A solution is made by mixing 38.0 mL of ethanol, C2H6O, and 62.0 mL of water. Assuming ideal behavior, what is the vapor pressure of the solution at 20 °C?
To find the vapor pressure of the solution at 20 °C, we can use Raoult's Law, which states that the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
Step 1: Calculate the mole fraction of ethanol (C2H6O):
Mole fraction = moles of ethanol / total moles of solution
To calculate the moles of ethanol, we need to know the density of ethanol and its molar mass. Given that the density of ethanol is 0.789 g/mL and its molar mass is 46.07 g/mol, we can calculate the moles of ethanol as follows:
Moles of ethanol = (Volume of ethanol in mL) x (density of ethanol in g/mL) / (molar mass of ethanol in g/mol)
= (38.0 mL) x (0.789 g/mL) / (46.07 g/mol)
Step 2: Calculate the moles of water:
Moles of water = (Volume of water in mL) x (density of water in g/mL) / (molar mass of water in g/mol)
= (62.0 mL) x (1.00 g/mL) / (18.02 g/mol)
Step 3: Calculate the total moles of the solution:
Total moles of solution = moles of ethanol + moles of water
Step 4: Calculate the mole fraction of ethanol:
Mole fraction of ethanol = Moles of ethanol / total moles of solution
Step 5: Find the vapor pressure of ethanol at 20 °C:
The vapor pressure of pure ethanol at 20 °C is 43.9 mmHg.
Step 6: Calculate the vapor pressure of the solution:
Vapor pressure of the solution = Mole fraction of ethanol x Vapor pressure of pure ethanol at 20 °C
By following these steps and plugging in the numbers, you should be able to calculate the vapor pressure of the solution at 20 °C.
You will need density to convert to grams, then convert to mols ethanol and mol H2O.
mol fraction EtOH = XEtOH = nEtOH/total mols
XH2O = nH2O/total mols.
Then pH2O = XH2O*PoH2O
pEtOH = XEtOH*PoEtOH</sb>
Ptotal = pEtOH + pH2O