H2O + KMnO4 + KCl + As4O6 = HCl + MnCl2 + K3AsO4

H_2O water + KMnO_4 potassium permanganate + KCl potassium chloride + As4O6 ⟶ HCl hydrogen chloride + MnCl_2 manganese(II) chloride + K3AsO4

Balance the chemical equation algebraically: H_2O + KMnO_4 + KCl + As4O6 ⟶ HCl + MnCl_2 + K3AsO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 KCl + c_4 As4O6 ⟶ c_5 HCl + c_6 MnCl_2 + c_7 K3AsO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn, Cl and As: H: | 2 c_1 = c_5 O: | c_1 + 4 c_2 + 6 c_4 = 4 c_7 K: | c_2 + c_3 = 3 c_7 Mn: | c_2 = c_6 Cl: | c_3 = c_5 + 2 c_6 As: | 4 c_4 = c_7 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 18/5 c_2 = 8/5 c_3 = 52/5 c_4 = 1 c_5 = 36/5 c_6 = 8/5 c_7 = 4 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 18 c_2 = 8 c_3 = 52 c_4 = 5 c_5 = 36 c_6 = 8 c_7 = 20 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 18 H_2O + 8 KMnO_4 + 52 KCl + 5 As4O6 ⟶ 36 HCl + 8 MnCl_2 + 20 K3AsO4

+ + + As4O6 ⟶ + + K3AsO4

water + potassium permanganate + potassium chloride + As4O6 ⟶ hydrogen chloride + manganese(II) chloride + K3AsO4

Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + KCl + As4O6 ⟶ HCl + MnCl_2 + K3AsO4 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: 18 H_2O + 8 KMnO_4 + 52 KCl + 5 As4O6 ⟶ 36 HCl + 8 MnCl_2 + 20 K3AsO4 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 | 18 | -18 KMnO_4 | 8 | -8 KCl | 52 | -52 As4O6 | 5 | -5 HCl | 36 | 36 MnCl_2 | 8 | 8 K3AsO4 | 20 | 20 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 18 | -18 | ([H2O])^(-18) KMnO_4 | 8 | -8 | ([KMnO4])^(-8) KCl | 52 | -52 | ([KCl])^(-52) As4O6 | 5 | -5 | ([As4O6])^(-5) HCl | 36 | 36 | ([HCl])^36 MnCl_2 | 8 | 8 | ([MnCl2])^8 K3AsO4 | 20 | 20 | ([K3AsO4])^20 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])^(-18) ([KMnO4])^(-8) ([KCl])^(-52) ([As4O6])^(-5) ([HCl])^36 ([MnCl2])^8 ([K3AsO4])^20 = (([HCl])^36 ([MnCl2])^8 ([K3AsO4])^20)/(([H2O])^18 ([KMnO4])^8 ([KCl])^52 ([As4O6])^5)

Construct the rate of reaction expression for: H_2O + KMnO_4 + KCl + As4O6 ⟶ HCl + MnCl_2 + K3AsO4 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: 18 H_2O + 8 KMnO_4 + 52 KCl + 5 As4O6 ⟶ 36 HCl + 8 MnCl_2 + 20 K3AsO4 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 | 18 | -18 KMnO_4 | 8 | -8 KCl | 52 | -52 As4O6 | 5 | -5 HCl | 36 | 36 MnCl_2 | 8 | 8 K3AsO4 | 20 | 20 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 | 18 | -18 | -1/18 (Δ[H2O])/(Δt) KMnO_4 | 8 | -8 | -1/8 (Δ[KMnO4])/(Δt) KCl | 52 | -52 | -1/52 (Δ[KCl])/(Δt) As4O6 | 5 | -5 | -1/5 (Δ[As4O6])/(Δt) HCl | 36 | 36 | 1/36 (Δ[HCl])/(Δt) MnCl_2 | 8 | 8 | 1/8 (Δ[MnCl2])/(Δt) K3AsO4 | 20 | 20 | 1/20 (Δ[K3AsO4])/(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 = -1/18 (Δ[H2O])/(Δt) = -1/8 (Δ[KMnO4])/(Δt) = -1/52 (Δ[KCl])/(Δt) = -1/5 (Δ[As4O6])/(Δt) = 1/36 (Δ[HCl])/(Δt) = 1/8 (Δ[MnCl2])/(Δt) = 1/20 (Δ[K3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium permanganate | potassium chloride | As4O6 | hydrogen chloride | manganese(II) chloride | K3AsO4 formula | H_2O | KMnO_4 | KCl | As4O6 | HCl | MnCl_2 | K3AsO4 Hill formula | H_2O | KMnO_4 | ClK | As4O6 | ClH | Cl_2Mn | AsK3O4 name | water | potassium permanganate | potassium chloride | | hydrogen chloride | manganese(II) chloride | IUPAC name | water | potassium permanganate | potassium chloride | | hydrogen chloride | dichloromanganese |

| water | potassium permanganate | potassium chloride | As4O6 | hydrogen chloride | manganese(II) chloride | K3AsO4 molar mass | 18.015 g/mol | 158.03 g/mol | 74.55 g/mol | 395.68 g/mol | 36.46 g/mol | 125.8 g/mol | 256.212 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | | gas (at STP) | solid (at STP) | melting point | 0 °C | 240 °C | 770 °C | | -114.17 °C | 652 °C | boiling point | 99.9839 °C | | 1420 °C | | -85 °C | | density | 1 g/cm^3 | 1 g/cm^3 | 1.98 g/cm^3 | | 0.00149 g/cm^3 (at 25 °C) | 2.98 g/cm^3 | solubility in water | | | soluble | | miscible | | surface tension | 0.0728 N/m | | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | | | odor | odorless | odorless | odorless | | | |