A solution containing 26.05 mg of an unknown protein per 23.5 mL solution was found to have an osmotic pressure of 3.75 torr at 44 C.
What is the molar mass of the protein?
pi=MRT
You know pi (osmotic pressure. I would convert that to atmospheres (3.75/760 = ?? although 3.75 atm sounds more like an osmotic pressure).Solve for M = molarity.
Then M = moles/L. You know M and L, calculate moles, then use moles = grams/molar mass. Knowing M and grams, calculate molar mass.
I don't understand how you get the M. I know that M = moles/L, but the problem gives mg and ml so how do we find the molarity?
To determine the molar mass of the protein, we can use the formula for osmotic pressure:
π = (n/V)RT
Where:
π = osmotic pressure
n = moles of solute
V = volume of solution in liters
R = ideal gas constant (0.0821 L * atm / mole * K)
T = temperature in Kelvin
In this case, we have the osmotic pressure (π), volume (V), and temperature (T), but we need to determine the moles of solute (n) to proceed.
To calculate the moles of solute, we need to convert the mass of the protein to moles. The moles of solute can be determined using the formula:
n = mass / molar mass
Given that the mass of the protein is 26.05 mg, we can rewrite the formula as:
n = 0.02605 g / molar mass
Now, we can substitute the known values into the first equation to solve for the molar mass:
π = (n/V)RT
3.75 torr = (0.02605 g / molar mass) / (23.5 mL / 1000 L) * 0.0821 L * atm / mole * K * (44 + 273.15 K)
First, convert the volume from milliliters to liters by dividing by 1000:
23.5 mL / 1000 L = 0.0235 L
Then, convert torr to atm by dividing by 760:
3.75 torr / 760 = 0.00493 atm
Substituting the known values:
0.00493 atm = (0.02605 g / molar mass) / 0.0235 L * 0.0821 L * atm / mole * K * 317.15 K
Simplifying the equation:
0.00493 = (0.02605 / molar mass) * 0.0821 * 317.15
Rearranging the equation to solve for the molar mass:
molar mass = 0.02605 / (0.00493 * 0.0821 * 317.15)