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What mass of sugar C12H22O11 (M0=342) must be dissolved in 4.0kgofH2O to yield a solution that will freeze at 3.720C?
(Take Kf=1.860Cm1).

Answer
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Hint:
As we know that, the colligative properties depend upon the number of solute particles. There are four types of colligative properties in which by one property, the above question can be solved.

Complete step by step solution
It is known that as the sugar (solute) is dissolved in water it occupies the position of water and now there is a small number of molecules of water so the freezing point becomes low and that is known by depression in freezing point.

For depression in freezing point of a solvent, we have a relationship between the depression in the freezing point and molality of the solution that can be written as follows:
ΔTf=Kfm

Here, ΔTf is represented as the depression in the freezing point of the solvent, Kf is the molal depression constant for the given solvent and m is the molality of the solution.
We are given as
Kf=1.860Cm1=274.86Km1
M0=342
M2=4kg
ΔTf=3.720C=269.28K
Now, first of all we will calculate the molality by the above equation.
269.28K=274.86Km1×mm=269.28K274.86Km1=0.98m
Now, we know that molarity is defined as the number of solute particles dissolved in per kilogram of solvent. The solvent is water and suppose w0 is weight of sugar which is our question.
molality(m)=(w0/M0)solvent(g)×1000(ii)
Now, putting the values in the above equation, we get,
w0=4kg×0.98m×0.342kgmole=1.34kg

Therefore, the mass of the sugar is 1.34kg.

Note:

We can also calculate the other values by using the above formula such as depression in freezing point, weight of solvent etc.