find 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 be7.60 torr ant 25 celcious Degree.

pi = MRT. Remember to convert pi from torr to atm. Solve for M = molarity, then

M = mols/L and solve for mols in the 200 mL. Finally, mols = grams/molar mass. You have mols and grams, solve for molar mass.

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To find the average molar mass of polyethylene, we need to use the equation for osmotic pressure. The equation is:

π = CRT

Where:
π = osmotic pressure in Pascals
C = concentration in mol/L
R = ideal gas constant (8.314 J/(mol·K))
T = temperature in Kelvin

First, let's convert the osmotic pressure from torr to Pascals:
1 torr = 133.322 Pa

So, 7.60 torr = 7.60 x 133.322 Pa = 1016.4512 Pa

Next, we need to calculate the concentration of the polymer in mol/L. We know that 4.40 g of the polymer is dissolved in 200.0 mL of solution. We need to convert the volume to L and use the formula:

C = (m/M) / V

Where:
C = concentration in mol/L
m = mass of the polymer in grams
M = molar mass of the polymer in g/mol
V = volume of the solution in L

First, let's convert the volume to liters:
200.0 mL = 200.0/1000 = 0.200 L

Now we can calculate the concentration:
C = (4.40 g / M) / 0.200 L

To find M, the molar mass of polyethylene, we need to know the molecular formula of polyethylene. Let's assume it is the simplest form, which is (CH2)n. The molar mass of carbon (C) is approximately 12.01 g/mol, and the molar mass of hydrogen (H) is approximately 1.01 g/mol.

So the molar mass of polyethylene is approximately M = 2n * 1.01 g/mol + n * 12.01 g/mol

Now we can substitute the values and simplify the concentration equation:

C = (4.40 g / [(2n * 1.01 g/mol) + (n * 12.01 g/mol)]) / 0.200 L

Simplifying further:

C = (4.40 g / [(2.02n + 12.01n) g/mol]) / 0.200 L
C = (4.40 g / [14.03n g/mol]) / 0.200 L
C = (22.0 / [14.03n]) mol/L
C = 1.567 / n mol/L

Now we can substitute the values in the osmotic pressure equation and solve for n:

π = CRT
1016.4512 Pa = (1.567 / n) mol/L * 8.314 J/(mol·K) * (25 + 273.15) K
1016.4512 = 340.965 / n
n = 340.965 / 1016.4512

Finally, we can calculate the average molar mass using the derived value of n. We substitute n back into the molar mass equation:

M = 2n * 1.01 + n * 12.01
M = (2 * [340.965 / 1016.4512]) * 1.01 + ([340.965 / 1016.4512]) * 12.01

Simplifying the equation will give you the average molar mass of polyethylene.