A crystal particle of pure \(\mathrm{NaCl}\) is dissolving in an aqueous liquid (water) solution at \(18^{\circ} \mathrm{C}\). The dissolution of the particle is controlled by mass transfer. The aqueous solution is at a mass fraction of \(\mathrm{NaCl}=0.25\).

Data: Solubility of \(\mathrm{NaCl}\) in water at \(18^{\circ} \mathrm{C}=0.2647\) mass fraction. \(\mathrm{MW} \mathrm{NaCl}=58.45\).

Density pure solid \(\mathrm{NaCl}=2.163 \mathrm{~g} / \mathrm{cm}^{3}\).

Density of aqueous solution of \(\mathrm{NaCl}=1.20 \mathrm{~g} / \mathrm{cm}^{3}\) (assume constant).

Density of pure water \(=1.0 \mathrm{~g} / \mathrm{cm}^{3}\). MW pure water \(=18\).

Diffusivity \(\mathrm{NaCl}\)-water at \(18^{\circ} \mathrm{C}=1.24 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}\). Mass transfer coefficient \(\mathrm{k}=1.8 \times\) \(10^{-6} \mathrm{~m} / \mathrm{s}\).

a. Assume the particle is spherical with an initial particle diameter \(D=1.64 \mathrm{~mm}\). Find the particle diameter after \(7200 \mathrm{~s}\).

b. Assume the particle is a cube with an initial particle length \(\mathrm{L}=1.64 \mathrm{~mm}\). Find the particle length after \(7200 \mathrm{~s}\).