Respuesta :
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:
[tex]\pi=icRT[/tex]
where,
[tex]\pi[/tex] = 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 = [tex]0.0820\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the solution = [tex]25^oC=[273.15 +25]=298.15 K[/tex]
Putting values in above equation, we get:
[tex]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[/tex]
The concentration of solute is [tex]2.4278\times 10^{-5} mol/L[/tex]
Volume of the solution = V =0.137 L
Moles of β‑Galactosidase = n
[tex]C=\frac{n}{V(L)}[/tex]
[tex]n=2.4278\times 10^{-5} mol/L\times 0.137 L[/tex]
[tex]n=3.3261\times 10^{-6} mol[/tex]
To calculate the molecular mass of solute, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Moles of β‑Galactosidase = [tex]3.3261\times 10^{-6} mol[/tex]
Given mass of β‑Galactosidase= 0.387 g
Putting values in above equation, we get:
[tex]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[/tex]
Hence, the molar mass of unknown β‑Galactosidaseis 116,352.97 g/mol.
