Question

Which of the following will have the highest freezing point at one atmosphere?
A: \[0.1M\] \[NaCl\] solution
B: \[0.1M\] sugar solution
C: \[0.1M\] \[BaC{l_2}\] solution
D: \[0.1M\] \[FeC{l_3}\]solution

Answer 1

Hint: Freezing point refers to the temperature at which liquid and solid form of the same material/substance are said to be in equilibrium and possess the similar vapour pressure. Freezing point depression is the lowering of freezing point of the solvent with the addition of solute to a solvent.

Complete step by step answer:
The lowering of freezing point or freezing point depression is a colligative property which depends upon the number of the solute particles. As the number of particles increases, the freezing point decreases. When salt is added to water, this indicates that dissolved foreign particles have been introduced into the water. Freezing point of the water keeps on lowering as more and more particles are appended till the point when salt stops getting dissolved. This is the reason that salt is employed for melting the ice and snow and also keeps them from re-freezing. Actually, the principle on which salt works is lowering of the melting or freezing point of the water. This effect is known as depression in freezing point. A compound which yields more ions into an aqueous solution lowers the freezing point of that solution more. Now, let us look at each of the solution given in the options:
The concentration of each solution is the same i.e.\[0.1M\]. Now, we will check the dissociation of each of these ionic compounds in aqueous solution which is depicted below in the equations:
$
  NaCl \to N{a^ + } + C{l^ - } \\
  Sugar \to Sugar(aq) \\
  BaC{l_2} \to B{a^{2 + }} + 2C{l^ - } \\
  FeC{l_3} \to F{e^{3 + }} + 3C{l^ - } \\
$
It is clear from the above chemical equations that \[NaCl\] yields two ions (i.e. one sodium and one chloride ion), \[BaC{l_2}\] yields three ions (i.e. one barium and two chloride ions),\[FeC{l_3}\] yields four ions (i.e. one iron and three chloride ions) and sugar is not dissociated into ions. As \[FeC{l_3}\] solution comprises the maximum number of solute particles, its freezing point will be the lowest and sugar solution comprises the minimum number of solute particles so its freezing point will be the highest.

So, the correct answer is Option B.

Note: Depression in freezing point is directly proportional to the molality of the added solute. The formula used is:
$\Delta {T_f} = i \times {K_f} \times m$
Where, $\Delta {K_f} = $ depression in freezing point
$i = $ Van’t Hoff factor
${K_f} = $ cryoscopic constant
 $m = $molality