# Freezing Point Depression of an Aqueous Solution

The freezing point of a one molal
solution of a non-volatile solute decreases by a constant amount for a
given solid. So basically freezing point depression
deals with a solute and a solvent. And by adding the solute to the solvent the
solvents freezing point decreases So if you take water for example, it freezes at
zero point zero degrees Celsius. So that water as a solvent because you put
things into water for them to dissolve in it like sugar is a solute which goes
into water and dissolve. So waters the solvent it’s what makes other things
dissolve. Now if you add a solute to the water it has the potential to make the
freezing point depress or go lower. And so then the freezing point of water will
be negative something. So that’s what we’re looking at here we’re adding sodium chloride to the water, and the sodium chloride is a solute. And so the
sodium chloride the solute and the solvent water forms a solution and so
now we’re wondering what the freezing point is going to be because the sodium
chloride is going to cause freezing point depression. And we call this an aqueous solution because there’s water involved so the solution is going to be liquid. All right so the equation we use this this one right here. So it obviously has two parts. So the first part is the freezing point depression. And then the second part is made of KF which is the molal freezing point constant. And then we have M which is molality. So now what we need to do is go ahead and start looking at what we already have and then plugging those things into the equation. So we know that the molarity of sodium chloride is 1.5
molal, the KF for water is negative one point eight six degrees Celsius over molal and the freezing point of water is zero point zero degrees Celsius. So we can go ahead and begin to plug this in to our equations. So what we’re looking
for here is the freezing point of the solution. Basically after everything is combined the sodium chloride and the water. We’re wondering what the final freezing point is going to be. So first, though we need to know just what the freezing point of sodium chloride is and then we’ll go from there. So we can go ahead and plug in KF which is negative one point eight six degrees Celsius over molal. Then we can multiply that by 1.5m. Before we calculate
anything we already know that m and m we’re going to cross out because m is in
the denominator here and in the numerator here. So those can cross out. And then we know what the freezing point of water is but we don’t we’re not going
to use that yet we’re gonna go ahead and calculate this I’ll save you that step. So that answer is going to be negative two point seven nine degrees Celsius because M and M are crossing out So we’re left with degrees Celsius. So now we’re going to take the freezing point of water which is zero point zero degrees Celsius, and add it to negative two point seven nine degrees Celsius, which remember is the freezing point depression. In other words that’s how much sodium chloride is going to cause the freezing point to depress. So we add
those together. And so this equation or the answer to this equation is pretty
obvious but we still need to work through it. So this is the answer to the
equation this is the freezing point of the solution in water because remember
we were looking at this right here what is the freezing point of a one point
five molal sodium chloride solution in water. And the freezing point is negative
two point seven nine degrees Celsius because this negative two point seven
nine degrees Celsius right here is the freezing point depression. And so it just so happens that since we’re starting with the freezing point of zero degrees that this the the freezing point depression and the freezing point of the
whole solution are the same number. 