Answer:
22.55 mmHg (0.03 atm)
Step-by-step explanation:
According to Raoult's law, the vapor pressure (Psolution) of a solution is given by:
Psolution = Xsolvent x Psolvent
Where Xsolvent is the mole fraction of the solvent in the solution and Psolvent is the vapor pressure of the pure solvent.
From the data, we have: Psolvent = 25.76 mmHg
We have to calculate Xsolvent, which is equal to the moles of solvent divided into the total number of moles.
The solution is composed of the solute (glucose) dissolved in the solvent (water). So, the total number of moles is calculated from the moles of solute and solvent.
To calculate the moles of solute (glucose), we divide the mass of glucose into its molar mass:
moles of glucose = mass/molar mass = 550 g/(180.2 g/mol) = 3.05 mol
The same for the moles of solvent (water). The mass of water is obtained from the product of the volume and density:
mass of water = volume x density = 1020.0 mL x 1.00 g/mL = 1020.0 g
molar mass H₂O = (1 g/mol x 2) + 16 g/mol = 18 g/mol
moles of water = mass water/molar masss = 1020.0 g/(18 g/mol) = 56.67 mol
Now, we can calculate Xsolvent:
Xsolvent = moles of water/total moles
total moles = moles glucose + moles water = 3.05 mol + 56.67 mol = 59.72 mol
⇒ Xsolvent = 56.67 mol/(59.72 mol) = 0.9489
Finally, we calculate the vapor pressure of the solution:
Psolution = 0.9489 x 23.76 mmHg = 22.55 mmHg
22.55 mmHg x 1 atm/760 mmHg = 0.03 atm