If I have liquid that contains 10% metanol, that freezes on -20C. How many etanol i must add?

I used f-la delT=Kf*b b=10,75
m=? where i use proc. of metanol and etanol. What graphic or f-la i use for this?
Thank you

To determine how much ethanol you need to add to the liquid containing 10% methanol to prevent it from freezing at -20°C, you can use the concept of freezing point depression. The freezing point depression is the difference between the freezing point of the pure solvent and the freezing point of the solution.

To calculate the freezing point depression, you can use the formula:

ΔT = Kf * m * i

Where:
- ΔT is the freezing point depression
- Kf is the cryoscopic constant (which is specific to the solvent)
- m is the molality of the solution (moles of solute per kilograms of solvent)
- i is the van 't Hoff factor, which represents the number of particles formed when the solute dissociates (in this case, i = 2 for both methanol and ethanol)

Given that the molality (m) of the solution is 10.75, you can substitute the values into the formula to find the freezing point depression (ΔT).

ΔT = Kf * m * i

However, you have not provided the cryoscopic constant (Kf) specific to the solvent you are using, which is necessary to calculate the freezing point depression.

Once you have determined the freezing point depression, you can calculate the new freezing point of the solution by subtracting the freezing point depression from the freezing point of the pure solvent. In this case, the freezing point of the pure solvent is -20°C.

New freezing point = -20°C - ΔT

To achieve a desired freezing point, you need to keep adding ethanol until you obtain the desired freezing point or until the methanol concentration reaches the minimum necessary to prevent freezing at that temperature. The exact amount of ethanol required will depend on the specific cryoscopic constant and the desired freezing point.