Consider a hypothetical protein, Fobin, that contains two Fb groups, each containing a chromium metal that binds to a single molecule of oxygen. The reaction mechanism is expressed as:

$O_2+F{b}_{2}F{b}_2{O}_2$

$O_2+F{b}_2{O}_{2}F{b}_2{O}_4$

Find:

$($a$)$ Develop relationships for the equilibrium constants, ${}_{c1}$ and ${}_{c2}$ for the first and second reaction steps, respectively, in terms of $O_2$ partial pressure and molar concentrations of the three Fobin species.

$($b$)$ Develop a relationship for the fractional saturation of Fobin solely in terms of $O_2$ partial pressure.