Partial pressures and mole fractions

[johnny b]

Homework Statement

A solution of ethanol (eth) and chloroform (chl) at 45°C with xeth = 0.9900 has a vapor pressure of 177.95 torr. At this high dilution of chloroform, the solution can be assumed to be ideally dilute. The vapor pressure of pure ethanol at 45°C is 172.76 torr.
(a) Find the partial pressures of the gases in equilibrium with the solution
(b) Find the mole fractions in the vapor phase
(c) Find the Henry’s Law constant for chloroform in ethanol at 45°C
(d) Predict the vapor pressure and vapor-phase mole fractions at 45°C for a chloroform-ethanol solution with xeth = 0.9800. Compare with the experimental values P = 183.38 torr and =0.9242.

Homework Equations

partial pressure = total pressure x mole fraction
X(gas) = P / P(total)
Total vapor pressure = (X(eth)*P(eth)) + (X(chl)*P(chl))
K=P/x (henry's law constant)

The Attempt at a Solution

For part a, if I use the equation partial pressure = total pressure x mole fraction I get
p(eth)=0.99(177.95) --> p(eth)=171.0324 torr. x(chl)= 1-.99=.01
p(chl)=.01(177.95) --> (chl)=1.7276 torr.
is this right?

For part b assuming part a is right,
X(eth) = P(eth) / P(total)
x(eth)=(171.0324)/177.95 = 0.961
x(chl) 1-.961 = .039

part c:
Total vapor pressure = (X(eth)*P(eth)) + (X(chl)*P(chl))
177.95torr = (0.99*172.76) + (.01*P(chl))
P(chl)=691.76 torr = 0.910atm
K=P(chl)/x
K=0.910 atm/.01 = 91 atm <--- the x that I use is .01 right? not the .039 that I found in part b?

d:
This one I'm not sure about. The only thing I could think of is from the given part:
177.95 torr / .9900 = p / .9800
then p= 176.15 but this doesn't seem right and I don't know how to find the vapor-phase mole fractions

Sorry it's so much but I really want to make sure I'm doing this right. Any help is appreciated!

 

[Borek]

partial pressure = total pressure x mole fraction

Not total pressure, but pressure above pure substance.

 

[johnny b]

Then how do I find partial pressure? And are the rest of the parts right? Thanks for the reply

 

[Borek]

You are given pressure over a pure substance in the question.

 

[johnny b]

Oh ok so for part a I would use 172.76 instead of 177.95?
p(eth)=0.99(172.76)=171.0324 torr. x(chl)= 1-.99=.01
p(chl)=.01(172.76)=1.7276 torr. The answers came out the same I think I accidentally typed the wrong number in the calculator the first time..

 

[Borek]

p(chl) is wrong. You can't calculate partial pressure of the substance over solution using pressure over other pure substance.

However, you know total pressure over mixture and you have calculated partial pressure for one of two components.

 

[johnny b]

Oh yea duh I should have known that.
p(eth) = 171.0324 torr
Total pressure = partial pressure(eth) + partial pressure(chl)
177.95 = 171.0324 - p
p(chl) = 6.9175 torr

So fixing the other parts,
For part b,
X(eth) = P(eth) / P(total)
x(eth)=(171.0324)/177.95 = 0.961
x(chl) 1-.961 = .039

part c:
I use the partial pressure found in part a
K=P(chl)/x
K=6.9175 torr/.01 = 691.75 torr <--- the x that I use is .01 right? not the .039 that I found in part b since that was for the vapor phase?

d:
This one I'm not sure about. The only thing I could think of is from the given part:
177.95 torr / .9900 = p / .9800
then p= 176.15 but this doesn't seem right and I don't know how to find the vapor-phase mole fractions

 

[Borek]

Seems like approach to bc is OK, although I just skimmed.

d is just a direct application of both constants - one that was given and one that you have calculated.

 

[johnny b]

for part d I'm given x(eth)=0.9800 and I calculated x(eth)=0.961
I'm looking for the vapor pressure and vapor-phase mole fractions.. I'm really not sure how to apply the two constants together