Recall that the * partial pressure of a gas (P_{Gas})*in a mixture is given by:

$\overline{){{\mathbf{P}}}_{{\mathbf{gas}}}{\mathbf{=}}{{\mathbf{\chi}}}_{{\mathbf{gas}}}{{\mathbf{P}}}_{{\mathbf{total}}}}$

where **χ**** _{Gas}** = mole fraction of the gas and

**Isolating the mole fraction of the gas:**

$\frac{{\mathbf{P}}_{\mathbf{gas}}}{{\mathbf{P}}_{\mathbf{total}}}\mathbf{=}\frac{{\mathbf{\chi}}_{\mathbf{gas}}\overline{){\mathbf{P}}_{\mathbf{total}}}}{\overline{){\mathbf{P}}_{\mathbf{total}}}}\phantom{\rule{0ex}{0ex}}\overline{){{\mathbf{\chi}}}_{{\mathbf{gas}}}{\mathbf{=}}\frac{{\mathbf{P}}_{\mathbf{gas}}}{{\mathbf{P}}_{\mathbf{total}}}}$

At 20 ^{o}C the vapor pressure of benzene C_{6}H_{6} is 75 torr and that of toluene C_{7}H_{8} is 22 torr. Assume that benzene and toluene form an ideal solution.

In a solution composed of benzene and toluene that has a vapor pressure of 36 torr at 20 ^{o}C, what is the mole fraction of toluene?

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