# Balancing the reaction of potassium permanganate and sulfuric acid with hydrogen peroxide [duplicate]

A problem on redox reactions invites the reader to balance the actual reaction from which the redox simplification arose. After some hunting I found the balanced equation and attempted to re-derive the coefficients using:

$$\ce{a H_2SO_4 + b KMnO_4 + cH_2O_2 -> dK_2SO_4 + eMnSO_4 + fH_2O + gO}$$

We can quickly derive some valid relations by looking at each element:

$$\begin{array}{cll}\\ \ce{H}&\quad a+c &=& f\\ \ce{O}&\quad 4a+4b+2c&=& 4d+4e+f+g\\ \ce{S}&\quad a&=& d+e\\ \ce{K}&\quad b&=& 2d\\ \ce{Mn}&\quad b&=& e \end{array}$$

This can be massaged a little but because there are 5 equations and 7 unknowns it seems that the system is underdetermined.

If we let $a=3,~b=2,~c=5,~d=1,~e=2,~f=8,~g=10$ the equations all work.

My question is:

Could we arrive at these values without guessing or actually doing an experiment to measure (say) the oxygen evolved?

FWIW, I notice an old paper - J. Am. Chem. Soc. 1889, 11 (6), 94-98 - of which I can only see the first page seems to take a similar approach and gets two possible equations, maybe for the reason above.

• Shouldn't it be $g\ce{O2}$? Nascent oxygen doesn't exist, so is that an error in the reaction product? May 19 '18 at 9:29
• @GaurangTandon: I don't think it matters for purposes of balancing, if you look at the paper, the authors put it this way. Just divide by two to get the amount of oxygen gas. May 19 '18 at 9:31
• We could arrive at these values just as well as any other possible values, of which there are plenty. This is a sum of two reactions, and it could be balanced to anything. Related: chemistry.stackexchange.com/questions/64202/… May 19 '18 at 9:57
• @IvanNeretin: This seems like it may be an answer to the question, thanks. May 19 '18 at 12:33
• chemistry.stackexchange.com/questions/63369/… was marked as duplicate of that ^ May 19 '18 at 18:16