A cloud forms with a liquid water content of $10^-7$ m$^3$ water$/$m$^3$ air. Right before the cloud forms, the surrounding atmosphere contains $16$ ppbV nitric acid and $400$ ppmV of carbon dioxide.

a$.$ What can you say about the fate of nitric acid and carbon dioxide once the cloud forms? Explain why these compounds are treated differently.

b$.$ Calculate the pH of the cloud. State and justify any simplifications.

c$.$ Redo the calculation considering only the nitric acid $($ignore any acidity from CO$2).$ Discuss the implications.