Final answer:
To find the freezing point of a 5% glucose solution in water, you calculate the molality of a similar sugar solution, use the freezing point depression constant, and then adjust based on the different molar mass of glucose. Without specific masses or volumes, the exact freezing point cannot be determined from the options provided.
Step-by-step explanation:
To calculate the freezing point of a 5% glucose solution in water, we need to understand the colligative properties of solutions, particularly the freezing point depression. The freezing point depression (ΔTf) is given by the formula ΔTf = i * Kf * m, where 'i' represents the van't Hoff factor (number of particles the compound dissociates into, which for non-electrolytes like sugar is 1), 'Kf' is the freezing point depression constant for water (1.86°C/m), and 'm' is the molality of the solution.
Step 1: Calculate the molality (m) of the 5% cane sugar solution using its molar mass (342g/mol) and the given freezing point (271 K or -2.15°C). Assuming that the mass of the solution is 100g for simplicity, the mass of cane sugar is 5g, resulting in approximately 0.0146 mol. Since the mass of water would be 95g, this yields a molality of approximately 0.154 m.
Step 2: Using ΔTf = 1.86°C/m * 0.154 m for cane sugar, we get ΔTf to be about 0.286°C.
Step 3: Calculate the equivalent molality (0.154 m) for a 5% glucose solution by using its molar mass (180g/mol). This would result in more moles for the same mass percentage, leading to a higher freezing point depression.
Step 4: The new ΔTf for the glucose solution can then be calculated as 1.86°C/m * m (where m is greater than the molality calculated for cane sugar).
Step 5: Subtract the calculated ΔTf from the freezing point of pure water to find the freezing point of the 5% glucose solution in water.
Unfortunately, without the actual mass of the solution for the glucose, or additional data, it is not possible to carry out these calculations accurately. As such, we are not able to provide one of the answers as listed (A. 271.50K, B. 270.50K, C. 273.00K, D. 272.25K).