H2SO4 + KMnO4 + FeSO3 = H2O + K2SO4 + MnSO4 + Fe2(SO4)3

Input interpretation

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sulfuric acid + potassium permanganate + FeSO3 ⟶ water + potassium sulfate + manganese(II) sulfate + iron(III) sulfate hydrate

Balanced equation

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$Balance the chemical equation algebraically: + + FeSO3 ⟶ + + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 FeSO3 ⟶ c_4 + c_5 + c_6 + c_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Fe: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 12 c_7 S: | c_1 + c_3 = c_5 + c_6 + 3 c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 Fe: | c_3 = 2 c_7 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 14/3 c_2 = 2 c_3 = 10/3 c_4 = 14/3 c_5 = 1 c_6 = 2 c_7 = 5/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 14 c_2 = 6 c_3 = 10 c_4 = 14 c_5 = 3 c_6 = 6 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 + 6 + 10 FeSO3 ⟶ 14 + 3 + 6 + 5$

Balance the chemical equation algebraically: + + FeSO3 ⟶ + + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 FeSO3 ⟶ c_4 + c_5 + c_6 + c_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Fe: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 12 c_7 S: | c_1 + c_3 = c_5 + c_6 + 3 c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 Fe: | 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 = 14/3 c_2 = 2 c_3 = 10/3 c_4 = 14/3 c_5 = 1 c_6 = 2 c_7 = 5/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 14 c_2 = 6 c_3 = 10 c_4 = 14 c_5 = 3 c_6 = 6 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 + 6 + 10 FeSO3 ⟶ 14 + 3 + 6 + 5