A home supplies company decides to produce a reusable moisture absorber product for removing the water content in air in an enclosed space. A reduction in humidity is expected to help inhibit the growth of mold and mildew. As a measure of product performance, the moisture absorber should reduce the relative humidity of air in a closed coat cabinet with dimensions of \(2 \mathrm{~m} \times 1 \mathrm{~m} \times 1 \mathrm{~m}\) from \(90 \%\) to \(50 \%\) at \(25^{\circ} \mathrm{C}\).

(a) There are two common hygroscopic materials, silica gel and calcium chloride. Comment on their suitability as the raw materials for the intended product. What is the physicochemical behavior that governs the uptake of moisture in each material?

(b) Develop and solve the model for determining the specifications for this product. What is the minimum amount of silica gel to lower the humidity to \(50 \%\) ? What is the required amount of silica gel if the reduction is to be completed in two hours? Much information is available on silica gel in the literature. For example, the maximum moisture content of silica gel, defined as weight of water per unit weight of silica gel, is 0.26. The density of silica gel is \(2.64 \mathrm{~g} / \mathrm{cm}^{3}\). The diffusion coefficient of moisture in silica gel is \(0.37 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s}\).