Question

Q3. At 20 °C, the osmotic pressure of a polycarbonate was measured in chlorobenzene solution with the following results: Concentration (g/L) 1.95 2.93 3.915.86 Height of chlorobenzene (cm 0.20 0.36 0.53 0.98 Solvent density = 1.10 g/cm, polymer density = 1.20 g/cm3] Estimate the number average molecular weight Mn [Rz 8314 x 107 erg mol-1KY. (10 marks)

Answer 1

We will follow the following relation

π / c = RT / M + A2c

Where

π = osmotic pressure = height of chlorobenzene X density X acceleration due to gravity = hrg

g = acceleration due to gravity = 980 cm / second²

c = concentration (g / L)

R= gas constant = 8.314 X 10⁷ erg / mol K

M = molar mass of polymer = ?

T = temperature = 293 K

A2= viral coeffecient

Therefore

$\frac{h\rho g }{c}= \frac{RT}{M} + A_{2}c$

Or

$\frac{h }{c}= \frac{RT}{\rho gM} + \frac{A_{2}c}{\rho g}$

so if we plot a graph between h/c v/s c we will get intercept = $\frac{RT}{\rho gM}$

From which we can calculate the molar mass

concentration (g/L)	conce (g/mL)	height	h/c
1.95	0.00195	0.2	102.5641
2.93	0.00293	0.36	122.8669
3.91	0.00391	0.53	135.5499
5.86	0.00586	0.98	167.2355

The equation is

y = 16198x + 72.72

Here intercept = 72.72 = $\frac{RT}{\rho gM}$

Molar mass = 8.314 X 10⁷ X 293 / 1.10 X 9.8 X 10² X 72.72

Molar mass = 310745.61 g / mole