KOH + KMnO4 + BiCl3 = H2O + Cl2 + K2MnO4 + KBiO3

KOH potassium hydroxide + KMnO_4 potassium permanganate + BiCl_3 bismuth chloride ⟶ H_2O water + Cl_2 chlorine + K_2MnO_4 potassium manganate + KBiO3

Balance the chemical equation algebraically: KOH + KMnO_4 + BiCl_3 ⟶ H_2O + Cl_2 + K_2MnO_4 + KBiO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 BiCl_3 ⟶ c_4 H_2O + c_5 Cl_2 + c_6 K_2MnO_4 + c_7 KBiO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn, Bi and Cl: H: | c_1 = 2 c_4 K: | c_1 + c_2 = 2 c_6 + c_7 O: | c_1 + 4 c_2 = c_4 + 4 c_6 + 3 c_7 Mn: | c_2 = c_6 Bi: | c_3 = c_7 Cl: | 3 c_3 = 2 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 5 c_3 = 1 c_4 = 3 c_5 = 3/2 c_6 = 5 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 12 c_2 = 10 c_3 = 2 c_4 = 6 c_5 = 3 c_6 = 10 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 KOH + 10 KMnO_4 + 2 BiCl_3 ⟶ 6 H_2O + 3 Cl_2 + 10 K_2MnO_4 + 2 KBiO3

+ + ⟶ + + + KBiO3

potassium hydroxide + potassium permanganate + bismuth chloride ⟶ water + chlorine + potassium manganate + KBiO3

Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + BiCl_3 ⟶ H_2O + Cl_2 + K_2MnO_4 + KBiO3 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: 12 KOH + 10 KMnO_4 + 2 BiCl_3 ⟶ 6 H_2O + 3 Cl_2 + 10 K_2MnO_4 + 2 KBiO3 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 KOH | 12 | -12 KMnO_4 | 10 | -10 BiCl_3 | 2 | -2 H_2O | 6 | 6 Cl_2 | 3 | 3 K_2MnO_4 | 10 | 10 KBiO3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 12 | -12 | ([KOH])^(-12) KMnO_4 | 10 | -10 | ([KMnO4])^(-10) BiCl_3 | 2 | -2 | ([BiCl3])^(-2) H_2O | 6 | 6 | ([H2O])^6 Cl_2 | 3 | 3 | ([Cl2])^3 K_2MnO_4 | 10 | 10 | ([K2MnO4])^10 KBiO3 | 2 | 2 | ([KBiO3])^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 = ([KOH])^(-12) ([KMnO4])^(-10) ([BiCl3])^(-2) ([H2O])^6 ([Cl2])^3 ([K2MnO4])^10 ([KBiO3])^2 = (([H2O])^6 ([Cl2])^3 ([K2MnO4])^10 ([KBiO3])^2)/(([KOH])^12 ([KMnO4])^10 ([BiCl3])^2)

Construct the rate of reaction expression for: KOH + KMnO_4 + BiCl_3 ⟶ H_2O + Cl_2 + K_2MnO_4 + KBiO3 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: 12 KOH + 10 KMnO_4 + 2 BiCl_3 ⟶ 6 H_2O + 3 Cl_2 + 10 K_2MnO_4 + 2 KBiO3 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 KOH | 12 | -12 KMnO_4 | 10 | -10 BiCl_3 | 2 | -2 H_2O | 6 | 6 Cl_2 | 3 | 3 K_2MnO_4 | 10 | 10 KBiO3 | 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 KOH | 12 | -12 | -1/12 (Δ[KOH])/(Δt) KMnO_4 | 10 | -10 | -1/10 (Δ[KMnO4])/(Δt) BiCl_3 | 2 | -2 | -1/2 (Δ[BiCl3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) Cl_2 | 3 | 3 | 1/3 (Δ[Cl2])/(Δt) K_2MnO_4 | 10 | 10 | 1/10 (Δ[K2MnO4])/(Δt) KBiO3 | 2 | 2 | 1/2 (Δ[KBiO3])/(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 = -1/12 (Δ[KOH])/(Δt) = -1/10 (Δ[KMnO4])/(Δt) = -1/2 (Δ[BiCl3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[Cl2])/(Δt) = 1/10 (Δ[K2MnO4])/(Δt) = 1/2 (Δ[KBiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium permanganate | bismuth chloride | water | chlorine | potassium manganate | KBiO3 formula | KOH | KMnO_4 | BiCl_3 | H_2O | Cl_2 | K_2MnO_4 | KBiO3 Hill formula | HKO | KMnO_4 | BiCl_3 | H_2O | Cl_2 | K_2MnO_4 | BiKO3 name | potassium hydroxide | potassium permanganate | bismuth chloride | water | chlorine | potassium manganate | IUPAC name | potassium hydroxide | potassium permanganate | trichlorobismuthane | water | molecular chlorine | dipotassium dioxido-dioxomanganese |

| potassium hydroxide | potassium permanganate | bismuth chloride | water | chlorine | potassium manganate | KBiO3 molar mass | 56.105 g/mol | 158.03 g/mol | 315.3 g/mol | 18.015 g/mol | 70.9 g/mol | 197.13 g/mol | 296.076 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | melting point | 406 °C | 240 °C | 231 °C | 0 °C | -101 °C | 190 °C | boiling point | 1327 °C | | 447 °C | 99.9839 °C | -34 °C | | density | 2.044 g/cm^3 | 1 g/cm^3 | 4.75 g/cm^3 | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | | solubility in water | soluble | | | | | decomposes | surface tension | | | | 0.0728 N/m | | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | 41 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | odorless | | odorless | | |