Animated Solution for Chemistry - Solutions: 1 molal aqueous solution of an electrolyte $A_2{B}_3$ is 60% ionised. The boiling point of the solution at 1 atm is ………… K (Rounded off to the nearest integer). [Given, $K_b$ for $(H_{2}O)=0.52{\text{ K kg mol}}^{-1}$]

The Power of Ions

Imagine you are standing in a kitchen, boiling a pot of pure water. You know it boils at exactly $373.15\text{ K}$ (or $100^{\circ }\text{C}$). But what happens when you toss in a handful of a mysterious electrolyte, say $A_2{B}_3$? The water suddenly needs more heat to boil! This phenomenon is known as Boiling Point Elevation, and it is a classic colligative property.

In this problem, we are given a $1\text{ molal}$ aqueous solution of $A_2{B}_3$. The catch? It is only $60\%$ ionized. Let's break down how this partial ionization affects the boiling point.

First, we need to understand the master equation for boiling point elevation:

Here, $\Delta T_b$ is the elevation in boiling point, $i$ is the van't Hoff factor, $K_b$ is the molal elevation constant ($0.52{\text{ K kg mol}}^{-1}$ for water), and $m$ is the molality ($1\text{ molal}$). The only missing piece of the puzzle is the van't Hoff factor, $i$.

To find $i$, we must look at how $A_2{B}_3$ behaves in water. When it dissolves, it dissociates into its constituent ions:

From one molecule of $A_2{B}_3$, we get $2$ ions of $A^{+3}$ and $3$ ions of $B^{-2}$. This means the total number of ions produced upon complete dissociation, $n$, is $2+3=5$.

However, the problem states that the electrolyte is only $60\%$ ionized. This means the degree of dissociation, $\alpha$, is $0.6$. We can relate $i$, $n$, and $\alpha$ using the formula:

Substituting our values:

So, our effective number of particles per formula unit in the solution is $3.4$.

Now that we have the van't Hoff factor, we can easily calculate the elevation in boiling point:

This means the boiling point of the water has increased by $1.768\text{ K}$. To find the final boiling point of the solution, $T_b$, we add this elevation to the boiling point of pure water:

The question asks us to round off to the nearest integer. Rounding $374.918$ gives us our final answer:

This problem beautifully illustrates how the microscopic behavior of ions directly impacts the macroscopic physical properties of a solution. Always remember to account for the degree of dissociation when dealing with weak or partially ionized electrolytes!