What will be the vapor pressure at 25 degree C of a 30.0% (by mass) solution of glucose, C6H12O6 (a non-electrolyte-molar mass = 180 g/mol), in water? The vapor pressure of water at 25 degree C is 23.8 mm Hg.
Psolvent = XsolventPosolvent.
You will need to calculate the mol fraction, X of the solvent in 30.0% by mass glucose.
To calculate the vapor pressure of the solution, we need to determine the mole fraction of the solvent in the solution.
The mole fraction (X) of the solvent can be calculated by dividing the moles of the solvent by the total moles in the solution.
First, let's calculate the moles of glucose (C6H12O6) and water (H2O) in the solution.
Given:
Mass percentage of glucose in the solution = 30.0%
Molar mass of glucose (C6H12O6) = 180 g/mol
Vapor pressure of water at 25°C = 23.8 mm Hg
Step 1: Calculating the moles of glucose (C6H12O6):
Mass of glucose = (30.0/100) * Total mass of the solution
= (30.0/100) * Mass of solution
Step 2: Calculating the moles of water (H2O):
Mass of water = Total mass of the solution - Mass of glucose
= Mass of solution - Mass of glucose
Step 3: Calculating the mole fraction of the solvent (water):
Mole fraction (X solvent) = Moles of water / (Moles of glucose + Moles of water)
Step 4: Calculating the vapor pressure of the solution:
Vapor pressure of the solution (P solvent) = X solvent * P° solvent
Now we can follow these steps to find the solution.
Step 1: Calculating the moles of glucose (C6H12O6):
Mass of solution = 100 g (assuming a total mass of 100 g for simplicity)
Mass of glucose = (30.0/100) * 100 g = 30.0 g
Moles of glucose = Mass of glucose / Molar mass of glucose
Moles of glucose = 30.0 g / 180 g/mol = 0.16667 mol
Step 2: Calculating the moles of water (H2O):
Mass of water = Mass of solution - Mass of glucose
= 100 g - 30.0 g = 70.0 g
Moles of water = Mass of water / Molar mass of water
Molar mass of water = 18 g/mol (approximately)
Moles of water = 70.0 g / 18 g/mol = 3.8889 mol
Step 3: Calculating the mole fraction of the solvent (water):
Mole fraction (X solvent) = Moles of water / (Moles of glucose + Moles of water)
X solvent = 3.8889 mol / (0.16667 mol + 3.8889 mol) = 0.9581
Step 4: Calculating the vapor pressure of the solution:
Vapor pressure of the solution (P solvent) = X solvent * P° solvent
P solvent = 0.9581 * 23.8 mm Hg ≈ 22.83 mm Hg
Therefore, the vapor pressure of the 30.0% (by mass) solution of glucose in water at 25°C is approximately 22.83 mm Hg.