H2O + MnSO4 + K2S2O8 = H2SO4 + HMnO4 + KHSO4

Input interpretation

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water + manganese(II) sulfate + potassium persulfate ⟶ sulfuric acid + HMnO4 + potassium bisulfate

Balanced equation

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$Balance the chemical equation algebraically: + + ⟶ + HMnO4 + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 HMnO4 + c_6 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Mn, S and K: H: | 2 c_1 = 2 c_4 + c_5 + c_6 O: | c_1 + 4 c_2 + 8 c_3 = 4 c_4 + 4 c_5 + 4 c_6 Mn: | c_2 = c_5 S: | c_2 + 2 c_3 = c_4 + c_6 K: | 2 c_3 = c_6 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 5/2 c_4 = 1 c_5 = 1 c_6 = 5 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 2 c_3 = 5 c_4 = 2 c_5 = 2 c_6 = 10 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 + 2 + 5 ⟶ 2 + 2 HMnO4 + 10$

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 HMnO4 + c_6 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Mn, S and K: H: | 2 c_1 = 2 c_4 + c_5 + c_6 O: | c_1 + 4 c_2 + 8 c_3 = 4 c_4 + 4 c_5 + 4 c_6 Mn: | c_2 = c_5 S: | c_2 + 2 c_3 = c_4 + c_6 K: | 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 5/2 c_4 = 1 c_5 = 1 c_6 = 5 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 2 c_3 = 5 c_4 = 2 c_5 = 2 c_6 = 10 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 + 2 + 5 ⟶ 2 + 2 HMnO4 + 10