Calculating the Freezing Point of Mercury Under Pressure

[winterwind]

Homework Statement

The enthalpy of fusion of mercury is 2.292 kJ/mol, and its normal freezing point is 234.3 K with a change in molar volume of +0.517 cm/mol on melting. At what temperature will the bottom of a column of mercury (density 13.6 g /cm³) of height 10.0 m be expected to freeze?

Homework Equations

p = \rhogh

p = p* + [(\Delta_fusH)/(T*\Delta_fusV)]/(T - T*)

The Attempt at a Solution

I calculated the pressure in the column of mercury using the first equation provided above. I then solved the second equation for T, plugged in the given values, with p*= 101 kPa and T* = 234.3 K (the normal pressure and boiling point).

I get an answer of 234.2 K, which doesn't make sense, since when you raise the pressure, shouldn't you get a higher temperature freezing/melting point? I would expect it changes more than 0.1 K anyways.

Am I using the correct equation?

Thanks!

 

[Bystander]

I get an answer of 234.2 K, which doesn't make sense, since when you raise the pressure, shouldn't you get a higher temperature freezing/melting point?

What's the slope of the m.p. line? Positive? Or, negative?

I would expect it changes more than 0.1 K anyways.

Water changes 0.01 K/atm, and has which slope?

Am I using the correct equation?

Yes.