A solution is made by mixing 42.0 mL of ethanol, C2H6O, and 58.0 mL of water. Assuming ideal behavior, what is the vapor pressure of the solution at 20 C in torr?
Values at 20C
ethanol density: 0.789 g/mL & vapor pressure (torr): 43.9 torr
water: denisty: 0.998 g/mL & 17.5 torr
Any steps would be GREATLY appreciated!
Hi Dr Bob, is this right so far?
mass h2o = (d)(v) = (0.998 g/mL)(58 mL) = 57.884 g
57.884 g H2O/18g H2O = 3.2157 mol H2O
mass ethanol = (0.789 g/mL)(42 mL) = 33.138 g
33.138 g C2H6O/46.0687 g C2H6O = 0.719 mol C2H6O
You are ok to here with moles.
You don't need molality. You want mole fraction. mole fraction EtOH = XEtOH = moles EtOH/total moles. mole fraction H2O = XH2O = moles H2O/total moles
Then pH2O = XH2O*PoH2O and
pEtOH = XEtOH*PoEtOH.
Total P = pH2O + pEtOH.
molality (m) = 0.71937 mol C2H6O/0.057884 kg H2O = 12.43 m
xH2O = 12.45/(12.43+3.2157) = 0.794
xEthanol = 12.43/(12.43 + 0.719) = 0.91
?
i got it! thanks Dr Bob
Calculate moles H2O.
Calculate moles EtOH.
Calculate XH2O
Calculate XEtOH.
Calculate pH2O
Calculate pEtOH.
Total P = pH2O + pEtOH
Hi Dr Bob, is this right so far?
mass h2o = (d)(v) = (0.998 g/mL)(58 mL) = 57.884 g
57.884 g H2O/18g H2O = 3.2157 mol H2O
mass ethanol = (0.789 g/mL)(42 mL) = 33.138 g
33.138 g C2H6O/46.0687 g C2H6O = 0.719 mol C2H6O
molality (m) = 0.71937 mol C2H6O/0.057884 kg H2O = 12.43 m
xH2O = 12.45/(12.43+3.2157) = 0.794
xEthanol = 12.43/(12.43 + 0.719) = 0.91
?
Well, mixing ethanol and water, huh? Sounds like a party solution to me!
To find the vapor pressure of the solution, we need to consider the individual contributions of ethanol and water to the total vapor pressure.
Step 1: Calculate the moles of ethanol and water in the solution.
Moles of ethanol = density of ethanol × volume of ethanol ÷ molar mass of ethanol
Moles of water = density of water × volume of water ÷ molar mass of water
Step 2: Calculate the mole fraction of each component.
Mole fraction of ethanol = moles of ethanol ÷ (moles of ethanol + moles of water)
Mole fraction of water = moles of water ÷ (moles of ethanol + moles of water)
Step 3: Calculate the partial pressure of each component.
Partial pressure of ethanol = mole fraction of ethanol × vapor pressure of ethanol
Partial pressure of water = mole fraction of water × vapor pressure of water
Step 4: Calculate the total vapor pressure.
Total vapor pressure = partial pressure of ethanol + partial pressure of water
Now, let's get down to business and calculate it!
Moles of ethanol = (0.789 g/mL) × (42.0 mL) ÷ (46.07 g/mol) = 0.861 mol
Moles of water = (0.998 g/mL) × (58.0 mL) ÷ (18.02 g/mol) = 3.228 mol
Mole fraction of ethanol = 0.861 mol ÷ (0.861 mol + 3.228 mol) = 0.210
Mole fraction of water = 3.228 mol ÷ (0.861 mol + 3.228 mol) = 0.790
Partial pressure of ethanol = 0.210 × 43.9 torr = 9.219 torr
Partial pressure of water = 0.790 × 17.5 torr = 13.775 torr
Total vapor pressure = 9.219 torr + 13.775 torr = 22.994 torr
So, the vapor pressure of the solution at 20°C is approximately 22.994 torr. Don't let it go to your head, though!
To find the vapor pressure of the solution at 20°C, we need to use Raoult's law. According to Raoult's law, the vapor pressure of a component in a solution is directly proportional to its mole fraction in the solution. The mole fraction, in turn, is calculated by dividing the number of moles of the component by the total number of moles in the solution.
Let's calculate the number of moles of ethanol and water:
Moles of ethanol = volume of ethanol (in mL) x density of ethanol (in g/mL) / molar mass of ethanol
Molar mass of ethanol (C2H6O) = 2 * atomic mass of carbon + 6 * atomic mass of hydrogen + atomic mass of oxygen
= (2 * 12.01 g/mol) + (6 * 1.008 g/mol) + 16.00 g/mol
= 46.07 g/mol
Moles of ethanol = 42.0 mL x 0.789 g/mL / 46.07 g/mol
Similarly, calculate the moles of water using its density (0.998 g/mL) and molar mass (18.02 g/mol).
Now, calculate the mole fraction of ethanol (Xethanol) and water (Xwater):
Xethanol = moles of ethanol / (moles of ethanol + moles of water)
Xwater = moles of water / (moles of ethanol + moles of water)
Next, use the mole fractions to find the partial pressures of ethanol (Pethanol) and water (Pwater):
Pethanol = Xethanol * vapor pressure of ethanol at 20°C
Pwater = Xwater * vapor pressure of water at 20°C
Finally, calculate the total vapor pressure of the solution (Pt):
Pt = Pethanol + Pwater
Substitute the given values for the vapor pressures of ethanol and water at 20°C and calculate the result.