Let a, b, c, d be coefficients for the balanced reaction:
a HC₂H₃O₂ + b KNO₂ → c KC₂H₃O₂ + d HNO₂
Count the elements among the reactants and products:
H: 4a = 3c + d
C: 2a = 2c
O: 2a + 2b = 2c + 2d
K: b = c
N: b = d
Suppose we let b = 1. Then both c = 1 and d = 1, and in the O equation we have
2a + 2 = 2 + 2 ⇒ 2a = 2 ⇒ a = 1
(Note that the equations for H and C also hold up.)
So the balanced reaction is simply
1 HC₂H₃O₂ + 1 KNO₂ → 1 KC₂H₃O₂ + 1 HNO₂
