A solution prepared by adding 0.17 g of a

polymer to 0.6 L of toluene (methylbenzene, a
common solvent) showed an osmotic pressure
of 0.808 Torr at 21â—¦C. What is the molar mass
of the polymer?
Answer in units of g/mol.

pi = MRT

pi = 808 torr. Convert to atm.
M = ?
R = 0.08206
T = 21 C. Convert to kelvin.

Solve for molarity = M
Then M = mols/L with L = 0.6
Find mols. Finally, mol = grams/molar mass. You know mols and grams, solve for molar mass. Post your work if you get stuck.

I do not understand how to get the last step.

You solved for M in pi = MRT and you want to find molar mass.

M = mols/L. You know M from the above, you know L (0.6), solve for mols like this. mols = M x 0.6 = ?. Knowing mols, use mols = grams/molar mass, then molar mass = grams/mols.

To determine the molar mass of the polymer, we can use the equation for osmotic pressure:

π = MRT

Where:
π = osmotic pressure in atm
M = molar mass of the solute in g/mol
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature in Kelvin

First, let's convert the given osmotic pressure to atm:
1 Torr = 1/760 atm
So, 0.808 Torr = 0.808/760 atm = 0.00106316 atm

Next, convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T = 21°C + 273.15 = 294.15 K

Now, we rearrange the equation to solve for the molar mass of the polymer:
M = πRT / P

Substituting the given values:
M = (0.00106316 atm) * (0.0821 L·atm/(mol·K)) * (294.15 K) / (0.17 g) = 14165.68 g/mol

Therefore, the molar mass of the polymer is approximately 14165.68 g/mol.