the average molar mass of polyethylene when 4.40 g of the polymer is dissolved in benzene to produce 200.0 mL of solution and the osmotic pressure is found to be ...
To calculate the average molar mass of polyethylene from the given information, we need to use the formula for osmotic pressure:
π = MRT
Where:
π = osmotic pressure in atmosphere (atm)
M = molarity of the solution in mol/L
R = ideal gas constant = 0.0821 L*atm/(mol*K)
T = temperature in Kelvin (K)
First, let's convert the volume of the solution from mL to L:
200.0 mL = 200.0/1000 L = 0.2000 L
Next, we need to calculate the molarity (M) of the solution. Molarity is defined as the number of moles of solute divided by the volume of the solution in liters.
M = moles of solute / volume of solution in liters
Since we know the mass of the polymer (4.40 g), we need to convert it to moles using the molar mass of polyethylene (CH₂) which is approximately 28 g/mol.
moles of polyethylene = mass / molar mass
moles of polyethylene = 4.40 g / 28 g/mol = 0.15714 mol
Now, we can calculate the molarity:
M = 0.15714 mol / 0.2000 L = 0.7857 M
Now, we can substitute the values into the osmotic pressure formula:
π = MRT
π = (0.7857 M) * (0.0821 L*atm/(mol*K)) * T
Unfortunately, we're missing the value for temperature (T). The osmotic pressure depends on temperature, so we need that information to complete the calculation.
Please provide the temperature (T) in Kelvin (K).
To find the average molar mass of polyethylene given the information about its solution and the osmotic pressure, we can use the formula:
Molar mass = (RT) / (V × π)
Where:
- Molar mass is the average molar mass of the polymer (in grams per mole, g/mol)
- R is the ideal gas constant, approximately 0.0821 L·atm/(mol·K)
- T is the temperature in Kelvin (K)
- V is the volume of the solution (in liters, L)
- π is the osmotic pressure (in atm)
However, in order to proceed with the calculations, we need the osmotic pressure value. Could you please provide the osmotic pressure value?