Chemistry - Change of freezing point

[ChemistryJack]

Homework Statement

The enthalpy of fusion of mercury is 2.292kJ/mol and its normal freezing point s 234.3K with a change in molar volume of +0.517cm^3 /mol on melting. At what temperature will the bottom of a column of mercury (density 13.6 g/cm^3) of height 10.0m be expected to freeze.

Homework Equations

The Attempt at a Solution

I'm really not sure how to go about this. I though I could work out the Potential energy, using P = mgh. Then maybe take this off the enthalpy of fusion. I don't want the answer, but some though-provoking advice would be much appreciated. Thanks!

 

[Borek]

Phase transition, pressure, temperature, volume change and enthalpy - that cries for a specific equation (relation). It is most often used for boiling points, but it works for every transition.

 

[ChemistryJack]

Clausius-Clapeyron?

 

[Borek]

That's what I would try.

 

[DeeNos]

I would approach this problem by first considering the basic concepts of enthalpy and molar volume. Enthalpy is a measure of the total energy of a system, while molar volume is the volume occupied by one mole of a substance. In this case, we are dealing with the enthalpy of fusion, which is the energy required to change a substance from a solid to a liquid state.

Next, I would use the given values of the enthalpy of fusion and the change in molar volume to calculate the change in energy per mole of mercury. This can be done by multiplying the molar volume change by the pressure and then dividing by the number of moles. This will give us the energy required to melt one mole of mercury.

Then, I would use this value to calculate the amount of energy required to melt a column of mercury with a height of 10.0m. This can be done by multiplying the energy per mole by the number of moles in the column, which can be calculated using the density of mercury and its molar mass.

Once we have the total energy required to melt the column of mercury, we can use this value to determine the temperature at which the mercury will freeze. This can be done by setting the energy required to melt the column equal to the enthalpy of fusion and solving for the temperature.

Overall, the key to solving this problem is to use the given information and basic principles of chemistry to calculate the energy required to melt the column of mercury and then use this value to determine the freezing temperature. I hope this helps!