Calculate the molecular weight of a small protein if a 0.32 g sample dissolved in 161 mL of H2O has an osmotic pressure of 9.0 mmHg at 25 degree celcius. (R=0.0821 L X atm/K X mol)
pi = MRT
Substitute and solve for M = molarity.
Then M = mols/L. Substitute 0.161 for L and solve for mols.
Then mols = n = grams/molar mass.
You know n and grams, solve for molar mass. By the way, pi must be in atm. pi = 9.0 mm/760 = ?
To calculate the molecular weight of a small protein, we can use the formula for osmotic pressure:
π = (n/V)RT
Where:
π = osmotic pressure
n = number of moles of solute
V = volume of solution
R = ideal gas constant
T = temperature in Kelvin
Rearranging the equation to solve for n (number of moles of solute):
n = (πV) / (RT)
Given:
π = 9.0 mmHg (pressure)
V = 161 mL = 0.161 L (volume)
R = 0.0821 L x atm / K x mol (ideal gas constant)
T = 25 °C = 25 + 273.15 K (temperature in Kelvin)
Converting pressure to atm:
1 atm = 760 mmHg
π = 9.0 mmHg / 760 mmHg/atm = 0.01184 atm
Substituting the values into the equation:
n = (0.01184 atm)(0.161 L) / (0.0821 L x atm / K x mol)(298.15 K)
Simplifying the equation:
n = 0.0016 mol
Finally, to calculate the molecular weight (M), we divide the mass of the sample (0.32 g) by the number of moles (0.0016 mol):
M = mass / moles = 0.32 g / 0.0016 mol = 200 g/mol
Therefore, the molecular weight of the small protein is 200 g/mol.
To calculate the molecular weight of a small protein using osmotic pressure, we can use the following equation:
Molecular weight = (RT)/(ΔP x V)
Where:
R is the ideal gas constant (0.0821 L x atm/K x mol)
T is the temperature in Kelvin (25 + 273.15 = 298.15 K)
ΔP is the osmotic pressure difference between the protein solution and pure solvent (9.0 mmHg)
V is the volume of the solvent in liters (161 mL = 0.161 L)
Now, let's plug in the values and calculate the molecular weight:
Molecular weight = (0.0821 L x atm/K x mol) x (298.15 K) / (9.0 mmHg x 0.161 L)
First, convert the osmotic pressure from mmHg to atm:
ΔP = 9.0 mmHg / 760 mmHg/atm = 0.0118 atm
Now, substitute the values into the formula:
Molecular weight = (0.0821 L x atm/K x mol) x (298.15 K) / (0.0118 atm x 0.161 L)
Now, let's calculate the molecular weight:
Molecular weight = 2021.4663 g/mol
Therefore, the molecular weight of the small protein is approximately 2021.47 g/mol.