A solution containing 26.40 mg of an unknown protein per 22.5 mL solution was found to have an osmotic pressure of 3.95 torr at 21 C. What is the molar mass of the protein?
Pi = MRT
You know Pi (osmotic pressure) which you want to convert to atmospheres. Use 0.08205 for R and convert T to Kelvin. Calculate M, molarity.
Then M = moles/L which allows you to calculate # moles.
Finally, # moles = g/molar mass which allows you to calculate molar mass. Post your work, preferably with the problem, on a new post, if you run into trouble.
6360.25
To find the molar mass of the protein, we can utilize the osmotic pressure equation. The osmotic pressure equation relates the osmotic pressure (π) of a solution to the concentration (c) of the solute (in mol/L) and the ideal gas constant (R) using the formula:
π = cRT
Where:
π = osmotic pressure (in atm or torr)
c = concentration of the solute (in mol/L)
R = ideal gas constant (0.0821 L·atm/(mol·K) or 62.36 torr·L/(mol·K))
T = temperature in Kelvin (K)
First, let's convert the given values into the appropriate units:
Solution concentration (c) = 26.40 mg/22.5 mL
We need to convert mg to grams by dividing by 1000:
c = (26.40 mg / 22.5 mL) * (1 g / 1000 mg) = 0.001173 g/mL
To convert g/mL to mol/L, we need to know the molecular weight of the protein.
Now, let's substitute the values into the osmotic pressure equation:
π = cRT
Rearranging the equation to solve for c:
c = π / (RT)
Since we are given the osmotic pressure (π = 3.95 torr), the ideal gas constant (R = 62.36 torr·L/(mol·K)), and the temperature (T = 21°C = 294 K), we can calculate the concentration (c) of the protein:
c = (3.95 torr) / (62.36 torr·L/(mol·K) * 294 K) = 0.0002203 mol/L
Now, we have the concentration (c) of the protein. To calculate the molar mass (M) of the protein, we can rearrange the formula:
c = moles of solute (mol) / volume of solution (L)
mol = c * volume of solution (L)
In our case, volume of solution = 22.5 mL = 0.0225 L. Substituting the values:
mol = (0.0002203 mol/L) * 0.0225 L = 0.000004958 mol
The molar mass (M) can be calculated using the formula:
M = mass of solute (g) / moles of solute (mol)
In our case, we have the mass of the protein (26.40 mg = 0.0264 g) and the moles of protein (0.000004958 mol). Substituting the values:
M = 0.0264 g / 0.000004958 mol ≈ 5315 g/mol
Therefore, the molar mass of the protein is approximately 5315 g/mol.