Finding the mole fraction (using vapor pressure)?

Question

A solution contains a mixture of pentane and hexane at room temperature. The solution has a vapor pressure of 259 torr . Pure pentane and hexane have vapor pressures of 425 torr and 151 torr , respectively, at room temperature.
What is the mole fraction of hexane? (Assume ideal behavior.)

I tried solving this several ways, but not even my book gives me any information about how to find mole fractions from vapor pressure.
Please explain!!

Dr.A · Accepted Answer

p ( hexane )= 151 X ( hexane)
X = mole fraction hexane = moles hexane / moles hexane + moles pentane)

Let Y = mole fraction pentane = moles pentane / moles hexane + moles pentane

X + Y= 1
Y = 1 - X

p ( pentane ) = Y x 425 = ( 1- X ) x 425 = 425 - 425 X

259 = p ( pentane ) + p ( hexane) = 151 X + 425 - 425 X = - 274 X + 425

- 166 = - 274 X

X = 0.606

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Finding the mole fraction (using vapor pressure)?

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