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(A) Osmotic pressure $(\pi)$ is given by the formula $\pi = CRT = \frac{n}{V}RT = \frac{w}{M 	imes V}RT$. For the same temperature and volume,$\pi$ i

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$3 \ g \ L^{-1}$ urea and $17.1 \ g \ L^{-1}$ sucrose

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(A) Osmotic pressure $(\pi)$ is given by the formula $\pi = CRT = \frac{n}{V}RT = \frac{w}{M 	imes V}RT$. For the same temperature and volume,$\pi$ is proportional to $\frac{w}{M}$. For urea $(M = 60 \ g \ mol^{-1})$: $A: \frac{3}{60} = 0.05 \ mol \ L^{-1}$ $B: \frac{6}{60} = 0.1 \ mol \ L^{-1}$ For sucrose $(M = 342 \ g \ mol^{-1})$: $17.1 \ g \ L^{-1}: \frac{17.1}{342} = 0.05 \ mol \ L^{-1}$ $34.2 \ g \ L^{-1}: \frac{34.2}{342} = 0.1 \ mol \ L^{-1}$ Comparing the values,$3 \ g \ L^{-1}$ urea $(0.05 \ mol \ L^{-1})$ and $17.1 \ g \ L^{-1}$ sucrose $(0.05 \ mol \ L^{-1})$ have the same molar concentration,hence the same osmotic pressure. Thus,the correct option is $A$.

Which of the following pairs of aqueous solutions exhibits the same osmotic pressure at the same temperature? $\left[ \text{Molar mass of urea} = 60 \ g \ mol^{-1}, \text{sucrose} = 342 \ g \ mol^{-1} \right]$

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