H2O + KMnO4 + MnCl2 = HCl + KCl + MnO2

H_2O water + KMnO_4 potassium permanganate + MnCl_2 manganese(II) chloride ⟶ HCl hydrogen chloride + KCl potassium chloride + MnO_2 manganese dioxide

Balance the chemical equation algebraically: H_2O + KMnO_4 + MnCl_2 ⟶ HCl + KCl + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 MnCl_2 ⟶ c_4 HCl + c_5 KCl + c_6 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn and Cl: H: | 2 c_1 = c_4 O: | c_1 + 4 c_2 = 2 c_6 K: | c_2 = c_5 Mn: | c_2 + c_3 = c_6 Cl: | 2 c_3 = c_4 + 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_2 = 1 c_3 = 3/2 c_4 = 2 c_5 = 1 c_6 = 5/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 2 c_3 = 3 c_4 = 4 c_5 = 2 c_6 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 KMnO_4 + 3 MnCl_2 ⟶ 4 HCl + 2 KCl + 5 MnO_2

+ + ⟶ + +

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

| water | potassium permanganate | manganese(II) chloride | hydrogen chloride | potassium chloride | manganese dioxide molecular free energy | -237.1 kJ/mol | -737.6 kJ/mol | -440.5 kJ/mol | -95.3 kJ/mol | -408.5 kJ/mol | -465.1 kJ/mol total free energy | -474.2 kJ/mol | -1475 kJ/mol | -1322 kJ/mol | -381.2 kJ/mol | -817 kJ/mol | -2326 kJ/mol | G_initial = -3271 kJ/mol | | | G_final = -3524 kJ/mol | | ΔG_rxn^0 | -3524 kJ/mol - -3271 kJ/mol = -252.8 kJ/mol (exergonic) | | | | |

Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + MnCl_2 ⟶ HCl + KCl + MnO_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: 2 H_2O + 2 KMnO_4 + 3 MnCl_2 ⟶ 4 HCl + 2 KCl + 5 MnO_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 H_2O | 2 | -2 KMnO_4 | 2 | -2 MnCl_2 | 3 | -3 HCl | 4 | 4 KCl | 2 | 2 MnO_2 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) MnCl_2 | 3 | -3 | ([MnCl2])^(-3) HCl | 4 | 4 | ([HCl])^4 KCl | 2 | 2 | ([KCl])^2 MnO_2 | 5 | 5 | ([MnO2])^5 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 = ([H2O])^(-2) ([KMnO4])^(-2) ([MnCl2])^(-3) ([HCl])^4 ([KCl])^2 ([MnO2])^5 = (([HCl])^4 ([KCl])^2 ([MnO2])^5)/(([H2O])^2 ([KMnO4])^2 ([MnCl2])^3)

Construct the rate of reaction expression for: H_2O + KMnO_4 + MnCl_2 ⟶ HCl + KCl + MnO_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: 2 H_2O + 2 KMnO_4 + 3 MnCl_2 ⟶ 4 HCl + 2 KCl + 5 MnO_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 H_2O | 2 | -2 KMnO_4 | 2 | -2 MnCl_2 | 3 | -3 HCl | 4 | 4 KCl | 2 | 2 MnO_2 | 5 | 5 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) MnCl_2 | 3 | -3 | -1/3 (Δ[MnCl2])/(Δt) HCl | 4 | 4 | 1/4 (Δ[HCl])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) MnO_2 | 5 | 5 | 1/5 (Δ[MnO2])/(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 = -1/2 (Δ[H2O])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/3 (Δ[MnCl2])/(Δt) = 1/4 (Δ[HCl])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/5 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium permanganate | manganese(II) chloride | hydrogen chloride | potassium chloride | manganese dioxide formula | H_2O | KMnO_4 | MnCl_2 | HCl | KCl | MnO_2 Hill formula | H_2O | KMnO_4 | Cl_2Mn | ClH | ClK | MnO_2 name | water | potassium permanganate | manganese(II) chloride | hydrogen chloride | potassium chloride | manganese dioxide IUPAC name | water | potassium permanganate | dichloromanganese | hydrogen chloride | potassium chloride | dioxomanganese