In a study designed to prepare new gasoline resistant coatings, a polymer chemist dissolves 6.053g of poly in enough water to make 100.0 mL of solution. At 25C, the osmotic pressure of this solution is 0.272 atm. What is the molar mass of the polymer sample?

To find the molar mass of the polymer sample, we can use the formula for osmotic pressure:

π = MRT

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

First, we need to convert the temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15
T(K) = 25 + 273.15 = 298.15 K

Next, we need to calculate the molar concentration (M):

M = (π) / (RT)

π = 0.272 atm
R = 0.0821 L·atm/(mol·K)
T = 298.15 K

M = (0.272 atm) / (0.0821 L·atm/(mol·K) * 298.15 K)

M = 0.272 / (24.47)

M = 0.0111 M

Now that we have the molar concentration (M) and the mass (grams) of the polymer (6.053 g), we can calculate the molar mass (Molar mass = mass / moles):

Molar mass = mass / moles

moles = mass / molar mass

Molar mass = 6.053 g / 0.0111 M

Molar mass = 546.85 g/mol

Therefore, the molar mass of the polymer sample is approximately 546.85 g/mol.

To find the molar mass of the polymer sample, we need to use the equation for osmotic pressure:

π = MRT

Where π is the osmotic pressure, M is the molar concentration, R is the ideal gas constant, and T is the temperature in Kelvin.

First, let's convert the given temperature from Celsius to Kelvin:

T = 25°C + 273.15 = 298.15 K

Next, we need to calculate the molar concentration (M) of the solution. Molar concentration is defined as moles of solute divided by volume of solution in liters:

M = moles of solute / volume of solution (in L)

First, we need to find the moles of solute. The solute in this case is the polymer, which weighs 6.053 grams.

To convert grams to moles, we need to divide the mass by the molar mass of the polymer. Let's call the molar mass of the polymer "Mm".

moles of solute = mass of polymer / molar mass of the polymer

Now, we can substitute this into the molar concentration equation:

M = (mass of polymer / molar mass of the polymer) / volume of solution (in L)

The volume of the solution is given as 100.0 mL, which is equal to 0.1 L.

Now we have all the information to find the molar mass (Mm). Rearranging the osmotic pressure equation, we get:

Mm = π / (RT)

Substituting the values we have:

Mm = (0.272 atm) / (0.0821 L·atm/mol·K * 298.15 K)

Now we can solve for Mm:

Mm = 0.272 atm / (24.455 L·mol⁻¹)

Mm ≈ 0.0111 mol L⁻¹

Thus, the molar mass of the polymer sample is approximately 0.0111 kg/mol.

pi = MRT

pi = 0.272 atm, you know R and T, calculate M = molarity.
M = moles/L. Knowing M and L, calculate moles. Then use moles = grams/molar mass to calculate molar mass.