Input interpretation
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + HNN congruent N hydrazoic acid ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + N_2 nitrogen
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + HNN congruent N ⟶ H_2O + K_2SO_4 + MnSO_4 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 HNN congruent N ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and N: H: | 2 c_1 + c_3 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 N: | 3 c_3 = 2 c_7 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 10 c_4 = 8 c_5 = 1 c_6 = 2 c_7 = 15 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 KMnO_4 + 10 HNN congruent N ⟶ 8 H_2O + K_2SO_4 + 2 MnSO_4 + 15 N_2