How many grams of sucrose (C₁₂H₂₂O₁₁, 342.3 g/mol) would be needed to make 2.5 L of a solution with an osmotic pressure of 14 atm at 25^$\circ$C (R = 0.0821 L·atm/K·mol) A) 0.57 g B) 6.8 g C) 2.0 * 10² g D) 4.9 * 10² g E) 5.8 * 10³ g

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Quizplus · Accepted Answer

To find the grams of sucrose needed, use the formula for osmotic pressure: $\pi = MRT$, where $\pi$ is the osmotic pressure, $M$ is the molarity, $R$ is the gas constant, and $T$ is the temperature in Kelvin. First, convert the temperature to Kelvin: $25^\circ C = 298 K$. Then, rearrange the formula to solve for $M$: $M = \frac{\pi}{RT}$. Plugging in the values gives $M = \frac{14}{0.0821 \times 298}$. This results in a molarity of approximately $0.57 M$. To find the grams of sucrose needed, multiply the molarity by the volume of the solution in liters and the molar mass of sucrose: grams = $0.57 M \times 2.5 L \times 342.3 g/mol$, which gives approximately $4.9 \times 10^2 g$.

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How Many Grams of Sucrose (C₁₂H₂₂O₁₁, 342 $\circ$ C (R = 0