Question

In comparison to a $0.01M$ solution of glucose, the depression in freezing point of a $0.01M$ $MgC{l_2}$ solution is?
A) The same.
B) About twice.
C) About three times.
D) About six times.

Answer 1

We all know depression in melting point is directly associated with van't Hoff factor $\left( i \right)$ consistent with which greater the worth of van't Hoff factor greater are going to be Depression in melting point.

Complete step by step answer:
We can calculate the melting point depression using the formula,
$\Delta Tf = i \times Kf \times molality$
Where , the melting point depression is denoted as $\Delta Tf$, $Kf$ is that the melting point depression constant, and that $i$ is that the van ‘t Hoff factor.
The van't Hoff factor $\left( i \right)$ is the total number of ions after dissociation or association or the total number of ions before dissociation or association.
Given,
The molality of glucose is $0.01M$.
The molality of $MgC{l_2}$ is$0.01M$.
${i_{glu\cos e}} = 1$
$\Delta T{f_{glu\cos e}} = 1 \times Kf \times 0.01$
The dissociation equation of magnesium chloride is,
$MgC{l_2}\xrightarrow{{}}M{g^{2 + }} + 2C{l^ - }$
$i = 3$
$\Delta T{f_{MgC{l_2}}} = 3 \times Kf \times 0.01$
$\Delta T{f_{MgC{l_2}}} = 3 \times \Delta T{f_{glu\cos e}}$
For $MgC{l_2}$ the van't Hoff factor $\left( i \right)$ is three as it dissociates into three ions and for glucose the van't Hoff factor $\left( i \right)$is one as it does not undergo any association or dissociation. Thus, greater the van't Hoff factor $\left( i \right)$ greater will be depression. So, depression in the freezing point of $MgC{l_2}$ is three times.

Therefore, the option C is correct.

Note:
As we know that the freezing point depression is the phenomena that describes why adding a solute to a solvent leads to the lowering of the melting point of the solvent. When a substance starts to freeze, the molecules hamper thanks to the decreases in temperature, and therefore the intermolecular forces start to require over. The molecules will then arrange themselves during a pattern, and thus become a solid. For instance, as water is cooled to the melting point, its molecules become slower and hydrogen bonds begin to stick more, eventually creating a solid. If salt is added to the water, the $N{a^ + }$ and $C{l^-}$ ions attract to the water molecules and interfere with the formation of the massive network solid referred to as ice. So as to realize a solid, the answer must be cooled to a good lower temperature.