A student adds 25 drops of cetyl alcohol in hexane, (solution concentration 1.08

Question

A student adds 25 drops of cetyl alcohol in hexane, (solution concentration 1.08 times 10^-4 g/mL) to form a monolayer of the alcohol on the surface of a Petri dish with area of 241 cm^2. The cetyl alcohol molecules are cylindrical with the diameter of the cylinder equal to one fifth of the length. Assume the long axis of the cylinder is perpendicular to the water surface. The medicine dropper used in this experiment was calibrated at 81 drops per milliliter. Using the above data and model, calculate Avogadros number.

Explanation / Answer

Volume of the solution = 25 drops / 81 drops/mL = 0.30864 mL
mass of cetyl alcohol in the monolayer = 1.08*10-4 g/mL * 0.30864mL = 3.3333*10-5 gm
Volume of cetyl alcohol in the monolayer, V = (3.3333*10-5 gm / 0.811 gm/cm3) = 4.11015*10-5 cm3
diameter = r / 2 = length / 5
Thickness of the monolayer, t = (4.11015*10-5 cm3 / 241 cm2) = 1.70545*10-7 cm
r = t/10 = 1.70545*10-8 ;
diameter = (1.70545*10-8) / 2 = 8.52725*10-9
length,h = 8.52725*10-9 * 5 = 4.263625*10-8 cm
Volume of the molecule, Vm = r2h = (t/10)2 * t = (1.70545*10-7 / 10)2*4.2636*10-8
Vm = 3.8958*10-23 cm3
Number of molecules = V/ Vm = ( 4.11015*10-5 / 3.8958*10-23 ) = 1.05502*1018
moles of cetyl alcohol = (3.3333*10-5 gm / 242.44 gm/mol) = 1.3748*10-7 mol
Avagadro's number = Number of molecules / moles of cetyl alcohol
Avagadro's number = (1.05502*1018) / (1.3748*10-7) = 7.6734*1024

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