[sharonO]

It seems mass balance should be an easy thing to do. But for some reason it doesn't click with me!

Especially when there are coefficients involved such as this:
AgI <-> Ag⁺ + I^-
Ag⁺  + 2NH₃ <-> Ag(NH3)₂⁺
NH₃ + H₂O <-> OH^- + NH₄⁺
2H₂O <-> H₃O⁺ + OH^-

Why is it C_NH3 = [NH₃] - 2[Ag(NH₃)₂⁺] - [NH₄⁺] ?

Don't you need 2 ammonia to produce the diamminesilver complex..??

Thanks!

[Borek]

Don't you need 2 ammonia to produce the diamminesilver complex..??

Yes, and that's exactly the reason why there is coefficient of 2. For every molecule of complex produced two molecules of ammonia are consumed.