid is equal to the derivative of the heat of sublimation with respect to temperature.

ADDENDUM

$$\Delta H_{sublimation}=RT^2\frac{d\ln{P}}{dT}=(\ln{10})RT^2\frac{d\log{P}}{dT}$$where log P is given by Eqn. 1.

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  • $\begingroup$ But here vapor pressure of solid zinc is not provided, no equation for solid Zinc, only for liquid zinc there is an equation, heat capacity of vapor and liquid is also not provided, heat capacity of solid zinc is also not given , all are unknown , impossible to find out $\endgroup$ – Sayantan Bhanja Sep 23 at 0:05
  • $\begingroup$ When they used the words "The vapor pressure of zinc varies...," what phase did you think they meant? $\endgroup$ – Chet Miller Sep 23 at 0:09
  • $\begingroup$ If it is of solid then , we must know the sublimation Temperature and Pressure , only then we can find heat of sublimation ,heat capacity of vapor is not given, heat capacity of solid and liquid zinc is also not given, $\endgroup$ – Sayantan Bhanja Sep 23 at 0:15
  • $\begingroup$ Read my answer again. $\endgroup$ – Chet Miller Sep 23 at 0:21
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    $\begingroup$ @BuckThorn. It follows from Hess' law that, at the triple point, the heat of fusion is equal to the heat of vaporization minus the heat of sublimation. $\endgroup$ – Chet Miller Sep 23 at 12:32

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