Question

At 10${}^\circ C$, the osmotic pressure of urea solution is 500 mm. The solution is diluted and the temperature is raised to 25${}^\circ C$, when the osmotic pressure is found to be 105.3 mm. Determine extent of dilution.

Answer 1

Hint: We should know that osmotic pressure is measured by the Van't Hoff equation. We should know about the definition of osmotic pressure.

Complete step by step solution:
Let us know about osmotic pressure first. We should know that osmotic pressure is the minimum pressure that must be applied to a solution to stop the flow of solvent molecules through a semipermeable membrane (osmosis). We should know that osmotic pressure can be calculated with the help of the following formula:
\[\pi =\text{iCRT}\]\[\]
Let us know about the formula in which,
π is the osmotic pressure
i is the Van’t Hoff factor
C is the molar concentration of the solute in the solution
R is the universal gas constant
T is the temperature
Let us know about the term osmosis. We should note that osmosis refers to the movement of solvent molecules through a semipermeable membrane from a low solute concentration region to a high solute concentration region.
Now, we will solve our question.

So, we have our formula of osmotic pressure that is \[\pi =\text{iCRT}\]\[\]
As urea is non-electrolyte we should note that, i=1

\[\begin{align}
  & {{\pi }_{\text{solution}}}=\text{i}{{\text{C}}_{\text{solution}}}\text{R}{{\text{T}}_{\text{1}~}}~\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\to \,\,\,\,\,\,\,\,\,\,\,\,\,Equation\,1 \\
 & {{\pi }_{\text{solution}}}=\text{i}{{\text{C}}_{\text{solution}}}\text{R}{{\text{T}}_{\text{2}}}~~\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\to \,\,\,\,\,\,\,\,\,\,\,\,\,Equation\,2 \\
\end{align}\]
Above is the equation for the osmotic pressure at different temperatures.

Now, we will divide the equation 1 and 2.
\[\dfrac{{{\pi }_{\text{urea}}}}{{{\pi }_{\text{solution}}}}\,=\,\dfrac{{{\text{C}}_{\text{urea}}}{{T}_{1}}}{{{\text{C}}_{\text{solution}}}{{\text{T}}_{\text{2}}}}\]
Now, we will put the values in the above formula. And after looking the values the equation will look like as follows:
\[\dfrac{{{\text{C}}_{\text{urea}}}}{{{\text{C}}_{\text{solution}}}}\,=\dfrac{\text{5}00\times \text{298}}{\text{1}0\text{5}\times \text{283}}\]

We will get this as:
\[\text{5}{{\text{C}}_{\text{solution}}}={{\text{C}}_{\text{urea}}}\]
This means the solution was diluted 5 times with respect to the urea concentration. So, we have calculated our answer.

Note: We should now take the example of plants to understand osmotic pressure. We should know that, if we provide sufficient water to the plant; its cells (which contain several salts) absorb water and expand. This expansion of plant cells increases the pressure exerted on their cell walls, causing them to stand upright. And if we apply insufficient water to the plant, its cells shrink due to loss of water. They lose their firm, upright posture.