H2SO4 + NaBiO3 + Mn(SO4) = H2O + Na2SO4 + HMnO4 + Bi2(SO4)3

Input interpretation

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sulfuric acid + sodium bismuthate + manganese(II) sulfate ⟶ water + sodium sulfate + HMnO4 + bismuth sulfate

Balanced equation

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$Balance the chemical equation algebraically: + + ⟶ + + HMnO4 + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 + c_6 HMnO4 + c_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Bi, Na and Mn: H: | 2 c_1 = 2 c_4 + c_6 O: | 4 c_1 + 3 c_2 + 4 c_3 = c_4 + 4 c_5 + 4 c_6 + 12 c_7 S: | c_1 + c_3 = c_5 + 3 c_7 Bi: | c_2 = 2 c_7 Na: | c_2 = 2 c_5 Mn: | c_3 = c_6 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 5/2 c_3 = 1 c_4 = 7/2 c_5 = 5/4 c_6 = 1 c_7 = 5/4 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 16 c_2 = 10 c_3 = 4 c_4 = 14 c_5 = 5 c_6 = 4 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 + 10 + 4 ⟶ 14 + 5 + 4 HMnO4 + 5$

Balance the chemical equation algebraically: + + ⟶ + + HMnO4 + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 + c_6 HMnO4 + c_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Bi, Na and Mn: H: | 2 c_1 = 2 c_4 + c_6 O: | 4 c_1 + 3 c_2 + 4 c_3 = c_4 + 4 c_5 + 4 c_6 + 12 c_7 S: | c_1 + c_3 = c_5 + 3 c_7 Bi: | c_2 = 2 c_7 Na: | c_2 = 2 c_5 Mn: | c_3 = c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 5/2 c_3 = 1 c_4 = 7/2 c_5 = 5/4 c_6 = 1 c_7 = 5/4 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 16 c_2 = 10 c_3 = 4 c_4 = 14 c_5 = 5 c_6 = 4 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 + 10 + 4 ⟶ 14 + 5 + 4 HMnO4 + 5