How Do Mole Fractions Determine Vapor Pressure in a Binary Solution?

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Discussion Overview

The discussion revolves around the calculation of mole fractions in a binary solution of benzene and toluene, specifically in relation to their vapor pressures at a given temperature. Participants explore the application of Raoult's Law and the relationship between mole fractions and vapor pressure in an ideal solution.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a problem involving the vapor pressures of pure benzene and toluene and seeks to determine their mole fractions in a solution with a known vapor pressure.
  • Another participant suggests using the equation for vapor pressure in terms of mole fractions, indicating that the mole fractions should sum to one.
  • A participant questions the necessity of knowing the moles of each component, proposing the assumption of 100 g of each for conversion to moles.
  • Another reply emphasizes that moles or masses are not needed and encourages focusing solely on mole fractions.
  • Participants are prompted to consider the definition of mole fractions and their additive property in mixtures.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the best approach to solve the problem, with differing opinions on the necessity of moles or masses and the focus on mole fractions.

Contextual Notes

Participants express uncertainty regarding the assumptions needed for calculations, particularly whether to use mass or mole-based approaches, and the implications of these choices on the solution.

Who May Find This Useful

This discussion may be useful for students studying physical chemistry, particularly those interested in vapor pressure, ideal solutions, and the application of Raoult's Law.

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Homework Statement


Benzene and toluene combine to form an ideal solution. At 80 C, vapor pressure of pure benzene is 800 mmHg and the vapor pressure of pure toluene is 300 mmHg. If the vapor pressure of the solution is 400 mmHg, what are the mole fractions of benzene and toluene?
(A) 60% benzene and 40% toluene
(B) 50% benzene and 50% toluene
(C) 40% benzene and 60% touene
(D) 20% benzene and 80% toluene

Homework Equations


Pv=xaPa + xbPb

The Attempt at a Solution


I could easily back solve by trying each one out. D is correct. (0.2)(800) + (0.8)(300) = 400 but I really wanted to try this problem using the equation above. Instead of backsolving, is there an accurate way to put this formula to use? Thanks in advance.
 
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Hint: xa + xb = ?
 
but we don't know the moles of either benzene or toluene. Is it safe to assume 100 g of each converted to moles?
 
Last edited:
You don't need moles nor masses. Deal with mole fractions only.

What is the definition of a mole fraction in a mixture? What do the mole fractions of a mixture always add up to?
 

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