If 6.38 g of a polyethylene glycol is dissolved in 7550 ml of water at 300 oK, the solution has an osmotic pressure of 0.171 torr. Calculate the molar mass (g/mol) of the polyethylene glycol.
pi = nRT
You know pi, R, and T (By the way, the new rules state that the degree sign is NOT used with Kelvin; i.e., you would write 300 Kelvin although 300o C is correct). Solve for n, then n = grams/molar mass to calculate molar mass.
pi* = MRT
slight typo here. M and not n.
M = molarity = moles/L. You have L and M, calculate moles. Then moles = grams/molar mass. Sorry 'bout that.
To calculate the molar mass of the polyethylene glycol, we can use the van't Hoff equation, which relates the osmotic pressure to the concentration of solute particles.
The van't Hoff equation is written as:
π = i x M x R x T
Where:
- π is the osmotic pressure
- i is the van't Hoff factor (the number of particles the solute breaks into in solution)
- M is the molarity (concentration in moles per liter) of the solute
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
First, let's convert the given volume of the solution to liters:
7550 ml = 7.550 L
Next, we need to calculate the molarity of the polyethylene glycol using the given mass and molar mass:
molarity = moles of solute / volume of solution in liters
To find the moles of polyethylene glycol, we divide the mass by the molar mass.
Now, rearrange the equation to solve for the molar mass (M):
M = moles of solute / molarity
Using the values given, including the osmotic pressure and temperature, we can rearrange the equation:
M = π / (i x R x T)
Substituting the values:
π = 0.171 torr
i is the van't Hoff factor (which we assume to be 1 since there is no information about it)
R = 0.0821 L·atm/(mol·K)
T = 300 K
Now plug in these values to calculate the molar mass (M).