What is the osmotic pressure at 17°C of an aqueous solution containing 1.75 g of sucrose (molar mass = 342 g mol−1) in 150 mL of solution? (R = 0.0821 L atm K−1 mol−1)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.81 atm
For a dilute solution, the osmotic pressure π is proportional to the molar concentration C of the solute: π = CRT, where C = n/V (moles of solute per litre of solution).
Moles of sucrose: \( n=\frac{1.75\ \mathrm{g}}{342\ \mathrm{g\,mol^{-1}}}=5.12\times10^{-3}\ \mathrm{mol} \)
Volume: 150 mL = 0.150 L
Temperature: 17°C = 17 + 273 = 290 K
\( \displaystyle \pi=\frac{n}{V}RT \)
\( \displaystyle \pi=\frac{5.12\times10^{-3}\ \mathrm{mol}}{0.150\ \mathrm{L}}\times0.0821\ \mathrm{L\,atm\,K^{-1}\,mol^{-1}}\times290\ \mathrm{K} \)
\( \displaystyle \pi=0.81\ \mathrm{atm} \)