Question

A decinormal solution of NaCl exerts an osmotic pressure of 4.26 atm at $27{}^\circ C$. Calculate the degree of dissociation of NaCl. ​
a.) 99%
b.) 87%
c.) 82.7%
d.) 50%

Answer 1

Hint: A decinormal solution of NaCl refers to a 10N solution of NaCl. With this in mind, try to solve the given question with the help of the Osmotic Pressure equation and your knowledge of the colligative properties of a solution.
Complete answer:
Let us first begin with understanding what the osmotic pressure of a solution is and how it's calculated, before applying this knowledge to help solve the given question.
Osmotic Pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in pure solvent by osmosis.
Osmosis occurs when two solutions containing different concentrations of solute are separated by a selectively permeable membrane. Solvent molecules pass preferentially through the membrane from the low-concentration solution to the solution with higher solute concentration. The transfer of solvent molecules will continue until equilibrium is attained.
Jacobus van 't Hoff found a quantitative relationship between osmotic pressure and solute concentration, expressed in the following equation:
$\pi =i\times cRT$
π is osmotic pressure, i is the dimensionless van 't Hoff index, c is the molar concentration of solute, R is the ideal gas constant, and T is the temperature in kelvins.
Now, let us try and solve the given question with this data.
Given,
Osmotic pressure = 4.26 atm
T = 27 + 273 = 300 K
C = 0.1
R = 0.821 L $atm\text{ }{{K}^{^{-}1}}mo{{l}^{^{-}1}}$
$\pi =i\times cRT$
That implies,
I = (4.26 / 0.1) × 0.821 × 300 = 0.173
i = Observed moles / Total moles = (1 + α) / 1
i = 1 + α
0.173 = 1 + α
α = 1 - 0.173 = 0.827 = 82.7 %
Therefore, we can now conclude that the answer to this question is c) 82.7%
Note:
The formula, $\pi =i\times cRT$, applies when the solute concentration is sufficiently low that the solution can be treated as an ideal solution. The proportionality to concentration means that osmotic pressure is a colligative property.