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Calculate the vapor pressure of water over a solution made by dissolving 225 g of glucose in 575 g of water at 35°C. (At 35°C, [tex]P^{\circ} = 42.2 \, \text{mmHg}[/tex])

A. 37.6 mmHg
B. 45.2 mmHg
C. 52.8 mmHg
D. 60.4 mmHg

Answer :

Final answer:

To calculate the vapor pressure of the solution, we can use Raoult's law. According to Raoult's law, the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent. In this case, we need to calculate the mole fraction of water and use the given vapor pressure of pure water to obtain the vapor pressure of the solution. The vapor pressure of the water over the solution is approximately 40.58 mmHg.

Explanation:

To calculate the vapor pressure of the solution, we can use Raoult's law. According to Raoult's law, the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent. The mole fraction of the solvent (water) can be calculated by dividing the moles of water by the total moles of solute and solvent.

First, we need to calculate the number of moles of glucose and water using their respective molar masses. The molar mass of glucose (C6H12O6) is 180.16 g/mol and the molar mass of water is 18.015 g/mol. moles of glucose = mass of glucose / molar mass of glucose = 225 g / 180.16 g/mol = 1.249 mol. moles of water = mass of water / molar mass of water = 575 g / 18.015 g/mol = 31.92 mol. The total moles of solute and solvent is the sum of the moles of glucose and water, which is 1.249 mol + 31.92 mol = 33.169 mol. Now we can calculate the mole fraction of water: mole fraction of water = moles of water / total moles = 31.92 mol / 33.169 mol = 0.963

Lastly, using Raoult's law, we can calculate the vapor pressure of the solution: vapor pressure of the solution = mole fraction of water × vapor pressure of pure water at the given temperature = 0.963 × 42.2 mmHg = 40.58 mmHg. Therefore, the vapor pressure of the water over the solution is approximately 40.58 mmHg, which is closest to option a) 37.6 mmHg.

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