What volume of eugenol will be present in 30 mL of distillate?

Question

The essential oil found in cloves, eugenol, can be isolated by steam distillation because it is insoluble in water and has a measurable vapor pressure at 100 °C even though it has a much higher boiling point than water. Use data from the table to calculate the volume of eugenol in 30 mL of distillate.

Molar Mass H2O: 18 g/mol
Molar Mass of Eugenol: 164 g/mol
Boiling point of H2O: 100 degrees C
Boiling point of Eugenol: 254 degrees C
Vapor Pressure at 100 degrees C: 760 mmHg
Vapor Pressure at 100 degrees C: 4.0 mmHg
Density of water: 1.0 g/mL
Density of Eugenol: 1.05 g/mL

V= [mole fraction x molar mass] / density

This is what i have done so far:
mH20: 0.9947 * 18 = 17.9046 / 1 g/mL = 17.9046
morg: 0.0053 * 164 = 0.8692/ 1.05 g/mL = 0.8278

V% = Vorg/(Vorg + VH2O) * 100

(0.8278/18.7324) * 100 = 4.419%

From this step I have no idea what to do please help.

Answer 1

%v/v = (volume eugenol/total vol)*100 = 4.42
total volume = 30 mL; therefore,
0.0442 = (volume eugenol/30)
volume eugenol = 0.0442*30 = ? but I would have done it in grams from the beginning and used density to convert to mL.

(m eug/mH2O) = (peug*164/pH2O*18)
(m eug/30) = (4*164/760*18)
m eug = about 1.44g and
volume = mass/density = 1.44/1.05 = about 1.37 mL
In this calculation I've assume the 30 mL distillate is ALL water which may not be quite right but with such low vapor pressures for eugenol that isn't far off. You can do back through it and put in 30 - 1.4 mL and recalculate it as another approximation but I don't think that will make much difference.