Question

A decimolar solution of $K_4\left[Fe{\left(CN\right)}_6\right]$ is $50\%$ dissociated at $300$ K. Calculate the osmotic pressure of solution.

(R= 0.0821 litre atm/K mol)

• A. $2.3$ atm
• B. $7.39$ atm
• C. $3.25$ atm
• D. None of these

Answer 1

The correct option is B $7.39$ atm

When the complex is not dissociated we can use Van't Haff equation to calculate normal osmotic pressure,

$p=C\times R\times T$

$⟹P=0.1\times 0.0821\times 300=2.462atm$

The given complex dissociates and it dissociates as follows,

$K_4\left[Fe\right(CN{)}_6]\to 4K^{+}+[Fe(CN{)}_6{]}^{4-}$

$(1-a)$ $4a$ $a$

Where a is degree of dissociation of the complex assuming initially 1 mole was present.

Moles after dissociation of the complex$=1-a+4a+a=1+4a$,

Since osmotic pressure is directly proportional to number of moles,

$\frac{p_{observed}}{p_{normal}}en=\frac{1+4a}{1}$

Given dissociation is 50% and hence a=0.5

So,

$\frac{p}{2.462}=1+4\times 0.5$

$⟹p=7.386atm$