I know that the redox couple MnO
4-/Mn
2+ is typically written MnO
4- + 8H
+ + 5e
- Mn
2+ + 4H
2O in acidic conditions and MnO
4- + 4H
2O + 5e
- Mn
2+ + 8OH
- in basic conditions. The second reaction is simply the first with the addition of 8K
w.
But then how is it admissible to add K
w so freely? I tried to analyse the redox potential of this couple as it varies based on pH, but I cannot come out with a decently consistent equation to express it. Based on the acidic-conditions reaction the Q term from the Nernst equation should be [Mn
2+]/[MnO
4-] * 1/[H
+]
8. But based on the basic-conditions reaction the Q term should be [Mn
2+]/[MnO
4-] * K
w8/[H
+]
8. This implies that a different method of calculating E (cell potential) would be needed based on conditions but this surely cannot be true as pH is continuous?
(Also, I am aware that in alkaline conditions Mn(OH)
2 precipitates. I will factor that into my calculations later using the K
sp, in a method I am accustomed to. But please do not worry about it for the sake of this problem.)