A closed bottle contains a solution of 5.0% by mass acetone [(CH3)2CO] in water. Calculate the vapour pressure (in kPa) of this solution at 25oC. The vapour pressure of pure water at 25oC is 3.17 kPa and that of pure acetone is 30.7 kPa.
To calculate the vapor pressure of the solution at 25°C, we can use Raoult's law, which states that the vapor pressure of a component in a solution is proportional to its mole fraction.
The mole fraction of acetone (CH3)2CO) in the solution can be calculated using the mass percent of acetone and the molar masses of acetone and water.
Step 1: Calculate the mole fraction of acetone (xCH3CO):
Mass percent of acetone = 5.0%
Mass percent of water = 100% - 5.0% = 95%
Assuming we have 100g of the solution:
- Mass of acetone (CH3CO) = 5.0g
- Mass of water = 95g
Molar mass of acetone (CH3CO) = 58.08 g/mol
Molar mass of water = 18.01528 g/mol
Number of moles of acetone (nCH3CO) = Mass of acetone / Molar mass of acetone
= 5.0g / 58.08 g/mol
= 0.086 mol
Number of moles of water (nH2O) = Mass of water / Molar mass of water
= 95g / 18.01528 g/mol
= 5.274 mol
Total moles in the solution (nTotal) = nCH3CO + nH2O
= 0.086mol + 5.274mol
= 5.36 mol
Mole fraction of acetone (xCH3CO) = nCH3CO / nTotal
= 0.086mol / 5.36 mol
= 0.016
Step 2: Calculate the vapor pressure of the solution using Raoult's Law:
Vapor pressure of solution = Vapor pressure of pure acetone (CH3CO) × Mole fraction of acetone (xCH3CO) + Vapor pressure of pure water × Mole fraction of water (xH2O)
Vapor pressure of solution = (30.7 kPa × 0.016) + (3.17 kPa × 0.984)
= 0.4912 kPa + 3.11728 kPa
= 3.60848 kPa
Therefore, the vapor pressure of the solution at 25°C is approximately 3.61 kPa.
To calculate the vapor pressure of the solution, we can use Raoult's law, which states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent in the solution.
First, let's determine the mole fraction of water and acetone in the solution:
Step 1: Calculate the moles of water and acetone in the solution.
We are given that the solution is 5.0% acetone by mass. Assuming we have 100 grams of the solution, this means we have 5 grams of acetone and 95 grams of water.
To calculate the moles of each component, we need to know their molar masses. The molar mass of water (H2O) is approximately 18.02 g/mol, and the molar mass of acetone ((CH3)2CO) is approximately 58.08 g/mol.
The moles of acetone can be calculated as follows:
moles acetone = mass acetone / molar mass acetone
moles acetone = 5 g / 58.08 g/mol
moles acetone = 0.0859 mol
The moles of water can be calculated as follows:
moles water = mass water / molar mass water
moles water = 95 g / 18.02 g/mol
moles water = 5.274 mol
Step 2: Calculate the mole fraction of acetone and water.
The mole fraction of a component in a solution is the ratio of the number of moles of the component to the total number of moles in the solution.
mole fraction acetone = moles acetone / (moles acetone + moles water)
mole fraction acetone = 0.0859 mol / (0.0859 mol + 5.274 mol)
mole fraction acetone = 0.0159
mole fraction water = moles water / (moles acetone + moles water)
mole fraction water = 5.274 mol / (0.0859 mol + 5.274 mol)
mole fraction water = 0.9841
Step 3: Calculate the vapor pressure of the solution using Raoult's law.
According to Raoult's law, the vapor pressure of the solution is the sum of the partial pressures of the solvent and solute.
P_solution = (mole fraction water) * (vapor pressure of water) + (mole fraction acetone) * (vapor pressure of acetone)
P_solution = (0.9841) * (3.17 kPa) + (0.0159) * (30.7 kPa)
P_solution = 3.124 kPa + 0.487 kPa
P_solution = 3.611 kPa
Therefore, the vapor pressure of the solution at 25oC is approximately 3.611 kPa.
If you assume this is an ideal solution. Take 100 g solution.
mass acetone = 5g
mols acetone = 5/molar mass = ?
mass H2O = 95 g
mols H2O = 95/molar mass H2O = ?
total mols = mols acetone = mols H2O = ?
Xacetone = mols fraction acetone = nacetone/total mols
xH2O = nH2O/total mols.
pacetone = Xacetone*Poacetone
pH2O = XH2O*PoH2O
Total P = pacetone + pH2O