H2O + K2MnO4 + K2S = S + KOH + MnO2

water + potassium manganate + K2S ⟶ mixed sulfur + potassium hydroxide + manganese dioxide

Balance the chemical equation algebraically: + + K2S ⟶ + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 K2S ⟶ 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, K, Mn and S: H: | 2 c_1 = c_5 O: | c_1 + 4 c_2 = c_5 + 2 c_6 K: | 2 c_2 + 2 c_3 = c_5 Mn: | c_2 = c_6 S: | c_3 = c_4 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 4 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 + + K2S ⟶ + 4 +

+ + K2S ⟶ + +

water + potassium manganate + K2S ⟶ mixed sulfur + potassium hydroxide + manganese dioxide

| water | potassium manganate | K2S | mixed sulfur | potassium hydroxide | manganese dioxide formula | | | K2S | | | Hill formula | H_2O | K_2MnO_4 | K2S | S | HKO | MnO_2 name | water | potassium manganate | | mixed sulfur | potassium hydroxide | manganese dioxide IUPAC name | water | dipotassium dioxido-dioxomanganese | | sulfur | potassium hydroxide | dioxomanganese