[Nathan]

At 25C the vapor pressures of pentane and hexane are 511 and 150 torr. The vapor in equilibrium with a pentane-hexane solution at 25C has a mole fraction of pentane equal to 0.15 at 25C. what is the mole fraction of pentane n the solution?

[valdorod]

I think you might have made a mistake typing the question.

... a pentane-hexane solution at 25C has a mole fraction of pentane equal to 0.15 at 25C. what is the mole fraction of pentane n the solution?

You are asking for the mole fraction of pentane in the solution, and the problem tells you that the mole fraction of pentane in the solution is 0.15.  Either no calculations are necessary, or the question was worded incorrectly.
hey