H2O + HNO3 + KMnO4 + TeO2 = KNO3 + Mn(NO3)2 + H6TeO6

Input interpretation

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water + nitric acid + potassium permanganate + tellurium dioxide ⟶ potassium nitrate + manganese(II) nitrate + telluric(VI) acid

Balanced equation

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

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 + c_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N, K, Mn and Te: H: | 2 c_1 + c_2 = 6 c_7 O: | c_1 + 3 c_2 + 4 c_3 + 2 c_4 = 3 c_5 + 6 c_6 + 6 c_7 N: | c_2 = c_5 + 2 c_6 K: | c_3 = c_5 Mn: | c_3 = c_6 Te: | c_4 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 3 c_3 = 1 c_4 = 5/2 c_5 = 1 c_6 = 1 c_7 = 5/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 12 c_2 = 6 c_3 = 2 c_4 = 5 c_5 = 2 c_6 = 2 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 + 6 + 2 + 5 ⟶ 2 + 2 + 5