A solution contains 0.02755 g of a protein in 25.0 mL of solution. The osmotic pressure is 3.22 torr at 298 K. What is the molecular weight of the protein?
pi = ZMRT.
pi should be in atm (3.22/760).
T must be in kelvin. Solve for M in mols/L. Then moles = grams/molecular weight.. You know grams and mols, solve for molecular weight.
How do I find mols?
To find the molecular weight of the 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 in liters
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
First, let's find the number of moles of solute (protein) using the given mass and the molecular weight.
1. Convert 0.02755 g to moles:
To do this, we need the molar mass of the protein. Let's use "X" to represent the molecular weight.
Moles of solute = mass (g) / molar mass (g/mol)
0.02755 g / X g/mol
2. Now, let's calculate the volume of the solution in liters:
Given volume = 25.0 mL
1 L = 1000 mL, so volume = 25.0 mL / 1000 = 0.025 L
3. Convert the temperature to Kelvin:
Kelvin temperature = 298 K
Now, we can rearrange the formula for osmotic pressure to solve for n (moles of solute):
n = (π * V) / (R * T)
Substituting the given values:
n = (3.22 torr * 0.025 L) / (0.0821 L·atm/(mol·K) * 298 K)
Simplifying the equation:
n = 0.0805 atm·L / (0.0821 L·atm/(mol·K) * 298 K)
n = 0.001061 mol
Finally, let's solve for the molecular weight (X):
0.001061 mol = 0.02755 g / X g/mol
Rearranging the equation to solve for X:
X = 0.02755 g / 0.001061 mol
Calculating the molecular weight:
X = 25.94 g/mol
Therefore, the molecular weight of the protein is approximately 25.94 g/mol.