Question

Which of the following aqueous solutions has the highest boiling point?
A.$$\text{0}\text{.1M KN}{\text{O}}_{\text{3}}$$
B.$$\text{0}\text{.1M N}{\text{a}}_3\text{P}{\text{O}}_4$$
C.$$\text{0}\text{.1M BaC}{\text{l}}_2$$
D.$$\text{0}\text{.1M }{\text{K}}_2\text{S}{\text{O}}_4$$

Answer 1

Hint: This question is actually from colligative property. We need to check the van’t Hoff factor and then we will calculate the colligative property known as elevation in boiling point. From this relation we can compare the boiling point of all of them. All the ionic salts dissociate in aqueous solution. So we need to consider the total number of ions after dissociation for calculation of Van’t Hoff factor.

Complete step by step answer:
Colligative properties are those properties which only depend upon the no. of moles of solute present in the solution and not on the nature of solute. Elevation in boiling point is one such colligative property. So this means that it will also depend on the number of moles.
In simple terms, elevation in boiling point $$\alpha$$ number of moles of solute present.
But as we see that all the options given to us are ionic solutes and we know ionic solutes dissociate into their respective ions in solution phase. So the number of moles they will give will vary according to their atomicity. For this, introduce a term $$i$$ that is the Van't Hoff factor. It is the ratio of no. of moles of moles of solute actually observed to the no. of moles of solute calculated.
Now we will see the dissociation of each of the compound given to us:
$$\text{KN}{\text{O}}_{\text{3}}\to {\text{K}}^{\text{ + }}{\text{ + NO}}_{\text{3}}^{\text{ - }}$$
Total number of ions given is 2, but initially we assumed to be 1.
Van’t Hoff factor will be : $${\displaystyle \frac{2}{1}}=2$$
$$\text{N}{\text{a}}_3\text{P}{\text{O}}_4\to 3\text{N}{\text{a}}^{\text{ + }}{\text{ + PO}}_4^{3-}$$
Total number of ions given is 4, but initially we assumed to be 1.
Van’t Hoff factor will be : $${\displaystyle \frac{4}{1}}=4$$
$$\text{ BaC}{\text{l}}_2\to \text{B}{\text{a}}^{\text{2 + }}\text{ + 2C}{\text{l}}^{-}$$
Total number of ions given is 3, but initially we assumed to be 1.
Van’t Hoff factor will be : $${\displaystyle \frac{3}{1}}=3$$
$${\text{K}}_2\text{S}{\text{O}}_4\to 2{\text{K}}^{\text{ + }}{\text{ + SO}}_4^{2-}$$
Total number of ions given is 3, but initially we assumed to be 1.
Van’t Hoff factor will be : $${\displaystyle \frac{3}{1}}=3$$
The order of boiling point will be the same as the order of elevation in boiling point. So . From the above equations, equation 2 has the highest value of . Hence it has the highest elevation in boiling point and boiling point.

So the correct option is B.

Note:
There are various applications of boiling point such as, it is used in the calculation of molar mass of the compound. Elevation in boiling point plays an integral role in sugar refining too. We can see a real life example of elevation in boiling point. When you boil normal water and a solution of salt in water, the latter one will take more time in boiling. Due to elevation in boiling point the boiling point of salt solution increases.