Question

What is the numerical value of osmotic pressure of 1 M urea solution if numerical value of osmotic pressure of 0.5 M urea solution is 'x'?

• A. x
• B. x/2
• C. 2x
• D. 3x

Hint:

Osmotic pressure is a colligative property—it depends purely on the NUMBER of solute particles! Doubling the concentration directly doubles the number of particles, which always doubles the osmotic pressure.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the mathematical relationship between the osmotic pressures of two urea solutions with different molar concentrations, assuming temperature remains constant.

Step 2: Detailed Explanation:
The osmotic pressure ($\pi$) of a dilute solution is directly given by the van 't Hoff equation:
$\pi = iCRT$
where:
$i$ = van 't Hoff factor (for urea, a non-electrolyte, $i=1$)
$C$ = Molar concentration of the solution
$R$ = Universal gas constant
$T$ = Absolute temperature
Since $i, R$, and $T$ are identical constants for both solutions, the osmotic pressure is strictly directly proportional to the molar concentration:
$\pi \propto C$
Therefore, we can set up a simple ratio:
$\frac{\pi_1}{C_1} = \frac{\pi_2}{C_2}$
Given the first scenario:
Concentration $C_1 = 0.5 \text{ M}$ yields an osmotic pressure $\pi_1 = x$.
For the second scenario:
Concentration $C_2 = 1.0 \text{ M}$. We need to find $\pi_2$.
Substitute into the ratio:
$\frac{x}{0.5} = \frac{\pi_2}{1.0}$
Solve for $\pi_2$:
$\pi_2 = \frac{1.0}{0.5} \times x$
$\pi_2 = 2 \times x$
Because the concentration is exactly doubled (from 0.5 M to 1.0 M), the resulting osmotic pressure also perfectly doubles.

Step 3: Final Answer:
The numerical value is 2x, matching option (c).