The "Split and Mix" Solution Method
What is the "split and mix" solution method ?
This is a technique to grow large crystals step by step using the slowly cooling method. The goal is to get a warm solution which is almost perfectly saturated at this temperature. In this solution you can put smaller crystals or specimen to grow them bigger.
Lets give an example :
Take 1000 gms of a cold saturated solution of potassium alum, lets say its temperature is 20 C°, split in two portions of 500 gms each. Take one portion of 500 gms add some extra amount of potassium alum and heat it up until it boils (that is about 100 C°) then mix the cold and the hot solution to receive a warm solution which is exactly saturated at this resulting temperature.
There are two problems to solve :
1. What will be the resulting temperature ?
2. How much alum needs to be added to the boiling hot solution that the resulting solution is exactly saturated ?
problem is easy to solve if you use some simplifications.
Just multiply the mass of the cold solution (mc)
with its temperature (Tc) and the mass of the
hot solution (mh) with its temperature (Th),
add the two products and divide by the summ of the two
masses combined and you get the temperature of the mixed
In our example that will be with :
Okay, simplification one is of course that the
total mass of our hot solution will be more than 500 gms
as we are adding some extra amount of alum. This will
result in a slightly higher temperature of the resulting
Now we have a good clue what the temperature of our mixed solution will be.
Step two is to calculate the amount of alum which has to be added to the boiling hot solution. We need to know the saturation concentration of the cold and of the mixed solution as the difference between them has to be added.
The saturation concentration or the solubility of a substance is given in a solubility table at different temperatures in gms per 100 gms of water. Here is the solubility table of potassium alum :
of potassium alum in water
As you can see the saturation concentration
So the difference (that what you have to add) is 46.5 gms/100gms of water.
water is in the 1000 gms of cold solution we have been
starting with ?
so the 1000 gms of total starting solution contain :
in your boiling hot solution part of 500 gms you have to disolve an extra mount of :
So your complete recipe is :
Take 1000 gms of cold
saturated solution of potassium alum split in two
portions of 500 gms each.
Oops ! One last check. Are
you shure you will be able to disolve this additional
415.17 gms of alum in the 500 gms of cold saturated
so with the 415.17 gms of alum added you result will be a concentration of
Well as the solubility of alum in water at 80 C° is already 195 gms/100 gms of water that should be no problem !
However you might not hit
the exact saturation concentration and temperature.
If you receive an
undersaturated solution by this mehod your crystals may
For better results you always have to adjust the add-on amount. Don´t stick to the calculated value it can only be a good estimate.
Using the slowly cooling method to grow specimens the add-on amount should be in the range of 20 - 60 gms per 100 gms of water. For single crystals you better work with an add-on amount of 5 - 30 gms per 100 gms of water.
However keep in mind, the
only thing you can vary is the ratio of how to split cold
and hot solution.
If for example you choose
to split into a large amount of cold and a small amount
of hot solution, your mixed solution temperature will be
lower, so also the saturation concentration and ergo the
add-on amount needed.
Now this example is a
little bit constructed to keep it simple. But what
happens if the temperature of your cold solution is lets
say 17 C° or 24 C°?
(solubility tables are not always perfectly exact...)
You can also estimate inbetween solubility values from a solubility diagramm or chart.
With Excel I got this
To calculate an inbetween solubility
value you need a temperature and solubility value below
the temperature in question (which we can call Tx).
To give an example we want to calculate the solubility of potassium alum at 53 C°. As lower border values we choose 50 C° with a solubility of 36.8 g/100g and as higher border values 60 C° with a solubility of 58.5 g/100g.
To much formulas ? Did not get it ? To much calculating back and for ?
There is hope !
This whole calculations can be done with the java-scripted "split and mix" solution calculator !
Just click on the button above.