Question

Β‑Galactosidase (β‑gal) is a hydrolase enzyme that catalyzes the hydrolysis of β‑galactosides into monosaccharides. A 0.410 g

sample of β‑galactosidase is dissolved in water to make 0.105 L
of solution, and the osmotic pressure of the solution at 25 ∘C
is found to be 0.832 mbar.
Calculate the molecular mass of β‑galactosidase.

Answer 1

Step-by-step explanation:

You can calculate the molecular mass of β-galactosidase using the formula for osmotic pressure:

π = (n/V)RT

Where:

π = Osmotic pressure

n = Number of moles of solute

V = Volume of solution in liters

R = Ideal gas constant (0.0831 L·bar/(K·mol))

T = Temperature in Kelvin

First, let's rearrange the formula to solve for n (number of moles):

n = (πV) / (RT)

Now, plug in the given values:

π = 0.832 mbar = 0.832 x 10^(-3) bar (since 1 mbar = 10^(-3) bar)

V = 0.105 L

R = 0.0831 L·bar/(K·mol)

T = 25°C = 25 + 273.15 K (convert to Kelvin)

n = (0.832 x 10^(-3) bar * 0.105 L) / (0.0831 L·bar/(K·mol) * 298.15 K)

Now, calculate n:

n ≈ 0.00457 moles

Now that you have the number of moles of β-galactosidase in the solution, you can calculate its molecular mass (M) using the formula:

M = (mass of solute) / (moles of solute)

Given:

Mass of β-galactosidase (m) = 0.410 g = 0.410 x 10^(-3) kg (since 1 g = 10^(-3) kg)

M = (0.410 x 10^(-3) kg) / 0.00457 moles

Now, calculate the molecular mass:

M ≈ 89.77 kg/mol

So, the molecular mass of β-galactosidase is approximately 89.77 g/mol.