A macromolecular colloid is dissolved at 5.00 g L^-1 in water and gives an osmotic pressure of 118.0 Pa at 298 K. Using pi = cRT with c in mol m^-3 and R = 8.314 J mol^-1K^-1, find the molar mass in g mol^-1, to the nearest integer.

JEE Main levelNumerical answerDifficulty 2 of 3sc141

A macromolecular colloid is dissolved at $5.00 g L^{- 1}$ in water and gives an osmotic pressure of $118.0 Pa$ at $298 K$ . Using $π = c RT$ with $c$ in $mol m^{- 3}$ and $R = 8.314 J mo l^{- 1} K^{- 1}$ , find the molar mass in $g mo l^{- 1}$ , to the nearest integer.

Numerical answer type, answer in g/mol, tolerance 5.

Mass concentration =

5.00 kg m^{- 3}

and

π = (w / M) RT

, so

M = wRT / π

M = 5.00 \times 8.314 \times 298/118.0 = 104.98 kg mo l^{- 1}

. This is about

1.05 \times 1 0^{5} g mo l^{- 1}

, i.e. 104982.