Partial Pressure: Understanding CHCl3 & (C2H5)2O

[Brimley]

Hello everyone, I'm trying to understand more about how partial pressure works and how to use chemical activity equation. My reference text uses the following example:

Note1: A solution is prepared by mixing 2 moles of CHCl₃ (chloroform) and 3 moles of (C₂H₅)₂O (diethyl ether).
Note2: The vapor pressures of the components at 17 degrees C are pCHCl₃ = 34 mmHg and p(C₂H5)₂O = 196 mmHg.
Note3: The vapor pressures of the pure liquids at 17 degrees C are p⁰CHCl₃ = 143 mmHg and p⁰(C₂H₅)₂O = 397 mmHg.

Using this information, shouldn't I be able to find the chemical activity for chloroform and ether?

Here are my tools:

a_B = p_B/p⁰_B

where

a_B = Chemical Activity
p_B = partial pressure of B ? (gas / liquid ?)
p⁰_B = vapor pressure of pure liquid B

I do not understand if this formula is complete or how to incorporate combining the moles of each substance or how temperature makes a difference. The reference texts just states that "the chemical activity of each substance can be obtained from the following formula" which is the formula I listed above. I also do not understand the distinction between Notes 2 and 3 regarding what the difference is between the vapor pressures of the "components" and of the "pure liquids" ... what does it mean for each?

Can anyone assist? Any all help is greatly appreciated!

 

[Borek]

Pressure of the component is just the partial pressure.

Pressure of pure liquid is a pressure of the saturated vapor that you would observe over the sample of a... pure liquid (100% of one component).

This is simple plug 'n chug.

 

[Brimley]

I do not understand if this formula is complete or how to incorporate combining the moles of each substance or how temperature makes a difference. The reference texts just states that "the chemical activity of each substance can be obtained from the following formula" which is the formula I listed above.

Hello Borek, in my first post I wrote the text above explaining my confusion. I don't know if the book gives more information than necessary in their example or not, but I don't see how the formula plugs and chugs for having different moles of each substance nor do I understand where temperature makes a difference.

Could you help explain if the formula takes that into account in some way ? (i.e. you can only use it if the measurements are taken at the same temperature?) Also, how does it address the different moles of the substances given that they are forming a solution?

 

[Borek]

Composition and temperature doesn't matter here - you can safely ignore them. Just use given pressures. Yes, it means you will calculate activities for the temperature at which pressures were measured.

For an ideal solution activity of a component should be identical to its molar fraction. Then the vapor pressure over the mixture follows Raoult's law (so partial pressure of the component can be calculated from its pressure over a pure component and its molar fraction in the mixture). For real solutions it is not exactly true.

So, if you have an ideal solution of a known composition, you can calculate activity of each component (simple - it will just equal its molar fraction) and use Raoult's law to calculate each component partial pressure, sum them and get total pressure. For a real solution you can do the same, but you can't calculate activities that easily. However, you can also do the reverse - knowing total pressure and partial pressure of a given component you can divide the latter by the former to get the component activity. That's what you have to do here.

 

[Brimley]

Okay, so if I'm understanding you correctly, all I need to do is the following:

a_CHCl3 = 34/143 = 0.2377
a_(C2H5)2O = 196/397 = 0.4937

Is this correct? Are there any units?

So was I correct to say that since the temperature at which these measurements were made was constant, that temperature is not needed in the calculation? Does that infer that if the measurements at different temperatures were made that I couldn't have performed this calculation?

Also, I didn't have to do any molar fractions then, correct?

 

[Borek]

Is this correct?

Looks OK.

Are there any units?

No, activity is unitless.

So was I correct to say that since the temperature at which these measurements were made was constant, that temperature is not needed in the calculation? Does that infer that if the measurements at different temperatures were made that I couldn't have performed this calculation?

Yes & yes.

Also, I didn't have to do any molar fractions then, correct?

Yes.