Animated Solution for Chemistry - Solutions: $K_{2}Hg{I}_4$ is $40\%$ ionised in aqueous solution. The value of its van't Hoff factor ($i$) is

Imagine you are standing in a chemistry lab, holding a beaker of pure water. You drop a pinch of potassium tetraiodomercurate, mathematically written as $K_2[Hg{I}_4]$, into the water.

What happens next is a beautiful microscopic dance.

Unlike simple salts like sodium chloride that completely shatter into individual atoms, coordination complexes have a secret. They possess a strong inner core that refuses to break apart.

When $K_2[Hg{I}_4]$ enters the aqueous arena, the water molecules surround it and pull away the loosely bound potassium ions.

However, the central mercury atom holds onto its four iodine partners with an iron grip. The coordinate covalent bonds are simply too strong for the water molecules to tear apart.

This partial shattering leads us to our first crucial realization. The dissociation reaction looks like this:

Look closely at the products. From a single parent molecule, we don't get five individual ions. We get exactly three distinct entities.

There are two potassium ions ($K^{+}$) and one intact complex ion ($[Hg{I}_4{]}^{2-}$).

Therefore, the number of particles produced per molecule, denoted by $n$, is exactly $3$.

Now, here is where the plot thickens. The question throws a curveball: the complex is only $40\%$ ionized.

What does this mean physically? It means that if you threw 100 molecules of $K_2[Hg{I}_4]$ into the water, only 40 of them would actually undergo the dissociation dance we just described.

The remaining 60 molecules would stubbornly stay completely intact as neutral $K_2[Hg{I}_4]$ units.

In chemistry, we represent this fraction using the degree of dissociation, denoted by the Greek letter $\alpha$.

Since $40\%$ of the molecules dissociate, our $\alpha$ is simply $0.4$.

To understand the overall effect of this partial dissociation on the properties of the solution, we need a single, powerful number. This is the van't Hoff factor, denoted by $i$.

The van't Hoff factor tells us the average number of particles floating in the solution for every single molecule we originally tossed in.

We can connect our degree of dissociation ($\alpha$) and the number of ions ($n$) to the van't Hoff factor using a brilliant mathematical bridge:

I know this equation might look a bit abstract, but let's take a breath and see how beautifully it works.

We have all our puzzle pieces ready. We know that $n=3$ and $\alpha =0.4$.

Let's carefully substitute these values into our master equation.

First, we solve the parenthesis. Three minus one gives us two.

Next, we multiply two by zero point four, which yields zero point eight.

Finally, adding this to one gives us our ultimate answer.

Did you get the feel of it? Our final van't Hoff factor is $1.8$.

This is a profound result. It tells us that, on average, every molecule of $K_2[Hg{I}_4]$ we added to the water effectively behaves like $1.8$ particles.

It's not $1$ particle (which would mean no dissociation), and it's not $3$ particles (which would mean $100\%$ dissociation). It sits perfectly in between, reflecting the reality of the $40\%$ ionization.

This single number, $1.8$, will now dictate how the solution behaves—how much its freezing point drops, or how high its boiling point rises. You have successfully decoded the microscopic reality of the solution!