H2SO4 + KMnO4 + K2SO3 = H2O + K2SO4 + MnSO4

Input interpretation

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sulfuric acid + potassium permanganate + potassium sulfite ⟶ water + potassium sulfate + manganese(II) sulfate

Balanced equation

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

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