β-Galactosidase (β-gal) is a hydrolase enzyme that catalyzes the hydrolysis of β-galactosides into monosaccharides. A 0.474 gram sample of β-galactosidase is dissolved in water to make 0.144 L of solution, and the osmotic pressure of the solution at 25 °C is found to be 0.701 mbar. Calculate the molecular mass of β-galactosidase.
I tried this
molar mass = (mass RT) / P(volume)
molar mass = 0.474 g (83.145 L·mbar/molK) (298K) / 0.144 L = 8.16X10^4 g/mol
but it was incorrect. please explain what im doing wrong?
pi = MRT
pi = osmotic pressure. I would convert the mbar to atm.
M = molarity in mols/L
R = 0.08206
T = 273 + C = ?
Solve for M. Then M = mols/L. You know M and and L, solve for mols.
Then mol = grams/molar mass. You know mols and grams, solve for molar mass. Post your work if you get stuck.
It seems like you're on the right track, but there might be a slight error in the calculation. Let's take a closer look at the equation you used:
molar mass = (mass RT) / (P * volume)
First, let's convert the osmotic pressure from mbar to atm because the gas constant (R) is usually expressed in atm.
0.701 mbar = 0.701 * (1 atm / 760 mbar) = 0.000922 atm
Now, let's substitute the values into the equation:
molar mass = (0.474 g * R * T) / (P * volume)
= (0.474 g * 0.0821 L·atm / mol·K * 298 K) / (0.000922 atm * 0.144 L)
= 10,700 g/mol
So, the molecular mass of β-galactosidase is approximately 10,700 g/mol.
In your calculation, you correctly used the formula to calculate the molar mass:
molar mass = (mass RT) / (P * V)
However, you made a mistake when converting the osmotic pressure from mbar to atm. The correct conversion factor is 1 atm = 1013.25 mbar.
So, let's re-calculate the molar mass using the correct conversion factor:
molar mass = (0.474 g * 0.0821 L·atm/(mol·K) * 298 K) / (0.701 mbar * 0.144 L * (1 atm/1013.25 mbar))
Simplify the equation:
molar mass = (0.474 g * 0.0821 * 298) / (0.701 * 0.144 * (1/1013.25))
molar mass ≈ 132,919 g/mol
So, the correct molecular mass of β-galactosidase is approximately 132,919 g/mol.
To calculate the molecular mass of β-galactosidase, you need to use the osmotic pressure equation, which is:
osmotic pressure (P) = (n/V)RT
Where:
P is the osmotic pressure
n is the number of moles of solute (in this case, β-galactosidase)
V is the volume of the solution
R is the ideal gas constant (0.083145 L·mbar/mol·K)
T is the temperature in Kelvin
First, let's rearrange the equation to solve for the number of moles of solute (n):
n = (P x V) / (RT)
Now, let's substitute the given values into the equation:
n = (0.701 mbar) x (0.144 L) / [(0.083145 L·mbar/mol·K) x (298 K)]
n = 0.1008 mol
Next, we can calculate the molecular mass of β-galactosidase by dividing the mass of the sample by the number of moles:
molecular mass = mass / moles
molecular mass = 0.474 g / 0.1008 mol
molecular mass = 4.7 g/mol
Therefore, the correct molecular mass of β-galactosidase is approximately 4.7 g/mol.