Page:Scientific Papers of Josiah Willard Gibbs.djvu/461

In case of one molecular formula in liquid and none in gas, we may give the molecules repelling forces which will make the gas possible. (?) [See p. 417.]

Deduce Ostwald's law in more general form.

Deduce interpolation formula.

What use can we make of Latent Differences? $\mu _{\text{A}},\mu _{\text{AA}},\mu _{\text{B}},\mu _{\text{BB}},\mu _{\text{AB}}$ all conform to law, I think.

[On the Equations of Electric Motion.]

[A somewhat abbreviated copy of a letter written four years earlier (in May 1899) to Professor W. D. Bancroft of Cornell University had been placed by Professor Gibbs between the pages of the manuscript, and was evidently intended to serve as a basis for the chapter "On the equations of electric motion" mentioned in the list on page 418.

Through the courtesy of Professor Bancroft the original letter has been placed at the disposal of the editors and is here given in full. The major portion of this letter was incorporated by Professor Bancroft in an article entitled "Chemical Potential and Electromotive Force" published after the death of Professor Gibbs, in the Journal of Physical Chemistry, vol. vii.,p. 416, June 1903.]

My dear Prof. Bancroft:

⁠A working theory of galvanic cells requires (as you suggest) that we should be able to evaluate the (intrinsic or chemical) potentials involved, and your formula

$d\mu =Rt\,d\log p,$

is all right as you interpret it. I should perhaps prefer to write

$\mu _{\text{D}}=B+{\frac {At}{M_{\text{D}}}}\log \gamma _{\text{D}},$

(1)

or⁠$\gamma _{\text{D}}d\mu _{\text{D}}={\frac {At}{M_{\text{D}}}}d\gamma _{\text{D}},$

(2)

for small values of $\gamma _{\text{D}}$, where $\gamma _{\text{D}}$ is the density of a component (say the mass of the solutum divided by the volume of the solution), $M_{\text{D}}$ its molecular weight (viz., for the kind of molecule which actually exists in the solution), $A$ the constant of Avogadro's Law $\left({\frac {pv}{mt}}={\frac {A}{M}}\right),$ and $B$ a quantity which depends upon the solvent and the solutum, as well as the temperature, but which may be regarded as independent of $\gamma _{\text{D}}$ so long as this is small, and which is practically independent of the pressure in ordinary cases.