A saturated solution is made by dissolving 0.325 g of a polypeptide (a substance formed by joining together in a chainlike fashion some number of amino acids) in water to give 1.37 L of solution. The solution has an osmotic pressure of 4.13 torr at 28 °C. What is the approximate molecular mass of the polypeptide? g/mol
pi = MRT
pi = 4.13 torr/760 = ? atm
M = unknown
R = 0.08205
T = 28 + 273 = ?
Solve for M in mols/L
You know M and L, solve for mols.
Then mol = grams/molar mass. Youj know grams and mols, solve for molar mass.
NOTE: In the future it would help if you would show what you know about the problem or how you think it should be approached. If you've done some calculations show that. It helps us do a better job of helping you.
So would you do M=RT/Pi
M=(301 x .08205)/.005
4939.41?
No, if pi = MRT then M = pi/RT
M = 0.00543/(0.08205*301) = about 0.000220M or mols/L.
M = mols/L
mols = M x L = 0.000220*1.37L = about 0.000301
mols = grams/molar mass or
molar mass = grams/mols = 0.325/0.000301 = ?
Note, however, that even if what you proposed were correct that you threw away two perfectly good numbers with that 0.005.
4.13/760 = 0.00543
To find the approximate molecular mass of the polypeptide, we can use the formula for osmotic pressure:
π = (n/V)RT
Where:
- π is the osmotic pressure
- n is the number of moles of solute
- V is the volume of the solution in liters
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
In this case, we are given the osmotic pressure (π = 4.13 torr), the volume of the solution (V = 1.37 L), and the temperature (T = 28°C = 301 K). We want to find the number of moles of solute (n) and then calculate the molecular mass.
First, let's calculate the number of moles of solute using the given mass and the molar mass of the polypeptide:
n = mass / molar mass
Given: mass = 0.325 g
To determine the molar mass of the polypeptide, we need to know the chemical formula or the number of amino acids in the polypeptide. Since that information is not provided, let's assume it consists of one amino acid for simplicity. The molar mass of one amino acid can vary, but for example, let's consider alanine, which has a molar mass of approximately 89.1 g/mol.
Using the above values, we can calculate the molar mass:
n = 0.325 g / 89.1 g/mol
Now that we have the number of moles (n), we can substitute it back into the osmotic pressure equation to solve for the molecular mass:
4.13 torr = (n / V) * R * T
Substituting the known values:
4.13 torr = (0.325 g / 89.1 g/mol) / 1.37 L * 0.0821 L·atm/(mol·K) * 301 K
Solving this equation will give us the approximate molecular mass of the polypeptide in g/mol.