Question

A millimolar solution of potassium ferricyanide is 70%, dissolved at $27{}^\circ C$ . Find out the osmotic pressure of the solution:
(A) 0.076 atm
(B) 2.76 atm
(C) 3.67 atm
(D) 9.67 atm

Answer 1

Hint: The dissociation reaction can help us solve the given question properly. The moles of the compounds present in the solution will contribute to the osmotic pressure.

Complete step-by-step answer:
Let us see the concept of osmotic pressure;
Osmotic pressure-
The minimum pressure which tends to be present on the solution side to avoid the inward flow of pure solvent across the semipermeable membrane.
This is expressed as,
\[\Pi =cRT\]
where,
$\Pi $ = osmotic pressure
c = molar concentration of solute
R = ideal gas constant
T = temperature (in kelvin)
Now, let us look into our given illustration;
Given that-
Potassium ferricyanide is dissociated as,
${{K}_{3}}\left[ Fe{{\left( CN \right)}_{6}} \right]\to 3{{K}^{+}}+Fe{{\left( CN \right)}_{6}}^{3-}$
Initially some millimolar potassium ferricyanide is present when there was no dissociation. After dissociation,
${{K}_{3}}\left[ Fe{{\left( CN \right)}_{6}} \right]=1-\dfrac{1\times 70}{100}=0.3mmol \\ 3{{K}^{+}}=\dfrac{70}{100}\times 3=2.1mmol \\
Fe{{\left( CN \right)}_{6}}^{3-}=\dfrac{70}{100}=0.7mmol \\ $
Thus, the total number of moles = 0.3+2.1+0.7 = 3.1mmol
Using the formula,
\[\Pi =cRT \\
\Rightarrow \Pi =3.1\times {{10}^{-3}}\times 0.084\times \left( 273+27 \right)K \\
\therefore \Pi =0.076atm \\
\]

Therefore, option (A) is correct.

Note: Do note while using the units while solving such problems. Usage of improper can make you reach the solution which would be one of the options too but will actually be wrong. So, make a note to use proper units.