Question

Calculate the mass of $$N{H}_{4}Cl$$ that must be completely dissolved in 1 liter of aqueous solution to attain an osmotic pressure of $$5$$ atm at $$298K$$. Assume ideal behavior.

Answer 1

Hint: We need to know that the ammonium chloride is a chemical compound having the chemical formula, $$N{H}_{4}Cl$$. It is a white crystalline compound which is highly soluble in water. The ammonium chloride is a slightly acidic compound. And the ammonium chloride is mainly used as a fertilizer as the nitrogen source. And ammonium chloride is also used in medicine. In the case of osmosis, it takes place two solutions having different concentrations which are separated by a membrane.

Complete answer:
According to the question,
The volume of the solution, V is equal to 1 liter.
The osmotic pressure is equal to, $$\pi =5atm$$
Temperature, T$$=298K$$
And here we have to find out the weight of ammonium chloride. The ammonium chloride undergoes complete dissociation in the solution and there is a formation of ammonium and chloride ions. Let’s see the reaction,
$$N{H}_{4}Cl\to N{H}_4^{+}+C{l}^{-}$$
Hence, Van’t Hoff factor, ‘i’ of ammonium chloride $$={\displaystyle \frac{no.ofparticlesinsolution}{no.ofparticlestaken}}$$
Here, the number of particles in the solution is equal to two and the number of particles taken is equal to one. Hence,
Let’s see the formula of osmotic pressure, $$\pi =icRT$$
Where, i is the Van’t Hoff factor
And c is the molar concentration of the solute present in the solution. Which is also equal to, $$c={\displaystyle \frac{w}{MV}}$$. Therefore,
 $$\pi ={\displaystyle \frac{w}{MV}}RTi$$
Substitute the given values in above equation, will get;
$$5={\displaystyle \frac{w}{53.5}}\times 0.0821\times 298\times 2$$
By rearranging the equation, I will get the value of mass of ammonium chloride.
$$w={\displaystyle \frac{10.9}{2}}=5.47g$$
Hence, the weight of ammonium chloride is equal to $$5.47g$$.

Note:
We have to remember that the osmotic pressure is the minimum pressure required to apply a solution to prevent or restrict the inward flow of the pure solvent across the semipermeable membrane. And the osmotic pressure is also the tendency of the solution for taking the pure solvent using osmosis. The osmosis is explained on the basis of movement of particles. The osmosis is the process of movement of particles from a range of higher concentration to the lower concentration. This process occurs in all living beings. It will help with the movement of particles in and out from the cells.