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According to my textbook, for Raoult's law, we have:

$$μ_i(\mathrm{vap}) = μ_i^* (p_i^*,T) + RT \ln⁡ x_i$$

where $μ_i^* (p_i^*,T)$ is the chemical potential at $T$ and $p_i^*$, the pressure of pure $i$. So, when $x_i=1$, we have $μ_i (vap)=μ_i^* (p_i^*,T)$. That's okay and makes sense.

For Henry's law, we have:

$$μ_i(\mathrm{vap}) = μ_i^∞ (p_j^*,T) + RT \ln⁡ x_i$$

where $μ_i^∞ (p_j^*,T)$ is the chemical potential at $T$ and $p_j^*$, the pressure of pure $j$ (the other component of the mixture). So, when $x_i = 1$ we have $μ_i^∞ (p_j^*,T) = μ_i^∞ (p_j^*,T)$ and that doesn't make any sense, since we have $i$ pure and the equation says that the chemical potential is the chemical potential of pure $j$.

Am I interpreting something wrongly?

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  • $\begingroup$ Your last equality has two identical symbols on both sides of the = sign ! You simply repeat the same symbols on both sides. These formula cannot be different. It is like writing an equation : a = a. $\endgroup$ – Maurice Feb 15 '20 at 9:03
  • $\begingroup$ In addition to Maurice's comment, your last statement "we have i pure and the equation says that de chemical potential is the chemical potencial of pure j" is inconsistent with the equations you have written, which describe the chemical potential of i (not j). $\endgroup$ – Buck Thorn Feb 15 '20 at 10:34
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The first equation is for the chemical potential of species i in an ideal liquid solution, neglecting the Poynting correction. The second equation is an approximation to the chemical potential of species i in a real solution in the region of low values of the mole fraction of i, and apparently includes both the Poynting correction, hence evaluation of the chemical potential at the total pressure p (not just pj) as well as a term for RT times the natural log of the infinite dilution activity coefficient of species i. So the equation only applies at low values of the mole fraction, and the first term in the equation represents the extrapolation of the low mole fraction limiting behavior to a mole fraction of 1.

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