Question

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

• A. 6.2 atm
• B. 7.4 atm
• C. 5.4 atm
• D. 7.9 atm

Answer 1

Answer: (B)

7.4 atm

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

One molecule of $K_4\left[Fe\right(CN{)}_6]$ dissociates to give 5 ions.

Since $K_4\left[Fe\right(CN{)}_6]$ is 50% dissociated, if we start with 2 molecules of $K_4\left[Fe\right(CN{)}_6]$, one molecule of $K_4\left[Fe\right(CN{)}_6]$ will dissociate to provide 5 ions and one molecule of $K_4\left[Fe\right(CN{)}_6]$ remains undissociated. Thus, from two molecules of $K_4\left[Fe\right(CN{)}_6]$, we get 6 particles.

The Van't Hoff's factor $i=\frac{\text{actual number of particles}}{\text{expected number of particles}}=\frac{6}{2}=3$

The osmotic pressure $\pi =iCRT$

$\pi =3\times 0.1mol/L\times 0.08206Latm/mol/K\times 300K$

$\pi =7.4atm$

Note: Decimolar means 0.1 mol/L