Input interpretation
potassium permanganate + hydrogen peroxide ⟶ water + oxygen + potassium hydroxide + manganese dioxide
Balanced equation
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 K, Mn, O and H: K: | c_1 = c_5 Mn: | c_1 = c_6 O: | 4 c_1 + 2 c_2 = c_3 + 2 c_4 + c_5 + 2 c_6 H: | 2 c_2 = 2 c_3 + c_5 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_3 = c_2 - 1/2 c_4 = c_2/2 + 3/4 c_5 = 1 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_3 = c_2 - 1 c_4 = c_2/2 + 3/2 c_5 = 2 c_6 = 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 3 and solve for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 2 c_4 = 3 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 + 3 ⟶ 2 + 3 + 2 + 2
Structures
+ ⟶ + + +
Names
potassium permanganate + hydrogen peroxide ⟶ water + oxygen + potassium hydroxide + manganese dioxide
Reaction thermodynamics
Gibbs free energy
| potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | manganese dioxide molecular free energy | -737.6 kJ/mol | -120.4 kJ/mol | -237.1 kJ/mol | 231.7 kJ/mol | -379.4 kJ/mol | -465.1 kJ/mol total free energy | -1475 kJ/mol | -361.2 kJ/mol | -474.2 kJ/mol | 695.1 kJ/mol | -758.8 kJ/mol | -930.2 kJ/mol | G_initial = -1836 kJ/mol | | G_final = -1468 kJ/mol | | | ΔG_rxn^0 | -1468 kJ/mol - -1836 kJ/mol = 368.3 kJ/mol (endergonic) | | | | |
Chemical names and formulas
| potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | manganese dioxide Hill formula | KMnO_4 | H_2O_2 | H_2O | O_2 | HKO | MnO_2 name | potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | manganese dioxide IUPAC name | potassium permanganate | hydrogen peroxide | water | molecular oxygen | potassium hydroxide | dioxomanganese