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A solution contains non volatile solute of molecular mass $M_2$. Which of the following can be used to calculate the molecular mass of solute in terms of osmotic pressure : -
(Note: $m_2$ = mass of solute, V = volume of solution, $\pi$ = osmotic pressure)
(Note: $m_2$ = mass of solute, V = volume of solution, $\pi$ = osmotic pressure)
A
$M_2 = \left(\dfrac{m_2}{\pi}\right)VRT$
B
$M_2 = \left(\dfrac{m_2}{V}\right)\dfrac{RT}{\pi}$
C
$M_2 = \left(\dfrac{m_2}{V}\right)\pi RT$
D
$M_2 = \left(\dfrac{m_2}{V}\right)\dfrac{\pi}{RT}$
Detailed Solution
Van't Hoff equation: $\pi V = nRT$, where $n = \dfrac{m_2}{M_2}$.
$\pi V = \dfrac{m_2}{M_2}RT$
$\Rightarrow M_2 = \dfrac{m_2RT}{\pi V} = \left(\dfrac{m_2}{V}\right)\dfrac{RT}{\pi}$
$\pi V = \dfrac{m_2}{M_2}RT$
$\Rightarrow M_2 = \dfrac{m_2RT}{\pi V} = \left(\dfrac{m_2}{V}\right)\dfrac{RT}{\pi}$