Hydrogen embrittlement weakens the mechanical strength of cast iron. This phenomenon frequently occurs in cast-iron pressure vessels containing hydrogen (H₂) gas. The H₂ gas dissolves into the iron metal (Fe) and diffuses into the solid nonporous Fe by an interstitial diffusion mechanism. The H₂ gas does not have to penetrate very far into the iron to have a negative effect on the mechanical strength of iron. In the present situation, 100% H₂ gas at 100°C is contained within a cylindrical iron vessel of inner 1.0 m and wall thickness of 2.0 cm. The solubility of hydrogen in iron at 100°C is 2.2 × 10^-7 mole H (1.33 × 10¹⁷ atoms H)/g Fe. The diffusion coefficient of hydro gen atoms in solid Fe is 124.0 × 10^-9 cm²/s at 100°C. Initially, there are no H atoms in the solid iron. How many hours will it take for the hydrogen level within the iron metal to reach 1.76 × 10^-7 mole H (1.06 × 10¹⁷ atoms H/g Fe) at a depth of 0.1 cm from the surface exposed to the hydrogen gas?