# Nernst Equation with Pressure Differences

## Main Question or Discussion Point

I'm working with the Nernst equation with pressure differences right now:

$E = E_t + \frac{RT}{nF}ln ((P/P_0)^{\Delta \eta_G})$

I'm assuming pure reactants here so, so I'm omitting the product terms: $\frac{\Pi_{products} x_i ^{\nu_i}}{\Pi_{reactants} x_i ^{\nu_i}}$ which would normally also go in the logarithm.

according to my solutions manual:
$\Delta \eta_G = \nu_P - \nu_R$

$\Delta \eta_G$ is referred to as "the change in the number of moles" and it looks like the value should be -1.5. However, I'm not sure how they would get that from the stoichiometry of the hydrogen-oxygen reaction:

$H_2 + \frac{1}{2}O_2 = H_2 O$

$1 H_2 O - (1 H_2 + \frac{1}{2}O_2) = -0.5$ less moles overall. I'm not sure how they got -1.5. I'm not sure what "nu" is for products and reactants and it's real meaning.

It is the same problem as the difference between Kp and Kc and how to convert between them. $\Delta \eta_G$ takes into account only gaseous substances, as it is related to the change in volume of the reaction mixture (and water, being liquid with volume orders of magnitude lower, can be safely ignored).