Interpretation: The mole fraction of benzene in the original solution needs to be determined.
Concept Introduction: The ratio of number of moles of a substance in a compound to the total number of moles of the compound is said to be mole fraction. The formula is:
Answer to Problem 129CP
The mole fraction of benzene in the original solution is
Explanation of Solution
Given:
Vapor pressure of pure benzene is 750.0 torr and of pure toluene is 300.0 torr.
The mole fraction in the given vapor is 0.714.
Since, the sum of all mole fractions in a given mixture is 1 so, the mole fraction of toluene in solution II is:
Where
Substituting the value of mole fraction of benzene in solution II as:
The formula for a partial pressure of a gas in mixture is:
Where
Rearranging the equation as:
The above equation is written in terms of benzene in solution II as:
According to Raoult’s Law,
Where
The value for,
Solving for
Thus, the mole fraction of benzene in solution II is 0.5 and the mole fraction of toluene in solution II is (1.0 -0.5) is 0.5.
Now, in order to calculate the mole fraction of benzene in original solution:
Let
Now, the equation (1) for solution (I) can be written as:
Rewriting the above equation using Raoult’s law as:
Since, the solution behaves ideally, so
Substituting the values:
Solving for
Hence, the mole fraction of benzene in the original solution is
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Chapter 17 Solutions
CHEM.PRINC.W/OWL2+REBATE+2 SUPPL.>IP<
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