HCl + KMnO4 = H2O + O2 + KCl + MnCl2

HCl hydrogen chloride + KMnO_4 potassium permanganate ⟶ H_2O water + O_2 oxygen + KCl potassium chloride + MnCl_2 manganese(II) chloride

Balance the chemical equation algebraically: HCl + KMnO_4 ⟶ H_2O + O_2 + KCl + MnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 KMnO_4 ⟶ c_3 H_2O + c_4 O_2 + c_5 KCl + c_6 MnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, Mn and O: Cl: | c_1 = c_5 + 2 c_6 H: | c_1 = 2 c_3 K: | c_2 = c_5 Mn: | c_2 = c_6 O: | 4 c_2 = c_3 + 2 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 = 3 c_2 = 1 c_3 = 3/2 c_4 = 5/4 c_5 = 1 c_6 = 1 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 12 c_2 = 4 c_3 = 6 c_4 = 5 c_5 = 4 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 HCl + 4 KMnO_4 ⟶ 6 H_2O + 5 O_2 + 4 KCl + 4 MnCl_2

+ ⟶ + + +

hydrogen chloride + potassium permanganate ⟶ water + oxygen + potassium chloride + manganese(II) chloride

| hydrogen chloride | potassium permanganate | water | oxygen | potassium chloride | manganese(II) chloride molecular free energy | -95.3 kJ/mol | -737.6 kJ/mol | -237.1 kJ/mol | 231.7 kJ/mol | -408.5 kJ/mol | -440.5 kJ/mol total free energy | -1144 kJ/mol | -2950 kJ/mol | -1423 kJ/mol | 1159 kJ/mol | -1634 kJ/mol | -1762 kJ/mol | G_initial = -4094 kJ/mol | | G_final = -3660 kJ/mol | | | ΔG_rxn^0 | -3660 kJ/mol - -4094 kJ/mol = 433.9 kJ/mol (endergonic) | | | | |

Construct the equilibrium constant, K, expression for: HCl + KMnO_4 ⟶ H_2O + O_2 + KCl + MnCl_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 12 HCl + 4 KMnO_4 ⟶ 6 H_2O + 5 O_2 + 4 KCl + 4 MnCl_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i HCl | 12 | -12 KMnO_4 | 4 | -4 H_2O | 6 | 6 O_2 | 5 | 5 KCl | 4 | 4 MnCl_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 12 | -12 | ([HCl])^(-12) KMnO_4 | 4 | -4 | ([KMnO4])^(-4) H_2O | 6 | 6 | ([H2O])^6 O_2 | 5 | 5 | ([O2])^5 KCl | 4 | 4 | ([KCl])^4 MnCl_2 | 4 | 4 | ([MnCl2])^4 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([HCl])^(-12) ([KMnO4])^(-4) ([H2O])^6 ([O2])^5 ([KCl])^4 ([MnCl2])^4 = (([H2O])^6 ([O2])^5 ([KCl])^4 ([MnCl2])^4)/(([HCl])^12 ([KMnO4])^4)

Construct the rate of reaction expression for: HCl + KMnO_4 ⟶ H_2O + O_2 + KCl + MnCl_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 12 HCl + 4 KMnO_4 ⟶ 6 H_2O + 5 O_2 + 4 KCl + 4 MnCl_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i HCl | 12 | -12 KMnO_4 | 4 | -4 H_2O | 6 | 6 O_2 | 5 | 5 KCl | 4 | 4 MnCl_2 | 4 | 4 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term HCl | 12 | -12 | -1/12 (Δ[HCl])/(Δt) KMnO_4 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) O_2 | 5 | 5 | 1/5 (Δ[O2])/(Δt) KCl | 4 | 4 | 1/4 (Δ[KCl])/(Δt) MnCl_2 | 4 | 4 | 1/4 (Δ[MnCl2])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/12 (Δ[HCl])/(Δt) = -1/4 (Δ[KMnO4])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/5 (Δ[O2])/(Δt) = 1/4 (Δ[KCl])/(Δt) = 1/4 (Δ[MnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium permanganate | water | oxygen | potassium chloride | manganese(II) chloride formula | HCl | KMnO_4 | H_2O | O_2 | KCl | MnCl_2 Hill formula | ClH | KMnO_4 | H_2O | O_2 | ClK | Cl_2Mn name | hydrogen chloride | potassium permanganate | water | oxygen | potassium chloride | manganese(II) chloride IUPAC name | hydrogen chloride | potassium permanganate | water | molecular oxygen | potassium chloride | dichloromanganese