A large sheet of material (50 mathrm{~mm}) thick contains dissolved hydrogen (left(mathrm{H}_{2} ight)) having a uniform concentration

A large sheet of material \(50 \mathrm{~mm}\) thick contains dissolved hydrogen \(\left(\mathrm{H}_{2}\right)\) having a uniform concentration of \(3 \mathrm{kmol} / \mathrm{m}^{3}\). The sheet is exposed to a fluid stream that causes the concentration of the dissolved hydrogen to be reduced suddenly to zero at both surfaces. This surface condition is maintained constant thereafter. If the mass diffusivity of hydrogen is \(8 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}\), how much time is required to bring the density of dissolved hydrogen to a value of \(1.2 \mathrm{~kg} / \mathrm{m}^{3}\) at the center of the sheet?