A polymer solution of concentration $2.0 g L^{- 1}$ at $300 K$ supports a column of solution rising by $1.02 cm$ above the solvent in an osmometer. Take solution density $1000 kg m^{- 3}$ , $g = 9.8 m s^{- 2}$ and $R = 8.314 J mo l^{- 1} K^{- 1}$ . The molar mass of the polymer (in $g mo l^{- 1}$ ) is closest to

Answer: A

The hydrostatic pressure equals

π

π = ρ g h = 1000 \times 9.8 \times 0.0102 = 100.0

Pa. Concentration

= 2000

g/m

^{3}

= 2000/ M

mol/m

^{3}

, and

π = (2000/ M) RT

. So

M = 2000 \times 8.314 \times 300/100.0 = 49904 g mo l^{- 1} \approx 5.0 \times 1 0^{4}