Question

β‑Galactosidase (β‑gal) is a hydrolase enzyme that catalyzes the hydrolysis of β‑galactosides into monosaccharides. A 0.387 g sample of β‑galactosidase is dissolved in water to make 0.137 L of solution, and the osmotic pressure of the solution at 25 ∘ C is found to be 0.602 mbar. Calculate the molecular mass of β‑galactosidase.molecular mass: ____ g/mol.

Answer 1

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:

$\pi=icRT$

where,

$\pi$ = 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 = $0.0820\text{ L atm }mol^{-1}K^{-1}$

T = temperature of the solution = $25^oC=[273.15 +25]=298.15 K$

Putting values in above equation, we get:

$0.000594 atm=1\times c\times 0.0821\text{ L.atm }mol^{-1}K^{-1}\times 298.15 K\\\\c=2.4278\times 10^{-5} mol/L$

The concentration of solute is $2.4278\times 10^{-5} mol/L$

Volume of the solution = V =0.137 L

Moles of β‑Galactosidase = n

$C=\frac{n}{V(L)}$

$n=2.4278\times 10^{-5} mol/L\times 0.137 L$

$n=3.3261\times 10^{-6} mol$

To calculate the molecular mass of solute, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Moles of β‑Galactosidase = $3.3261\times 10^{-6} mol$

Given mass of β‑Galactosidase= 0.387 g

Putting values in above equation, we get:

$3.3261\times 10^{-6} mol =\frac{0.387 g}{\text{Molar mass of solute}}\\\\\text{Molar mass of solute}=116,352.97 g/mol$

Hence, the molar mass of unknown β‑Galactosidaseis 116,352.97 g/mol.