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(B) The osmotic pressure $\pi$ is given by $\pi = h \cdot d \cdot g$,where $h$ is the height of the solution column,$d$ is the density,and $g$ is the

Vedclass · Accepted Answer

$25.2 	imes 10^3 \, g/mol$

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(B) The osmotic pressure $\pi$ is given by $\pi = h \cdot d \cdot g$,where $h$ is the height of the solution column,$d$ is the density,and $g$ is the acceleration due to gravity.Given: $h = 11 \, cm = 0.11 \, m$,$d = 0.9 \, g/mL = 900 \, kg/m^3$,$C = 10 \, g/L = 10/M \, mol/L = 10/M 	imes 10^3 \, mol/m^3$,$T = 27 + 273 = 300 \, K$,$R = 8.314 \, J/(mol \cdot K)$.Using $\pi = CRT$:$h \cdot d \cdot g = (C/M) \cdot R \cdot T$$0.11 	imes 900 	imes 9.8 = (10/M) 	imes 10^3 	imes 8.314 	imes 300$$970.2 = (24942000 / M)$$M = 24942000 / 970.2 \approx 25708 \, g/mol$.Using the standard approximation $\pi = h \cdot d \cdot g$ and converting units to $atm$:$\pi = (11 \, cm 	imes 0.9 \, g/mL) / (13.6 \, g/mL 	imes 76 \, cm) \approx 0.00958 \, atm$.Using $\pi = CRT$ with $C = 10/M \, g/L$:$0.00958 = (10/M) 	imes 0.0821 	imes 300$$M = (10 	imes 0.0821 	imes 300) / 0.00958 \approx 25.2 	imes 10^3 \, g/mol$.

$A$ solution of polystyrene in benzene contains $10 \, g/L$. The equilibrium height of the column of solution having density $0.9 \, g/mL$ in the osmometer is $11 \, cm$ at $27 \, ^\circ C$. What is the average molar mass of polystyrene? (Assume the solution is ideal)

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