Using Interfacial Mass Transfer Phenomena formulas please calculate

Shrinking Core$/$Sphere Reaction Diffusion

Pure spherical sulphur particles of $50\mathrm{.}0mm$ are burnt in air to produce sulphur dioxide. The

reaction takes place according to the equation:

$S_{(s)}+O_{2(g)}S{O}_{2(g)}$

The results from the experiment performed to determine the controlling mechanism are given

table $1.$ Assuming the reaction proceeds by shrinking core model and that the surface

diffusion mechanism is discounted.

Table $1$: Combustion of a sulphur particle

a$)$ Draw sketches to represent the three possible mechanisms that can be applied to the

combustion of carbon particles labelling all key parts.

b$)$ With the appropriate form of the reaction equation and Fick's $1$st Law Derive the

shrinking sphere model expression for a reaction$-$controlled system.

c$)$ Using the data in Table $1$ make necessary calculations to test the three possible

mechanisms. Show the sample calculation at time of $20$ minutes and tabulate all

necessary results in a neatly laid out table and plot a graph showing the models fitted

to the data. $[$Ans: Shrinking core model$]$

d$)$ Find the time constant and write down the simplified equation for calculating the time

it would take to reach any given conversion for the mechanism identified in part $c.$

Ans: $\{$:$t={120\mathrm{.}65}^{**}(1-3(1-xb{)}^{\frac{2}{3}}+2(1-xb))]$