Input interpretation
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + C_2H_2 acetylene ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + HO_2CCO_2H oxalic acid
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + C_2H_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + HO_2CCO_2H Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 C_2H_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 HO_2CCO_2H Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and C: H: | 2 c_1 + 2 c_3 = 2 c_4 + 2 c_7 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 C: | 2 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 = 5/4 c_4 = 3 c_5 = 1 c_6 = 2 c_7 = 5/4 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 12 c_2 = 8 c_3 = 5 c_4 = 12 c_5 = 4 c_6 = 8 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2SO_4 + 8 KMnO_4 + 5 C_2H_2 ⟶ 12 H_2O + 4 K_2SO_4 + 8 MnSO_4 + 5 HO_2CCO_2H
Structures
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Names
sulfuric acid + potassium permanganate + acetylene ⟶ water + potassium sulfate + manganese(II) sulfate + oxalic acid