Solving a Mole Fraction Problem with X & Y @ 250°C

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Discussion Overview

The discussion revolves around a problem involving the calculation of the minimum mole fraction of liquid X required for a mixture of two liquids to boil at a specified temperature of 250°C, given their vapor pressures. The focus is on the application of Raoult's Law and the calculation of total vapor pressure in a liquid mixture.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the problem, stating that their calculations do not yield the expected results for the total pressure needed for boiling.
  • Another participant questions the initial assumption that the total pressure is 1500 mm Hg and prompts for the correct expression for total vapor pressure over the mixture.
  • A third participant proposes a formula for total vapor pressure, applying Raoult's Law, and calculates the mole fraction of liquid X, arriving at approximately 53.33%.
  • A later reply confirms that the calculation appears correct without providing further verification.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial total pressure assumption, and there is uncertainty regarding the correct approach to the problem. However, there is agreement on the application of Raoult's Law in the calculations presented.

Contextual Notes

There are limitations regarding the assumptions made about total pressure and the need for clarity on the definitions used in the calculations. The discussion does not resolve these issues.

MeKnos
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this problem should be simple, but i must be doing it wrong.

At 250 degrees Celsius, a certain liquid X has a vapor pressure of 900 mm Hg and a second liquid Y has a pressure of 600 mm Hg. What is the minimum mole fraction of X necessary for the mixture to boil at this temperature (assume atmosphere pressure is 1 atm).

MY WORK:

Since I know that the total pressure at this temperature is 1500 mm Hg, and only 760 mm Hg is needed, then only about 51% of the pressures are needed. But when I do (51%)(900) and (49%)(600), it doesn't add up to 760 mm Hg.

When I do guess and check, i get about 53.3% of compound X. How do you do this problem!
Thank you.
 
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What is expression that describes total vapor pressure over the mixture?

Hint: total pressure is not 1500 mmHg.
 
Borek said:
What is expression that describes total vapor pressure over the mixture?

Hint: total pressure is not 1500 mmHg.

I think I got it, but I just want to confirm the answer.

Ptot= (Xa)Px + (1-Xa)Py.
760 = (Xa)900 + 600 - (Xa)600
760 - 600 = 160 = 300(Xa)

Xa = 160/300 = 53.33%?
 
Looks OK.
 

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