
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) $\frac{{{P}_{1}}}{{{P}_{1}}+{{P}_{2}}}=\frac{{{P}_{2}}}{{{P}_{1}}+{{P}_{2}}}$
Answer
164.7k+ views
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 pressure
Complete 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.
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 pressure
Complete 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.
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