Panel 5: Some chemical equations cannot be balanced.

For example, (NH4)2 SO4 NH4OH + SO2 cannot be balanced, which is consistent with the failure to observe such a reaction in the laboratory..

Some chemical reactions can be balanced by different sets of coefficients.

Unbalanced reaction: CO + CO2 + H2 CH4+H2O
CO + CO2 + 7 H2 2 CH4 + 3 H2O
2 CO + CO2 + 10 H2 3 CH4 + 4 H2O
CO + 2 CO2 + 11 H2 3 CH4 + 5 H2O
Each of these three reactions conserves the number of carbon, oxygen and hydrogen atoms, and have been observed to occur under different conditions.

Both of these examples come from an article by G.R.Blakley in Journal of Chemical Education, vol.59, p.728, 1982, which treats the mathematics of equation balancing. This article may be of interest to chemists with a background in linear algebra.