a .72g sample of polyvinyl chloride is dissolved in 250.0ml of a suitable solvent at 25C. the solution has an osmotic pressure of 1.67mmHg.What is the molar mass of the PVC?
pi = MRT
Solve for M
M = moles/L
Solve for moles.
moles = grams/molar mass
Solve for molar mass.
To find the molar mass of polyvinyl chloride (PVC), 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 solvent in liters
- R is the ideal gas constant (0.0821 L·atm/(K·mol))
- T is the temperature in Kelvin
First, convert the osmotic pressure to atm:
1.67 mmHg = 1.67/760 atm = 0.0022 atm
Convert the volume of the solvent to liters:
250.0 ml = 250.0/1000 L = 0.250 L
The temperature is given as 25°C, which needs to be converted to Kelvin:
T = 25°C + 273.15 = 298.15 K
Now, rearrange the equation to solve for the number of moles (n):
n = (πV)/(RT)
Substitute the values into the equation:
n = (0.0022 atm * 0.250 L) / (0.0821 L·atm/(K·mol) * 298.15 K)
Calculate n:
n = 0.0000234 mol
Next, we can calculate the molar mass (M) using the formula:
M = mass of solute (in grams) / number of moles
The mass of the solute is given as 0.72 g, so substitute the values into the equation:
M = 0.72 g / 0.0000234 mol
Calculate the molar mass:
M ≈ 30,769 g/mol
Therefore, the molar mass of polyvinyl chloride (PVC) is approximately 30,769 g/mol.
To find the molar mass of polyvinyl chloride (PVC), we can use the formula:
Molar mass = (RT) / (πV)
Where:
R is the ideal gas constant (0.0821 L·atm/(mol·K) or 8.314 J/(mol·K))
T is the temperature in Kelvin (25°C = 298 K)
π is the osmotic pressure in atmospheres (1.67 mmHg = 0.0022 atm)
V is the volume of the solution in liters (250.0 mL = 0.250 L)
First, let's convert the osmotic pressure to atmospheres:
1 mmHg = 0.00131579 atm
So, 1.67 mmHg = 1.67 * 0.00131579 atm = 0.0022 atm
Now, let's substitute the values into the formula:
Molar mass = (0.0821 * 298) / (0.0022 * 0.250)
Next, we need to determine the number of moles (n) of PVC in the solution.
The relationship between moles, mass, and molar mass is given by:
Moles = Mass / Molar mass
n = (0.72 g) / (Molar mass)
Now, we can substitute this relationship into the equation:
Molar mass = (0.0821 * 298) / (0.0022 * 0.250) * (0.72 g) / (Molar mass)
Now we can solve for Molar mass by cross multiplying:
Molar mass * (0.0821 * 298) = (0.0022 * 0.250) * (0.72 g)
Molar mass = [(0.0022 * 0.250) * (0.72 g)] / (0.0821 * 298)
Using a calculator to evaluate the right side of the equation, we find:
Molar mass ≈ 29.98 g/mol
Therefore, the molar mass of PVC is approximately 29.98 g/mol.