The solution containing 4g of polyvinyl chloride polymer in 1L of dioxane was found to have an osmotic pressure of 6 × 10^–4 atm at 300K. Molecular mass of polymer is?
[Give answer in multiple of 10⁵, rounded up to one decimal places]
Correct answer is between '1.5,1.7'. Can you explain this answer?

Question

The solution containing 4g of polyvinyl chloride polymer in 1L of dioxane was found to have an osmotic pressure of 6 × 10^–4 atm at 300K. Molecular mass of polymer is?
[Give answer in multiple of 10⁵, rounded up to one decimal places]

Correct answer is between '1.5,1.7'. Can you explain this answer?

Answer

Answer

The osmotic pressure of a solution can be calculated using the formula:

π = (n/V)RT

Where:
π = osmotic pressure
n = number of moles of solute
V = volume of solution
R = ideal gas constant
T = temperature in Kelvin

In this case, we are given that the solution contains 4g of polyvinyl chloride polymer. To calculate the number of moles of solute, we need to know the molar mass of polyvinyl chloride.

The molar mass of polyvinyl chloride is approximately 62.5 g/mol.

Number of moles of polyvinyl chloride = mass of polyvinyl chloride / molar mass of polyvinyl chloride
Number of moles of polyvinyl chloride = 4g / 62.5 g/mol
Number of moles of polyvinyl chloride = 0.064 mol

The volume of the solution is given as 1L.

Now we can substitute the values into the osmotic pressure formula:

π = (n/V)RT
π = (0.064 mol / 1L) * (0.0821 L atm / mol K) * T

Given that the osmotic pressure is 6 atm, we can rearrange the equation to solve for T:

T = (π * V) / (n * R)
T = (6 atm * 1L) / (0.064 mol * 0.0821 L atm / mol K)
T = 1120 K

Therefore, the temperature of the solution is 1120 Kelvin.

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