An aqueous fructose solution having a density of 1.049 g/cm³ is found to have an osmotic pressure of 17.0 atm at 25^$\circ$C. Find the temperature at which this solution freezes. [Given: for water K_f = 1.86 ^$\circ$C/m; molecular mass of fructose = 180.16 g/mol] A) -1.30^$\circ$C B) -1.41^$\circ$C C) -1.52^$\circ$C D) -1.57^$\circ$C E) -1.69^$\circ$C

Question

Quizplus · Accepted Answer

First, calculate the molarity of the fructose solution using the osmotic pressure formula $\pi = MRT$, where $\pi$ is the osmotic pressure (17.0 atm), $R$ is the gas constant (0.0821 L·atm/K·mol), and $T$ is the temperature in Kelvin (298K for 25°C). Solving for $M$, we get $M = \frac{\pi}{RT}$. Then, use the freezing point depression formula $\Delta T_f = K_f \cdot m$, where $K_f$ is the cryoscopic constant for water (1.86 °C/m) and $m$ is the molality of the solution. Since molality is moles of solute per kg of solvent, and given the density of the solution, convert the molarity to molality considering the volume and density of the solution. Finally, calculate the freezing point depression and subtract it from the normal freezing point of water (0°C) to find the freezing point of the solution. The calculations lead to a freezing point close to -1.41°C, making option B correct.

An Aqueous Fructose Solution Having a Density of 1 ∘\circ∘ C Find the Temperature at Which This Solution Freezes

An Aqueous Fructose Solution Having a Density of 1 $\circ$ C Find the Temperature at Which This Solution Freezes