The following were prepared by dissolving 10g of glucose (C₆H₁₂O₆) in 250 ml of water (P₁), 10g of sucrose (C₁₂H₂₂O₁₁) in 250ml of water (P₃). The right option for the decreasing order of osmotic pressure of these solutions is :

The correct option is P₂ > P₁ > P₃.

Note: In standard versions of this question, three solutions are compared: 10 g of glucose in 250 mL of water (P₁), 10 g of urea in 250 mL of water (P₂), and 10 g of sucrose in 250 mL of water (P₃). We will include the calculations for all three to provide a complete explanation.

1. Understanding Osmotic Pressure:
Osmotic pressure ($\pi$) is a colligative property, which means it depends on the number of solute particles in the solution. The formula for osmotic pressure is given by:

$\pi =iCRT$

where:
• $i$ is the van 't Hoff factor (which is 1 for non-electrolytes like glucose, urea, and sucrose because they do not dissociate in water).
• $C$ is the molar concentration (molarity) of the solution, which is equal to the number of moles of solute ($n$) divided by the volume of the solution ($V$).
• $R$ is the universal gas constant.
• $T$ is the absolute temperature.

Since the mass of each solute (10 g) and the volume of water (250 mL) are identical for all solutions, the concentration $C$ (and thus the osmotic pressure $\pi$) is inversely proportional to the molar mass ($M$) of the solute:

$\pi \propto \frac{1}{M}$

2. Molar Masses of the Solutes:
Let us calculate the molar mass for each solute:
• Glucose (C₆H₁₂O₆):
$M=(6\times 12)+(12\times 1)+(6\times 16)=72+12+96=180\text{g/mol}$
• Urea (CH₄N₂O):
$M=12+(4\times 1)+(2\times 14)+16=12+4+28+16=60\text{g/mol}$
• Sucrose (C₁₂H₂₂O₁₁):
$M=(12\times 12)+(22\times 1)+(11\times 16)=144+22+176=342\text{g/mol}$

3. Determining the Order of Osmotic Pressure:
Comparing the molar masses:

$M_{\text{urea}}<M_{\text{glucose}}<M_{\text{sucrose}}$

$60\text{g/mol}<180\text{g/mol}<342\text{g/mol}$

Since osmotic pressure is inversely proportional to the molar mass of the solute:

${\pi }_{\text{urea}}>{\pi }_{\text{glucose}}>{\pi }_{\text{sucrose}}$

Therefore, the decreasing order of osmotic pressure is:

$P_2>P_1>P_3$