HCl + K2MnO4 = H2O + Cl2 + KCl + MnCl2

HCl (hydrogen chloride) + K_2MnO_4 (potassium manganate) ⟶ H_2O (water) + Cl_2 (chlorine) + KCl (potassium chloride) + MnCl_2 (manganese(II) chloride)

Balance the chemical equation algebraically: HCl + K_2MnO_4 ⟶ H_2O + Cl_2 + KCl + MnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2MnO_4 ⟶ c_3 H_2O + c_4 Cl_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 = 2 c_4 + c_5 + 2 c_6 H: | c_1 = 2 c_3 K: | 2 c_2 = c_5 Mn: | c_2 = c_6 O: | 4 c_2 = c_3 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 = 8 c_2 = 1 c_3 = 4 c_4 = 2 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + K_2MnO_4 ⟶ 4 H_2O + 2 Cl_2 + 2 KCl + MnCl_2

+ ⟶ + + +

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

Construct the equilibrium constant, K, expression for: HCl + K_2MnO_4 ⟶ H_2O + 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 + K_2MnO_4 ⟶ 4 H_2O + 2 Cl_2 + 2 KCl + 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 K_2MnO_4 | 1 | -1 H_2O | 4 | 4 Cl_2 | 2 | 2 KCl | 2 | 2 MnCl_2 | 1 | 1 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) K_2MnO_4 | 1 | -1 | ([K2MnO4])^(-1) H_2O | 4 | 4 | ([H2O])^4 Cl_2 | 2 | 2 | ([Cl2])^2 KCl | 2 | 2 | ([KCl])^2 MnCl_2 | 1 | 1 | [MnCl2] 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) ([K2MnO4])^(-1) ([H2O])^4 ([Cl2])^2 ([KCl])^2 [MnCl2] = (([H2O])^4 ([Cl2])^2 ([KCl])^2 [MnCl2])/(([HCl])^8 [K2MnO4])

Construct the rate of reaction expression for: HCl + K_2MnO_4 ⟶ H_2O + 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 + K_2MnO_4 ⟶ 4 H_2O + 2 Cl_2 + 2 KCl + 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 K_2MnO_4 | 1 | -1 H_2O | 4 | 4 Cl_2 | 2 | 2 KCl | 2 | 2 MnCl_2 | 1 | 1 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) K_2MnO_4 | 1 | -1 | -(Δ[K2MnO4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Cl_2 | 2 | 2 | 1/2 (Δ[Cl2])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) MnCl_2 | 1 | 1 | (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) = -(Δ[K2MnO4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[Cl2])/(Δt) = 1/2 (Δ[KCl])/(Δt) = (Δ[MnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium manganate | water | chlorine | potassium chloride | manganese(II) chloride formula | HCl | K_2MnO_4 | H_2O | Cl_2 | KCl | MnCl_2 Hill formula | ClH | K_2MnO_4 | H_2O | Cl_2 | ClK | Cl_2Mn name | hydrogen chloride | potassium manganate | water | chlorine | potassium chloride | manganese(II) chloride IUPAC name | hydrogen chloride | dipotassium dioxido-dioxomanganese | water | molecular chlorine | potassium chloride | dichloromanganese

| hydrogen chloride | potassium manganate | water | chlorine | potassium chloride | manganese(II) chloride molar mass | 36.46 g/mol | 197.13 g/mol | 18.015 g/mol | 70.9 g/mol | 74.55 g/mol | 125.8 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | -114.17 °C | 190 °C | 0 °C | -101 °C | 770 °C | 652 °C boiling point | -85 °C | | 99.9839 °C | -34 °C | 1420 °C | density | 0.00149 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 1.98 g/cm^3 | 2.98 g/cm^3 solubility in water | miscible | decomposes | | | soluble | surface tension | | | 0.0728 N/m | | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | | odorless | | odorless |