Question

A solution containing 4g of polymer in a 4.0-litre solution at 27°C shows an osmotic pressure of 3.0×10-4 atm. The molar mass of the polymer in g/mol is

• A. 820000
• B. 82000
• C. 8200
• D. 820

Answer 1

Answer: (B)

82000

Answer 2

The osmotic pressure (π) of a solution is given by the formula:

π =Vn ​ RT ,

where n is the number of moles of solute, V is the volume of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

In this case, we are given that the osmotic pressure (π) is 3.0×10−43.0×10−4 atm, the volume (V) is 4.0 liters, and the temperature (T) is 27°C = 300 K.

We need to find the number of moles (n) of the polymer. Given that the mass of the polymer is 4 g, we can use its molar mass (M) to calculate n using the formula:

n =molar massmass​.

Substituting the values:

n =M 4g​.

Now, we can substitute the values of n , V , R , and T into the osmotic pressure formula and solve for M :

π =Vn ​ RT.

3.0×10−4 atm=4 g4.0 L××300 K3.0×10−4atm=4.0L M 4g​​× R ×300K.

Solving for M :

3.0×10−4atm×4.0L× R ×300K4g​.

Given that R is the ideal gas constant, which is approximately 0.08206 L atm/mol K0.08206L atm/mol K, we can substitute its value:

M=4 g3.0×10−4 atm×4.0 L×0.08206 L atm/mol K×300 K M =3.0×10−4atm×4.0L×0.08206L atm/mol K×300K4g​.

Solving for M :

M=82000 g/mol M =82000g/mol.

Hence, the molar mass of the polymer is approximately 82000 g/mol, which matches the given answer.

The correct option is(B): 82000