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At 88⁰C benzene has a vapour pressure of 900 torr and toluene has a vapour pressure of 360 torr. What is the mole fraction of benzene in the mixture with toluene that will be boil at 88⁰C at 1 atm pressure, benzene - toluene form an ideal solution

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Last updated date: 20th Jul 2024
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Answer
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Hint:The tendency of a substance to transition into a gaseous or vapour state is measured by vapour pressure, which rises with temperature. The boiling point of a liquid is defined as the temperature at which the vapour pressure at its surface equals the pressure exerted by its surroundings.

Complete answer:
The number of molecules of a certain ingredient in a mixture divided by the total number of moles in the mixture is known as the mole fraction. It's a means of describing a solution's concentration. The number of all the components' mole fractions is always one. Please notice that the mole fraction represents a fraction of molecules, and the mole fraction differs from the mass fraction when different molecules have different masses.
The partial vapour pressure of a solvent in a solution (or mixture) is equal to or equivalent to the vapour pressure of the pure solvent multiplied by its mole fraction in the solution, according to Raoult's theorem.
\[{P_{{\text{solution }}}} = {X_{{\text{solvent }}}}{P_{{\text{solvent }}}}\]
Now using the given data,
Vapour pressure of benzene = 900 torr
Vapour pressure of toluene = 360 torr
To find the mole fraction of benzene,
\[{x_{{\text{Benzene }}}} = \dfrac{{P - {P^{sat}}_{{\text{toluene }}}{\text{ }}}}{{{\text{ }}{P^{sat}}_{{\text{benzene }}}{\text{ }} - {P^{sat}}_{{\text{toluene }}}}}{\text{ }}\]
When solution boils at same temperature vapour pressure it is saturation pressure
\[{x_{{\text{Benzene }}}} = \dfrac{{{\text{760 - 360 }}}}{{{\text{ 900 - 360}}}}{\text{ }}\] [1 atm = 760 torr]
\[{x_{{\text{Benzene }}}} = 0.740{\text{ }}\]torr

Note:
The torr is a pressure unit that is specified as exactly \[\dfrac{1}{{760}}\] of a regular atmosphere on an absolute scale. As a result, one torr equals \[\dfrac{{101325}}{{760}}\]pascals. One torr was originally meant to be the same as one "millimetre of mercury," but redefinitions of the two units resulted in minor differences.