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# The Van’t Hoff factor, i for a $0.2$ molar aqueous solutions of urea isA) $0.2$B) $0.1$C) $1.2$D) $1.0$

Last updated date: 24th Mar 2023
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Hint: We need to know that the Van’t Hoff is one of the important factors in the solution. The association or dissociation of the solute particle in the solution was predicted by the increases or decreases calculated molar mass of the colligative property. The symbol of Van’t Hoff factor is i. The Van’t Hoff factor makes a relationship between observed property and actual property of the solution. The value of I is less than one means observed molar mass is greater than actual molar mass. Otherwise, the value of I is lesser than one means observed molar mass is lesser than actual molar mass.
Formula used:
The Van’t Hoff factor is defined as the ratio of the observed molar mass to the actual molar mass of the solution.
${\text{i = }}\dfrac{{{\text{observed molar mass of the solution}}}}{{{\text{actualmolarmassofthesoltion}}}}$

The Van’t Hoff factor is,
${\text{i = }}\dfrac{{{\text{observed colligative property}}}}{{{\text{actual colligative property}}}}$
The Van’t Hoff factor the given condition,
The actual molar mass of urea in aqueous solution is $0.2$.
The observed molar mass of urea in aqueous solution is $0.2$.
The Van’t Hoff factor is
${\text{i = }}\dfrac{{{\text{observed colligative property}}}}{{{\text{actual colligative property}}}}$
Now we can substitute the known values get,
${\text{i = }}\dfrac{{0.2}}{{{\text{0}}{\text{.2}}}}$
On simplification we get,
$= 1.0$
The Van’t Hoff factor, i for a $0.2$ molar aqueous solutions of urea is $1.0$

Hence, option D is correct.

Note:
We have to know that the nature of the solute and the solvent affect the properties of the solution. These affecting property of the solution by addition of solute in the solution is known as colligative property. There are four major colligative properties for ideal solution. There are relative lowering vapour pressures of the solution after addition of solute, the elevation of boiling point of the solution after addition of the solute, the depression of freezing point of the solution after addition of solute and the osmotic pressure of the solution. The above mentioned properties are caused due to the addition of solute in solution.