At 21.0 °C, a solution of 23.71 g of a nonvolatile, nonpolar compound in 30.64 g of ethylbromide, C2H5Br, had a vapor pressure of 319.7 torr. The vapor pressure of pure ethyl bromide at this temperature is 400.0 torr. Assuming an ideal solution, what is the molecular mass of the compound?
pEtBr = XEtBr*PoEtBr
319.7 = X*400
XEtBr = about 0.8 (estimated) see last post.
Xunk = 1-about 0.8 = about 0.2
mols unk = 23.71/molar mass or 23.71/Y.
mols EtBr = 30.64/109 = about 0.281
Then Xunk = mols unk/total mols.
0.2 = [(23.71g/Y)/(23.71Y)+(0.281)]
and solve for Y = molar mass unknown.
How do I solve for the y? I get
0.2=23.71g / 24.71+.281
Y. Y
But I don't know how to solve
Then Xunk = mols unk/total mols.
0.2 = [(23.71g/Y)/(23.71Y)+(0.281)]
and solve for Y = molar mass unknown.
I made a typo in the above. It should be
0.2 = [23.71/Y/(23.71/Y)+ (0.281)].
First the numerator = 0.2*denominator.
23.71/Y = [0.2*(23.71/Y) + (0.281)]
23.71/Y = (4.74/Y)+ 0.0562
Multiply through by Y
23.71 = 4.74 + 0.0562Y
23.71-4.74 = 0.0562Y = 18.97
Y = 18.97/0.0562 = 337.5 = molar mass of unknown.
You can check that, and should.
molar mass ethyl bromide = about 109
molar mass unknownh = about 337.5
mols ethyl bromide 30.64/109 = 0.281
mols unknown = 23.71/337.5 = 0.0702
total mols = sum = 0.351
Then Xethylbromide = 0.281/0.351 = 0.800
and
Xunknown = 0.0702/0.351 = 0.200
so it checks.
To find the molecular mass of the compound, we need to use Raoult's law, which relates the vapor pressure of a solution to the vapor pressure of the pure solvent and the mole fraction of the solute.
The equation for Raoult's law is:
Psolvent = Xsolvent * Psolvent°
Where:
Psolvent is the vapor pressure of the solvent in the solution
Xsolvent is the mole fraction of the solvent in the solution
Psolvent° is the vapor pressure of the pure solvent
In this case, the solvent is ethyl bromide (C2H5Br). We are given the vapor pressure of the solution (319.7 torr), the vapor pressure of the pure solvent (400.0 torr), and the mass of the solvent (30.64 g).
Let's calculate the mole fraction of the solvent first:
Mole fraction of solvent (Xsolvent) = moles of solvent / total moles in the solution
Moles of solvent can be calculated using the formula:
moles of solvent = mass of solvent / molar mass of solvent
The molar mass of ethyl bromide (C2H5Br) is calculated as:
Molar mass of ethyl bromide = (2 * atomic mass of carbon) + (5 * atomic mass of hydrogen) + atomic mass of bromine
Now let's calculate the mole fraction of the solvent:
Moles of solvent = 30.64 g / molar mass of ethyl bromide
Moles of solute (compound) = 23.71 g / molar mass of compound
Total moles in the solution = moles of solvent + moles of solute
Mole fraction of solvent (Xsolvent) = moles of solvent / total moles
Finally, we can use Raoult's law to find the molecular mass of the compound:
Psolvent = Xsolvent * Psolvent°
Psolvent° = (molality of solvent in solution) * Psolvent° of pure solvent
Let's calculate all the values and find the molecular mass of the compound.