Answer:
The molar mass of unknown β‑Galactosidaseis 116,352.97 g/mol.
Explanation:
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 = 0.602 mbar = 0.000602 bar
0.000602 bar = 0.000594 atm
(1 atm = 1.01325 bar)
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=[273.15 +25]=298.15 K](https://tex.z-dn.net/?f=25%5EoC%3D%5B273.15%20%2B25%5D%3D298.15%20K)
Putting values in above equation, we get:
![0.000594 atm=1\times c\times 0.0821\text{ L.atm }mol^{-1}K^{-1}\times 298.15 K\\\\c=2.4278\times 10^{-5} mol/L](https://tex.z-dn.net/?f=0.000594%20atm%3D1%5Ctimes%20c%5Ctimes%200.0821%5Ctext%7B%20L.atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20298.15%20K%5C%5C%5C%5Cc%3D2.4278%5Ctimes%2010%5E%7B-5%7D%20mol%2FL)
The concentration of solute is ![2.4278\times 10^{-5} mol/L](https://tex.z-dn.net/?f=2.4278%5Ctimes%2010%5E%7B-5%7D%20mol%2FL)
Volume of the solution = V =0.137 L
Moles of β‑Galactosidase = n
![C=\frac{n}{V(L)}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7Bn%7D%7BV%28L%29%7D)
![n=2.4278\times 10^{-5} mol/L\times 0.137 L](https://tex.z-dn.net/?f=n%3D2.4278%5Ctimes%2010%5E%7B-5%7D%20mol%2FL%5Ctimes%200.137%20L)
![n=3.3261\times 10^{-6} mol](https://tex.z-dn.net/?f=n%3D3.3261%5Ctimes%2010%5E%7B-6%7D%20mol)
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 β‑Galactosidase = ![3.3261\times 10^{-6} mol](https://tex.z-dn.net/?f=3.3261%5Ctimes%2010%5E%7B-6%7D%20mol)
Given mass of β‑Galactosidase= 0.387 g
Putting values in above equation, we get:
![3.3261\times 10^{-6} mol =\frac{0.387 g}{\text{Molar mass of solute}}\\\\\text{Molar mass of solute}=116,352.97 g/mol](https://tex.z-dn.net/?f=3.3261%5Ctimes%2010%5E%7B-6%7D%20mol%20%3D%5Cfrac%7B0.387%20g%7D%7B%5Ctext%7BMolar%20mass%20of%20solute%7D%7D%5C%5C%5C%5C%5Ctext%7BMolar%20mass%20of%20solute%7D%3D116%2C352.97%20g%2Fmol)
Hence, the molar mass of unknown β‑Galactosidaseis 116,352.97 g/mol.