Question

A spherical ball of solid, nonporous naphthalene, a "mothball," is suspended in still air. The naphthalene ball slowly sublimes, releasing the naphthalene vapor into the surrounding air by the molecular diffusion-limited process. Estimate the time required to reduce the diameter from 2.0 to 0.50 cm when the surrounding air is at 347 K and 1.0 atm. Naphthalene has a molecular weight of 128 g/mol, a solid density of 1.145 g/cm3, and diffusivity in the air of 8:19 10␣6 m2=s, and exerts a vapor pressure of 5.0 Torr (666 Pa) at 347 K.

Answer 1

The time required to reduce the diameter of solid spherical ball from 2 cm to 0.50 cm = 61.60 hours

Explanation:

Given that:

The bulk gas temperature T = 347 K

The pressure = 1.0 atm

Molecular weight of naphthalene = 128 g/mole

density of the solid = 1.145 g/cm³

diffusivity in the air of coefficient = 8.19 × 10 ⁻⁶ m²/s

vapor pressure = 5.0 Torr (666 Pa)

The shape of the ball in this given study is spherical. So, the first step we need to carry out is to state the general differential equation for the mass transfer in the system of the spherical coordinates. After that , we will make use of simplified differential expression form of Fick's Flux. From there we'll determine the surface concentration (c) of the species and finally determine the material balance equation on the naphthalene which will be used in solving the time required to reduce the diameter from 2.0 cm to 0.50cm.

THE DETAILED EXPLANATION OF WHAT WE JUST SAID CAN BE SEEN IN THE ATTACHED IMAGES BELOW.