<u>Answer:</u> The molar mass of unknown solute is 195.44 g/mol.
<u>Explanation:</u>
To calculate the concentration of solute, we use the equation for osmotic pressure, which is:
![\pi=icRT](https://tex.z-dn.net/?f=%5Cpi%3DicRT)
where,
= osmotic pressure of the solution = 0.750 atm
i = Van't hoff factor = 1 (for non-electrolytes)
c = concentration of solute = ?
R = Gas constant = ![0.0820\text{ L atm }mol^{-1}K^{-1}](https://tex.z-dn.net/?f=0.0820%5Ctext%7B%20L%20atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D)
T = temperature of the solution = ![25^oC=[273+25]=298K](https://tex.z-dn.net/?f=25%5EoC%3D%5B273%2B25%5D%3D298K)
Putting values in above equation, we get:
![0.750atm=1\times c\times 0.0820\text{ L.atm }mol^{-1}K^{-1}\times 298K\\\\c=0.0307mol/L](https://tex.z-dn.net/?f=0.750atm%3D1%5Ctimes%20c%5Ctimes%200.0820%5Ctext%7B%20L.atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20298K%5C%5C%5C%5Cc%3D0.0307mol%2FL)
The concentration of solute is 0.0307 mol/L
This means that, 0.0307 moles are present in 1 L of solution.
To calculate the molecular mass of solute, we use the equation:
![\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20moles%7D%3D%5Cfrac%7B%5Ctext%7BGiven%20mass%7D%7D%7B%5Ctext%7BMolar%20mass%7D%7D)
Moles of solute = 0.0307 mol
Given mass of solute = 6g
Putting values in above equation, we get:
![0.0307mol=\frac{6g}{\text{Molar mass of solute}}\\\\\text{Molar mass of solute}=195.44g/mol](https://tex.z-dn.net/?f=0.0307mol%3D%5Cfrac%7B6g%7D%7B%5Ctext%7BMolar%20mass%20of%20solute%7D%7D%5C%5C%5C%5C%5Ctext%7BMolar%20mass%20of%20solute%7D%3D195.44g%2Fmol)
Hence, the molar mass of unknown solute is 195.44 g/mol.