H2O + Cl2 + KCl + MnCl2 = HCl + KMnO4

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

Balance the chemical equation algebraically: H_2O + Cl_2 + KCl + MnCl_2 ⟶ HCl + KMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cl_2 + c_3 KCl + c_4 MnCl_2 ⟶ c_5 HCl + c_6 KMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, K and Mn: H: | 2 c_1 = c_5 O: | c_1 = 4 c_6 Cl: | 2 c_2 + c_3 + 2 c_4 = c_5 K: | c_3 = c_6 Mn: | c_4 = c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 5/2 c_3 = 1 c_4 = 1 c_5 = 8 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 5 c_3 = 2 c_4 = 2 c_5 = 16 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2O + 5 Cl_2 + 2 KCl + 2 MnCl_2 ⟶ 16 HCl + 2 KMnO_4

+ + + ⟶ +

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

| water | chlorine | potassium chloride | manganese(II) chloride | hydrogen chloride | potassium permanganate molecular free energy | -237.1 kJ/mol | 0 kJ/mol | -408.5 kJ/mol | -440.5 kJ/mol | -95.3 kJ/mol | -737.6 kJ/mol total free energy | -1897 kJ/mol | 0 kJ/mol | -817 kJ/mol | -881 kJ/mol | -1525 kJ/mol | -1475 kJ/mol | G_initial = -3595 kJ/mol | | | | G_final = -3000 kJ/mol | ΔG_rxn^0 | -3000 kJ/mol - -3595 kJ/mol = 594.8 kJ/mol (endergonic) | | | | |

Construct the equilibrium constant, K, expression for: H_2O + Cl_2 + KCl + MnCl_2 ⟶ HCl + KMnO_4 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 H_2O + 5 Cl_2 + 2 KCl + 2 MnCl_2 ⟶ 16 HCl + 2 KMnO_4 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 | 8 | -8 Cl_2 | 5 | -5 KCl | 2 | -2 MnCl_2 | 2 | -2 HCl | 16 | 16 KMnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 8 | -8 | ([H2O])^(-8) Cl_2 | 5 | -5 | ([Cl2])^(-5) KCl | 2 | -2 | ([KCl])^(-2) MnCl_2 | 2 | -2 | ([MnCl2])^(-2) HCl | 16 | 16 | ([HCl])^16 KMnO_4 | 2 | 2 | ([KMnO4])^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 = ([H2O])^(-8) ([Cl2])^(-5) ([KCl])^(-2) ([MnCl2])^(-2) ([HCl])^16 ([KMnO4])^2 = (([HCl])^16 ([KMnO4])^2)/(([H2O])^8 ([Cl2])^5 ([KCl])^2 ([MnCl2])^2)

Construct the rate of reaction expression for: H_2O + Cl_2 + KCl + MnCl_2 ⟶ HCl + KMnO_4 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 H_2O + 5 Cl_2 + 2 KCl + 2 MnCl_2 ⟶ 16 HCl + 2 KMnO_4 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 | 8 | -8 Cl_2 | 5 | -5 KCl | 2 | -2 MnCl_2 | 2 | -2 HCl | 16 | 16 KMnO_4 | 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 H_2O | 8 | -8 | -1/8 (Δ[H2O])/(Δt) Cl_2 | 5 | -5 | -1/5 (Δ[Cl2])/(Δt) KCl | 2 | -2 | -1/2 (Δ[KCl])/(Δt) MnCl_2 | 2 | -2 | -1/2 (Δ[MnCl2])/(Δt) HCl | 16 | 16 | 1/16 (Δ[HCl])/(Δt) KMnO_4 | 2 | 2 | 1/2 (Δ[KMnO4])/(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[H2O])/(Δt) = -1/5 (Δ[Cl2])/(Δt) = -1/2 (Δ[KCl])/(Δt) = -1/2 (Δ[MnCl2])/(Δt) = 1/16 (Δ[HCl])/(Δt) = 1/2 (Δ[KMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

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