It is found that lead from 2-mm-thick old paint on a certain wood surface has permeated to 1000 ppm at a depth of 2 mm below the outer wood surface. If the paint contains 20% (by mass) lead and was applied 20 years before the lead content to the wood was measured, estimate the diffusivity of the lead into the wood if it is found that the paint has lost 50% of the original amount of the lead. Assume that the lead did not diffuse into the air. Wood may be approximated as cellulose, C6 H10 O5, with molecular weight of 116, lead has molecular weight of 207, and the paint density may be taken as 1020 kg/m^3 when new.
What will be an ideal response?
The diffusivity may be approximated from Fick’s law for steady state conditions. Thus, we start with
The mass of lead per mol is its molecular weight, or
Mass of lead per mol = 0.207 kg/kg?mol
Mass of wood per mole = 115.884 kg/kg?mol and the mass fractions are
Generating a table for the molar/mass analysis
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