Answer :
Final answer:
The molar mass of the unknown protein is approximately 217 grams per mole (g/mol).
Explanation:
To find the molar mass of the unknown protein, you can use the formula for osmotic pressure and rearrange it to solve for the molar mass:
π = (n/V)RT
Where:
- π = osmotic pressure (in atm)
- n = moles of solute
- V = volume of solution (in liters)
- R = ideal gas constant (0.0821 L.atm/(mol.K))
- T = temperature (in Kelvin)
First, you need to convert the given temperature from Celsius to Kelvin:
T = 35.7°C + 273.15 = 308.85 K
Next, convert the osmotic pressure from mmHg to atm:
π = 3.91 mmHg / 760 mmHg/atm ≈ 0.005145 atm
Now, you can calculate the moles of solute (protein) using the given mass and volume:
Mass of protein (m) = 37.1 mg = 0.0371 g
Volume of solution (V) = 82.0 ml = 0.0820 L
Now, we can calculate moles of protein (n):
n = (0.0371 g) / (molar mass of protein)
Now, plug the values into the osmotic pressure equation:
0.005145 atm = (n / 0.0820 L) * (0.0821 L.atm/(mol.K)) * 308.85 K
Solve for n:
n = (0.005145 atm * 0.0820 L) / (0.0821 L.atm/(mol.K) * 308.85 K)
n ≈ 0.0001711 mol
Now that you know the moles of protein, you can solve for the molar mass:
0.0001711 mol = (0.0371 g) / (molar mass of protein)
Rearrange to find the molar mass of the protein:
Molar mass of protein = (0.0371 g) / 0.0001711 mol
Molar mass of protein ≈ 217 g/mol
So, the molar mass of the unknown protein is approximately 217 grams per mole (g/mol).
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