The vapor pressure of diethyl ether is 463.57 mm Hg at 25 degrees celsius. How many grams of aspirin C9H8O4, a non volatile nonelectrolyte (mw=180.1g/mol), must be added to 216.7g of ether to reduce the vapor pressure to 453.74 mm Hg.
Ether=74.12g/mol
so I did 463.57 - 453.74 = 7.600
Then I found moles of ether to be 4.0313.
I do not understand the next step to find Xether.
You had better subtract again. 7.600 is not right.
You need the mole fraction of ether. You get that by
pether = Xether*Po ether
You know partial pressure of ether to be 453.74 (that's what you want it to be)
You know Po ether to be 463.57. Solve for Xether.
I subtracted again and got 9.83.
So do I set it up like this
453.74= Xether * 463.57
Disregard question.
To find the amount of ether (diethyl ether, C4H10O) that needs to be added, we can set up the following equation:
(P1 * V1) / n1 = (P2 * V2) / n2
Where:
P1 = initial vapor pressure of ether (463.57 mm Hg)
V1 = volume of ether (unknown, since we are looking for Xether)
n1 = moles of ether (4.0313 moles, which you've calculated correctly)
P2 = final desired vapor pressure of ether (453.74 mm Hg)
V2 = volume of ether + volume of aspirin (216.7 g, given in the question)
n2 = moles of ether + moles of aspirin (unknown)
Now, let's solve for Xether:
(P1 * V1) / n1 = (P2 * V2) / n2
We know P1, V1, and n1. We also know P2, V2, and want to solve for n2.
Rearrange the equation to solve for n2:
n2 = (P2 * V2 * n1) / (P1 * V1)
Now, substitute the known values:
n2 = (453.74 mm Hg * 216.7 g * 4.0313 moles) / (463.57 mm Hg * Xether moles)
Now, rearrange the equation again to solve for Xether:
Xether = (453.74 mm Hg * 216.7 g * 4.0313 moles) / (463.57 mm Hg * n2)
To find the value of n2, we can use the molecular weight of aspirin and the given mass of aspirin:
n2 = (mass of aspirin in grams) / (molecular weight of aspirin in g/mol)
Substitute the values:
n2 = (Xg of aspirin) / (180.1 g/mol)
Substitute this value of n2 back into the equation for Xether:
Xether = (453.74 mm Hg * 216.7 g * 4.0313 moles) / (463.57 mm Hg * (Xg of aspirin / 180.1))
Now, plug in the values and solve for Xether:
Xether = (453.74 mm Hg * 216.7 g * 4.0313 moles) / (463.57 mm Hg * (Xg of aspirin / 180.1))
After calculating this expression, you will find the value of Xether, which represents the mass of ether needed to reduce the vapor pressure to 453.74 mm Hg.