Two solutions of $KN{{O}_{3}}$ and $$CH_{3}^{{}}COOH~$$ are prepared separately. Molarity of both is $0.1M$ and osmotic pressures are $${{P}_{1}}$$ and $${{P}_{2}}$$ respectively. The correct relationship between the osmotic pressures is :(A) $${{P}_{2}}{{P}_{1}}$$ (B) $${{P}_{1}}={{P}_{2}}$$ (C) $${{P}_{1}}{{P}_{2}}$$ (D) $\frac{{{P}_{1}}}{{{P}_{1}}+{{P}_{2}}}=\frac{{{P}_{2}}}{{{P}_{1}}+{{P}_{2}}}$

Question

Two solutions of $KN{{O}_{3}}$ ​ and $$CH_{3}^{{}}COOH~$$ are prepared separately. Molarity of both is $0.1M$ and osmotic pressures are $${{P}_{1}}$$ and $${{P}_{2}}$$ respectively. The correct relationship between the osmotic pressures is :(A) $${{P}_{2}}>{{P}_{1}}$$ (B) $${{P}_{1}}={{P}_{2}}$$ (C) $${{P}_{1}}>{{P}_{2}}$$ (D) $\frac{{{P}_{1}}}{{{P}_{1}}+{{P}_{2}}}=\frac{{{P}_{2}}}{{{P}_{1}}+{{P}_{2}}}$

Vedantu Content Team · Accepted Answer

Hint: The minimum pressure which is required to be applied to the solution to prevent the inward flow of the solvent across a semipermeable membrane is known as osmotic pressure. This process is known as osmosis. If there is no osmotic pressure, there will be no movement of solvent. It is a unidirectional process. It tends to make the concentration of solute across the two sides of the membrane equal.Formula Used: The formula used to calculate the osmotic pressure of a solution is:$P=icRT$; Where $i$= van’t hoff index$c$= Concentration of solute$R$= Gas constant$T$= Temperature (Kelvin) $P$= Osmotic pressureComplete Step by Step Answer:We will calculate the osmotic pressure for two solutions of $KN{{O}_{3}}$ ​ and $$CH_{3}^{{}}COOH~$$ each of concentration$0.1M$. Osmotic Pressure of $0.1M$ $KN{{O}_{3}}$: As $KN{{O}_{3}}$ is a strong electrolyte, it dissociates completely and gives 2 ions, so $i=2$ Thus, osmotic pressure will be ${{P}_{1}}=2\times 0.1\times R\times T$${{P}_{1}}=0.2RT$Osmotic Pressure of $0.1M$ $$CH_{3}^{{}}COOH~$$:As $$CH_{3}^{{}}COOH~$$ is a weak electrolyte, it does not dissociate completely, so $i=1$ Thus, osmotic pressure will be ${{P}_{2}}=1\times 0.1\times R\times T$${{P}_{2}}=0.1RT$We can observe that $${{P}_{1}}>{{P}_{2}}$$Correct Option: (C) $${{P}_{1}}>{{P}_{2}}$$. Note: The process of osmosis is important for the human body. In the human body, osmosis occurs in the small and large intestines. It plays an important role in the gastro-intestinal system and kidneys. It helps in getting all the essential nutrients from our food and also removes the waste products from the blood.