An aqueous solution of volume V ml contains a non-volatile solute of unknown mass $W_B \mathrm{~g}$ and molar mass $M_B \mathrm{~g} / \mathrm{mol}$. If the Osmotic pressure of the solution is 1.013 bar , which one of the following is the mathematical expression to be used to calculate $W_B$ ?

The osmotic pressure $\pi$ of a solution is given by the van't Hoff equation: $\pi = CRT$, where $C$ is the molar concentration of the solute in mol/L, $R$ is the universal gas constant, and $T$ is the temperature in Kelvin.

The molar concentration $C$ is defined as the number of moles of solute $n_B$ divided by the volume of the solution $V_L$ in liters. Given the mass of the solute $W_B$ in grams and its molar mass $M_B$ in g/mol, the number of moles is $n_B = \dfrac{W_B}{M_B}$.

The volume of the solution is given as $V$ ml. Converting this to liters, we have $V_L = \dfrac{V}{1000}$ L.

Substituting these into the expression for concentration: $C = \dfrac{n_B}{V_L} = \dfrac{W_B / M_B}{V / 1000} = \dfrac{W_B \times 1000}{M_B \times V}$.

Substituting $C$ back into the osmotic pressure equation: $\pi = \left( \dfrac{W_B \times 1000}{M_B \times V} \right) RT$.

Rearranging the equation to solve for $W_B$: $W_B = \dfrac{\pi M_B V}{1000 RT}$.

Answer: $W_B=\dfrac{\pi \mathrm{M}_{\mathrm{B}} V}{1000 \mathrm{RT}}$