Question

Square sheet of Naphthalene (57gm) and dimension of (10cm X 10cm) is placed on the floor of a room at temperature (25oC) and pressure (1 bar). Naphthalene starts to sublimate (change from solid to vapor). The concentration of naphthalene at the surface of the sheet is 1.25x10-4 mole fraction, and at 1mm away from the sheet is 1x10-6 mole fraction. If the diffusion coefficient of naphthalene is 5.9x10-2 cm2/sec and the molecular weight of naphthalene is 128 g/mol,

a- Calculate the diffusion rate of naphthalene. Given that Naphthalene is diffusing and air is non-diffusing.

b- Calculate the time required for the sheet of naphthalene to disappear (finish).

Useful information: R=0.08317 m3.bar/Kmol . K

Answer 1

Given that we have naphthalene sublimating to non diffusing air at and pressure , So we have a case of substance A-naphthalene diffusing in a stagnant B (air).

The equation of diffusion flux of A is given as,

is the length of the diffusion,

is the diffusivity of naphthalene in air,

is the concentration of naphthalene in air, which can be found out using the equation,

where is the pressure

Temperature,

is the mole fraction at 1 mm away,

is the mole fraction at surface of sheet,

So

,

Now rate of diffusion = flux of diffusion X area

area of the sheet of naphthalene diffusion is,

So diffusion rate,

So diffusion rate of naphthalene is 0.00106272 mol/h

b. Now we are told that the weight of naphthalene block is, 52 g

So the number of moles of naphthalene is,

Assuming the diffusion area remains constant till the naphthalene disappear,

We see that, time required  for the sheet of naphthalene to disappear is,