If I know the freezing point of two solutions, and combine them into one solution, what is the resulting freezing point?

I am not knowledgeable in chemistry in any way, so I'm sorry if I seem stupid or something.


Suppose I have two solutions which I know the freezing point of, and I combine them into one solution. How do I find the resulting freezing point?


For example, let's say I have 4 parts water and 1 part maple syrup. Freezing point of water is $0 \ ^oC$, and freezing point of maple syrup is about $ -13\ ^oC$ according to a page I found from a google search.


Intuition tells me it would just be a weighted average of all the things you're combining, assuming that there is no chemical reaction when you mix them. So for my water plus maple example, it would be
$$
\left( \frac{4}{(4 + 1)} \* 0 \right)+ \left( \frac{1}{(4 + 1)} \* -13 \right) = \frac{-13}{5} = -2.6 \ ^oC
$$.


Is this intuition correct or is it more complex than that?




In many cases, the freezing point of a mixture is *lower* than the freezing point of each component.


For example, table salt, $\ce{NaCl}$, melts at ~800°C. Water, $\ce{H2O}$, melts at 0°C. A mixture of salt and water can have a [melting point as low as -20°C!](https://www.engineeringtoolbox.com/sodium-chloride-water-d_1187.html). This is called [freezing point depression](https://en.wikipedia.org/wiki/Freezing-point_depression).


Another example is the melting point of mixed metals, i.e., an alloy. Tin, Sn and lead, Pb, are used to make classic solder. The melting point of Sn is ~230°C, and of Pb, ~330°C, [but a 60% Sn/40% Pb alloy melts about 180°C.](https://byjus.com/chemistry/eutectic-point/)


It is difficult to make a general statement about the melting point of mixtures. In some case, there might not be a freezing point depression, but in most, the freezing point does *not* vary linearly with concentration.


Don't despair though -- there *are* properties of sugar/water solutions that *do* vary *comparatively* linearly with concentration, such as the density and [index of refraction](https://physics.stackexchange.com/questions/346635/refractive-index-as-a-function-of-concentration-of-sugar-solution-and-wavelength). Those making alcohol from sugary solutions may use refractometers to check the amount of sugar. *Cheers! Salud! L'chaim! Skol!*


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