Napthalene (CioHs) is a traditional ingredient used in mothballs. You have a pro

Question

Napthalene (CioHs) is a traditional ingredient used in mothballs. You have a project to determine the properties of mothballs, including the sublimation of naphthalene under air flow with different flowrates. You experiment with naphthalene under conditions in which air is blown past a sphere of the material at a high speed in the turbulent range. The air is at 315 K and 1 atm, with an initial sphere diameter of 3.0 cm. After 25 minutes under these conditions, the sphere reaches a diameter of 2.8 cm (a) Calculate the average surface area of the sphere during this time and express the driving force of sublimation in terms of partial pressures. The density of solid naphthalene is 1.145 g/cm and the vapor pressure of naphthalene at 315 K can be assumed as 270 Pa. Solve for the mass transfer coefficient. (b) Calculate the mass transfer coefficient using molar concentrations as the driving force

Explanation / Answer

Since this is a sphere, where surface area is proportional to the square of radius,

Aavg = 4*pi*(R12 + R22)/2 = 4*3.14*(32 + 2.82)/2 = 105.7552 cm2

Volume of Naphthalene lost = 4/3*pi*(R13 - R23) = 4/3*3.14*(33 - 2.83) = 21.1343 cm3

Mass lost= volume lost x density = 21.1343 x 1.145 = 24.2 g

Mass flux = mass lost/time = 24.2 g/25 min = 0.968 g/min = 1.613 x 10-5 kg/s

Mass flux = k x (Patm - VP)

1.613 x 10-5 kg/s = k x (101325 Pa - 270 Pa)

k = 1.596 x 10-10 kg/Pa-s

Now, in terms of molar concentration,

kmolar = kpressure /RT

= 1.596 x 10-10 / (8.314 x 315)

kmolar = 6.096 x 10-14 kg/(mol/m3)-s

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