As water is transported through an iron distribution main, it develops a reddish color. Analysis of the water shows that pH $=7\mathrm{.}5,$ dissolved oxygen $=5$ mg$/$liter$,$ calcium hardness $=100$ mg$/$liter as CaCO$3,$ Na$+=30$ mg$/$liter$,$ the total alkalinity $=150$ mg$/$liter as CaCO$3,$ and the temperature $=25\backslash$deg C$.$

a$)$ Diagram the "corrosion cell" that is probably causing the red water. Indicate the important elements of the cell and give the chemical reactions that are taking place as well as the point in the corrosion cell where they are occurring.

b$)$ What is the value of the Langelier index?

c$)$ Give three specific actions that could reasonably be expected to eliminate or significantly reduce the problem.