If osmotic pressure of 4 %( w / v ) solution of sucrose is same as 2 %( w / v ) solution of ' X ', then the molecular mass of X( ~g / mol ) is

Step-by-step solution

4 % solution of sucrose ( w / v ) means 4 g of sucrose is dissolved in 100 mL of solution. Similarly, 2 %( w / v ) solution of ' X ' means 2 g of X present in 100 mL of solution. As we know that, osmotic pressure ( )= CRT or = n V R T ; where n= number of moles of solute. Since, ₁ (for sucrose solution) = ₂ (for X solution) n ₁ ~V ₁ RT = n ₂ ~V ₂ RT aligned & 4 342 = 2 Molecular weight & [ n = Mass of solute Molar mass of solute ] & Molecular weight = 2 4 342 aligned Molecular weight =171 ~g ~mol ⁻¹