The variation of the chemical potential (mu) of pure iron (Fe) as a function of

Question

The variation of the chemical potential (mu) of pure iron (Fe) as a function of particle size (r) can be approximated by the Thomson-Freundlich equation (a.k.a. Washburn equation) as mu_Fe(r) - mu_Fe^infinity = 2gammafe^V^degree_Fe/r = RTln [p_Fe(r)/p_Fe^infinity} where gamma_Fe is the surface energy of iron (0.204 J/m^2), Vdegree_Fe. is the molar volume (7.09 times 10^-6 m^3/mol), and P_Fe is the vapor pressure. The superscript infinity designated a flat surface for which r rightarrow infinity. (a) Calculate the particle size of iron particles for which the vapor pressure is increased by 20% relative to the vapor pressure of over a flat surface; (b) What is Ostwald ripening? Why

Explanation / Answer

I don't know what is the ostwald opening, however, i can help you in part a) cause we have all the data to calculate the particle size, in this case, r.

We'll use R = 8.3144 J/mol K cause Yfe and the molar volume is given in Joules, T = 298 K, and the values of pressure we don't know them, but the problem state that pressure is increased 20%, so if the pressure is 1, then with the increase of 20% becomes 1.2. Substituing these values we have:

2(0.204)(7.09x10-6) = r(8.3144*298) ln (1.2P/P)
2.89x10-6 = r(2477.69) ln(1.2)
2.89x10-6 / 2477.69ln(1.2) = r
r = 6.3975x10-9 m

Hope this helps

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