Develop the potential$/$pH equations $(8$ points$)$ and plot the lines on E vs pH diagram $(5$ points$)$ for stability between:

$($a$)$ WO$2/$W$2$O$5$ E$0=-0\mathrm{.}031$ V

$($b$)$ Pb$/$HPbO$2-$ E$0=0\mathrm{.}702$ V

All ionic activities are at $10-4$ g$/$L$.$ Identify the stable phases on the diagram $(2$ points$)$