Answer:
The correct answer is (d) 24.8 Torr
Explanation:
When a solute is added to a solvent, the water pressure of the solution is lower than the vapor pressure of the pure solvent. This is called <em>vapor pressure lowering</em> and it is given by the following expression:
Psolution= Xsolvent x Pºsolvent
We have to calculate Xsolvent (mole fraction of solvent) which is given by the number of moles of solute divided into the total number of moles.
First, we calculate the number of moles of solute and solvent. The solute is glucose (C₆H₁₂O₆), and its number of moles is calculated from the mass and the molecular weight (MM):
MM (C₆H₁₂O₆)= (12 g/mol x 6) + (1 g/mol x 12) + (16 g/mol x 6) = 180 g/mol
moles of glucose= mass/MM= (72.9 g)/)(180 g/mol)= 0.405 moles
The solvent is water (H₂O) and again we calculate the number of moles as follows:
MM(H₂O)= (1 g/mol x 2) + 16 g/mol = 18 g/mol
moles of water= mass/MM= (115 g)/(18 g/mol)= 6.389 moles
Now, we calculate the total number of moles (nt):
nt= moles of glucose + moles of water= 0.405 moles + 6.389 moles= 6.794 moles
The mole fraction of water (Xsolvent) is given by:
Xsolvent= moles of water/nt= 6.389 moles/6.794 moles= 0.940
Finally, the vapor pressure of water over the solution will be the following:
Psolvent= Xsolvent x Pºsolvent= 0.940 x 26.4 Torr= 24.8 Torr
the path length,
concentration of the solution.