Freezing of bulk salt water

[k911nick]

I have a spherical container (15.5m diameter, ~2000m3 volume) that is filled with salt water at atmospheric pressure. Salinity is ~35g/litre.

At what temperature will the contents first show signs of freezing?

And.....

If ambient temperature is at the initial freezing point of the liquid, how long will it take to completely freeze the contents of the container?

Similarly, if ambient is 5 degC below initial freezing point?

This has stumped myself and a colleague for a couple of hours, so some help would be appreciated!!

Also, explanation of workings would be helpful.

Many thanks.

[swansont]

http://en.wikipedia.org/wiki/Freezing-point_depression

http://chemistry.about.com/cs/howthingswork/a/aa120703a.htm

 

This is a colligative property, which means it depends on how many particles you have put into solution. The constant for water is 1.86 K/mole, but you cannot answer the question because you have not specified what salt is being used. A mole of NaCl gives 2 moles of solute, but for CaCl2 or MgCl2, you get 3.

 

There are also a lot of variables to consider for how long it will take to freeze.

[John Cuthber]

This ones easy "If ambient temperature is at the initial freezing point of the liquid, how long will it take to completely freeze the contents of the container?"

It won't. as soon as some ice forms the salt concentrationin the rest of the water will rise. This will lower the FP. That means that the external temperature is no longer below the FP and no more ice will form.

 

Saying "salt" without specifying which is generally taken to mean NaCl. Also 35g/l is about the salt concentration in sea water and I doubt that's a coincidence.

 

A bit of googling shows that the freeziong point of sea water is about -2C

If the abmient temp is just 5C below this (ie about -7C) then the stuff will never freeze solid.

As before as the ice forms the salt will be concentrated in the remaining water. It will reduce the freezing point.

To get it to freeze solid you would need to cool it to at least -21C (the eutectic point of ice and salt).

 

How long it would take to freeze is a much more complicated problem and there's not enough information given to answer it.