<u>Answer:</u> The molar mass of the unknown compound is 223.2 g/mol
<u>Explanation:</u>
To calculate the concentration of solute, we use the equation for osmotic pressure, which is:
![\pi=iMRT](https://tex.z-dn.net/?f=%5Cpi%3DiMRT)
where,
= osmotic pressure of the solution = 8.44 torr
i = Van't hoff factor = 1 (for non-electrolytes)
M = molarity of solute = ?
R = Gas constant = ![62.3637\text{ L torr }mol^{-1}K^{-1}](https://tex.z-dn.net/?f=62.3637%5Ctext%7B%20L%20torr%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:
![8.44torr=1\times M\times 62.3637\text{ L. torr }mol^{-1}K^{-1}\times 298K\\\\M=\frac{8.44}{1\times 62.3637\times 298}=4.54\times 10^{-4}M](https://tex.z-dn.net/?f=8.44torr%3D1%5Ctimes%20M%5Ctimes%2062.3637%5Ctext%7B%20L.%20torr%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20298K%5C%5C%5C%5CM%3D%5Cfrac%7B8.44%7D%7B1%5Ctimes%2062.3637%5Ctimes%20298%7D%3D4.54%5Ctimes%2010%5E%7B-4%7DM)
To calculate the molecular mass of solute, we use the equation used to calculate the molarity of solution:
![\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}](https://tex.z-dn.net/?f=%5Ctext%7BMolarity%20of%20the%20solution%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20solute%7D%5Ctimes%201000%7D%7B%5Ctext%7BMolar%20mass%20of%20solute%7D%5Ctimes%20%5Ctext%7BVolume%20of%20solution%20%28in%20mL%29%7D%7D)
We are given:
Molarity of solution = ![4.54\times 10^{-4}M](https://tex.z-dn.net/?f=4.54%5Ctimes%2010%5E%7B-4%7DM)
Given mass of unknown compound = 15.2 mg = 0.0152 g (Conversion factor: 1 g = 1000 mg)
Volume of solution = 150.0 mL
Putting values in above equation, we get:
![4.54\times 10^{-4}M=\frac{0.0152\times 1000}{\text{Molar mass of unknown compound}\times 150.0}\\\\\text{Molar mass of unknown compound}=\frac{0.0152\times 1000}{150.0\times 4.54\times 10^{-4}}=223.2g/mol](https://tex.z-dn.net/?f=4.54%5Ctimes%2010%5E%7B-4%7DM%3D%5Cfrac%7B0.0152%5Ctimes%201000%7D%7B%5Ctext%7BMolar%20mass%20of%20unknown%20compound%7D%5Ctimes%20150.0%7D%5C%5C%5C%5C%5Ctext%7BMolar%20mass%20of%20unknown%20compound%7D%3D%5Cfrac%7B0.0152%5Ctimes%201000%7D%7B150.0%5Ctimes%204.54%5Ctimes%2010%5E%7B-4%7D%7D%3D223.2g%2Fmol)
Hence, the molar mass of the unknown compound is 223.2 g/mol