How do you calculate the volume of cyclohexane and ethyl acetate needed for a mole fraction of ethyl acetate = 0.25 in a total volume = 10mL?

Let z be the volume (in mL) of ethyl acetate to be found.

Then the volume of cyclohexane is (10 - z).

Figure the number of moles of each component:

(z mL) x (0.902 g/ml) / (88.11 g/mol) = (0.0102372 z) mol ethyl acetate

((10 - z) mL) x (0.779 g/ml) / (84.16 g/mol) =

(0.0925618 - 0.00925618 z) mol cyclohexane

Substitute the two expressions for moles of component into

0.25 = (moles ethyl acetate/(moles cyclohexane + moles ethyl acetate))

0.25 = ((0.0102372 z) / ((0.0925618 - 0.00925618 z) + (0.0102372 z)))

Solve for z algebraically:

z = 2.32 mL ethyl acetate

10 - z = 7.68 mL cyclohexane

[Adjust the number of significant digits as you see fit.]

[I suspect there is a way to solve this problem with simpler algebra, but I don't see it just now.  I invite other answerers to demonstrate it.]

[Later: Yes! The method shown by hcbiochem is more to the point.]

So, to produce a mole fraction of 0.25 ethyl acetate, you will need 0.25 mol ethyl acetate and 0.75 mol cyclohexane. You can convert these to volumes as:

0.25 mol ethyl acetate X 88.11 g/mol / 0.902 g/mL = 24.4 mL

0.75 mol cyclohexane X 84.16 g/mol / 0.779 g/mL = 81.0 mL

The total volume of this solution is 105.4 mL

Now, you want these two volumes scaled to give you 10 mL:

24.4 mL ethyl acetate / 105.4 mL = x mL / 10 mL

x = 2.31 mL ethyl acetate and 10-2.31 = 7.69 mL cyclohexane

Hope that helps....