Wikipedia gives the following equation to calculate the moist adiabatic lapse rate $\Gamma_w$, assuming that there is only one condensible gas (water vapour) mixed in the "dry air":

$\Gamma_w = g\frac{\left(1+\frac{H_v r}{R_{sd}T} \right)}{\left(c_{pd} + \frac{H_{v}^2r}{R_{sw}T^2} \right)}$

Where:

• $\Gamma_{w}$: moist adiabatic lapse rate [K/m]
• $g$: gravitational acceleration [m/s2]
• $H_{v}$: latent heat of vaporization of water [J/kg]
• $R_{sd}$: specific gas constant of dry air [J/kg·K]
• $R_{sw}$: specific gas constant of water vapour [J/kg·K]
• $r={\frac {\epsilon e}{p-e}}$: mixing ratio of the mass of water vapour to the mass of dry air
• $\epsilon = \frac{R_{sd}}{R_{sw}}$: ratio of the specific gas constant of dry air to the specific gas constant for water vapour = 0.622 [dimensionless]
• $e$: water vapour pressure of the saturated air [Pa]
• $p$: pressure of the saturated air [Pa]
• $T$: temperature of the saturated air [K]
• $c_{pd}$: specific heat of dry air at constant pressure [J/kg·K]

What's the form of this equation when the atmosphere composition differs from Earth's, thus allowing multiple condensible gases or even be entirely composed of only one condensible gas (for example 100% water vapour)?