calculate the vapor pressureof a solution of 20.0g sucrose (C12H12O6) in 80.0g water at 25 degrees celsius (vapor pressure, P, of pure water at 25C is 24torr)
n sucrose = grams/molar mass
n H2O = grams/molar mass
XH2O = nH2O/total mols.
Psoln = XH2O*Popure water
To calculate the vapor pressure of a solution, we can use Raoult's law, which states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution.
First, let's calculate the mole fraction of water in the solution:
Moles of sucrose (C12H22O11) = mass / molar mass
Molar mass of sucrose (C12H22O11) = 342.3 g/mol
Moles of sucrose = 20.0 g / 342.3 g/mol ≈ 0.0583 mol
Moles of water = mass / molar mass
Molar mass of water (H2O) = 18.0 g/mol
Moles of water = 80.0 g / 18.0 g/mol ≈ 4.44 mol
Total moles in the solution = moles of sucrose + moles of water = 0.0583 mol + 4.44 mol = 4.4983 mol
Now, let's calculate the mole fraction of water:
Mole fraction of water = moles of water / total moles
Mole fraction of water = 4.44 mol / 4.4983 mol ≈ 0.986
According to Raoult's law, the vapor pressure of the solution (P) is equal to the mole fraction of water (X water) multiplied by the vapor pressure of pure water (P° water):
P = X water * P° water
Substituting the values:
P = 0.986 * 24 torr
Therefore, the vapor pressure of the solution of sucrose in water at 25 degrees Celsius is approximately 23.66 torr.