HCl + KMnO4 = H2O + O2 + Cl2 + KCl + MnCl2

HCl hydrogen chloride + KMnO_4 potassium permanganate ⟶ H_2O water + O_2 oxygen + Cl_2 chlorine + KCl potassium chloride + MnCl_2 manganese(II) chloride

Balance the chemical equation algebraically: HCl + KMnO_4 ⟶ H_2O + O_2 + Cl_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 Cl_2 + c_6 KCl + c_7 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 = 2 c_5 + c_6 + 2 c_7 H: | c_1 = 2 c_3 K: | c_2 = c_6 Mn: | c_2 = c_7 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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/3 - 2/3 c_3 = c_1/2 c_4 = (5 c_1)/12 - 4/3 c_5 = 1 c_6 = c_1/3 - 2/3 c_7 = c_1/3 - 2/3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 8 and solve for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 4 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + 2 KMnO_4 ⟶ 4 H_2O + 2 O_2 + Cl_2 + 2 KCl + 2 MnCl_2

+ ⟶ + + + +

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

| hydrogen chloride | potassium permanganate | water | oxygen | chlorine | potassium chloride | manganese(II) chloride molecular free energy | -95.3 kJ/mol | -737.6 kJ/mol | -237.1 kJ/mol | 231.7 kJ/mol | 0 kJ/mol | -408.5 kJ/mol | -440.5 kJ/mol total free energy | -762.4 kJ/mol | -1475 kJ/mol | -948.4 kJ/mol | 463.4 kJ/mol | 0 kJ/mol | -817 kJ/mol | -881 kJ/mol | G_initial = -2238 kJ/mol | | G_final = -2183 kJ/mol | | | | ΔG_rxn^0 | -2183 kJ/mol - -2238 kJ/mol = 54.6 kJ/mol (endergonic) | | | | | |

Construct the equilibrium constant, K, expression for: HCl + KMnO_4 ⟶ H_2O + O_2 + Cl_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: 8 HCl + 2 KMnO_4 ⟶ 4 H_2O + 2 O_2 + Cl_2 + 2 KCl + 2 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 | 8 | -8 KMnO_4 | 2 | -2 H_2O | 4 | 4 O_2 | 2 | 2 Cl_2 | 1 | 1 KCl | 2 | 2 MnCl_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) H_2O | 4 | 4 | ([H2O])^4 O_2 | 2 | 2 | ([O2])^2 Cl_2 | 1 | 1 | [Cl2] KCl | 2 | 2 | ([KCl])^2 MnCl_2 | 2 | 2 | ([MnCl2])^2 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])^(-8) ([KMnO4])^(-2) ([H2O])^4 ([O2])^2 [Cl2] ([KCl])^2 ([MnCl2])^2 = (([H2O])^4 ([O2])^2 [Cl2] ([KCl])^2 ([MnCl2])^2)/(([HCl])^8 ([KMnO4])^2)

Construct the rate of reaction expression for: HCl + KMnO_4 ⟶ H_2O + O_2 + Cl_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: 8 HCl + 2 KMnO_4 ⟶ 4 H_2O + 2 O_2 + Cl_2 + 2 KCl + 2 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 | 8 | -8 KMnO_4 | 2 | -2 H_2O | 4 | 4 O_2 | 2 | 2 Cl_2 | 1 | 1 KCl | 2 | 2 MnCl_2 | 2 | 2 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 | 8 | -8 | -1/8 (Δ[HCl])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) Cl_2 | 1 | 1 | (Δ[Cl2])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) MnCl_2 | 2 | 2 | 1/2 (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 = -1/8 (Δ[HCl])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = (Δ[Cl2])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[MnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium permanganate | water | oxygen | chlorine | potassium chloride | manganese(II) chloride formula | HCl | KMnO_4 | H_2O | O_2 | Cl_2 | KCl | MnCl_2 Hill formula | ClH | KMnO_4 | H_2O | O_2 | Cl_2 | ClK | Cl_2Mn name | hydrogen chloride | potassium permanganate | water | oxygen | chlorine | potassium chloride | manganese(II) chloride IUPAC name | hydrogen chloride | potassium permanganate | water | molecular oxygen | molecular chlorine | potassium chloride | dichloromanganese