Question

What is the freezing point for the solution of 2,000 grams of water (essentially 2L) and 684 grams of sucrose (molecular mass = 342 gram per mole) dissolved in it?
a.) $ - {1.86^0}C$
b.) $ - {6.78^0}C$
c.) $ - {3.72^0}C$
d.) $ - {51^0}C$

Answer 1

Hint: In order to solve this question, we will use some concept like when any solute is dissolved or put in a solvent the overall freezing point of the solvent decreases. As in the above question we will find the new freezing point as we know the freezing point of water is 0 degree Celsius. We will begin with calculating the moles of solute and the proceed accordingly

Complete step by step solution: Formula used- the freezing point depression
$\Delta T = {K_f}m$
Where $\Delta T$ is freezing point depression
${K_f}$ is the molal freezing point depression constant
$m$ is the molality of the solute.
Given
Mass of sucrose = 684g
Molecular mass of sucrose = 342g
Mass of water = 2000g = 2kg
Number of moles of sucrose = $\dfrac{{mass}}{{molecular\,mass}} = \dfrac{{684}}{{342}} = 2\,moles$
As we know that the molality of a solution is given as
$m = \dfrac{{{\text{number of moles}}}}{{{\text{volume of water in kg}}}}$
Using the above formula to find the molality of sucrose solution
$
  m = \dfrac{{{\text{number of moles}}}}{{{\text{volume of water in kg}}}} \\
  m = \dfrac{2}{2} = 1 \\
$
Now, using the formula of depression in freezing point to determine the change in the freezing point after addition of solute
$
  \Delta T = {K_f}m \\
  \Delta T = 1.86 \times 1 \\
  \Delta T = {1.86^0}C \\
$
As we know the freezing point of the water is 0 degree Celsius.
Therefore the freezing point of the solution will be
$
   = 0 - 1.86 \\
   = - {1.86^0}C \\
$

Hence, the correct option is A.

Note: As we know that the freezing point is a phenomena that tells us about why addition of solute to a solvent changes the freezing point of the solution. Once a material begins freezing, due to the decreases in temperature, the molecules slow down and the intermolecular forces start taking over. Instead the molecules are arranged in a pattern, and thus become solid. For example when water is cooled to the freezing point, the molecules become slower and hydrogen bonds tend to "stick" more and gradually create a solid.