KOH + I2 + As2O3 = H2O + KI + K3AsO4

KOH potassium hydroxide + I_2 iodine + As_2O_3 arsenic trioxide ⟶ H_2O water + KI potassium iodide + K3AsO4

Balance the chemical equation algebraically: KOH + I_2 + As_2O_3 ⟶ H_2O + KI + K3AsO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 I_2 + c_3 As_2O_3 ⟶ c_4 H_2O + c_5 KI + c_6 K3AsO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, I and As: H: | c_1 = 2 c_4 K: | c_1 = c_5 + 3 c_6 O: | c_1 + 3 c_3 = c_4 + 4 c_6 I: | 2 c_2 = c_5 As: | 2 c_3 = 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 = 10 c_2 = 2 c_3 = 1 c_4 = 5 c_5 = 4 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 KOH + 2 I_2 + As_2O_3 ⟶ 5 H_2O + 4 KI + 2 K3AsO4

+ + ⟶ + + K3AsO4

potassium hydroxide + iodine + arsenic trioxide ⟶ water + potassium iodide + K3AsO4

Construct the equilibrium constant, K, expression for: KOH + I_2 + As_2O_3 ⟶ H_2O + KI + 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: 10 KOH + 2 I_2 + As_2O_3 ⟶ 5 H_2O + 4 KI + 2 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 KOH | 10 | -10 I_2 | 2 | -2 As_2O_3 | 1 | -1 H_2O | 5 | 5 KI | 4 | 4 K3AsO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 10 | -10 | ([KOH])^(-10) I_2 | 2 | -2 | ([I2])^(-2) As_2O_3 | 1 | -1 | ([As2O3])^(-1) H_2O | 5 | 5 | ([H2O])^5 KI | 4 | 4 | ([KI])^4 K3AsO4 | 2 | 2 | ([K3AsO4])^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])^(-10) ([I2])^(-2) ([As2O3])^(-1) ([H2O])^5 ([KI])^4 ([K3AsO4])^2 = (([H2O])^5 ([KI])^4 ([K3AsO4])^2)/(([KOH])^10 ([I2])^2 [As2O3])

Construct the rate of reaction expression for: KOH + I_2 + As_2O_3 ⟶ H_2O + KI + 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: 10 KOH + 2 I_2 + As_2O_3 ⟶ 5 H_2O + 4 KI + 2 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 KOH | 10 | -10 I_2 | 2 | -2 As_2O_3 | 1 | -1 H_2O | 5 | 5 KI | 4 | 4 K3AsO4 | 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 | 10 | -10 | -1/10 (Δ[KOH])/(Δt) I_2 | 2 | -2 | -1/2 (Δ[I2])/(Δt) As_2O_3 | 1 | -1 | -(Δ[As2O3])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) KI | 4 | 4 | 1/4 (Δ[KI])/(Δt) K3AsO4 | 2 | 2 | 1/2 (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 = -1/10 (Δ[KOH])/(Δt) = -1/2 (Δ[I2])/(Δt) = -(Δ[As2O3])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/4 (Δ[KI])/(Δt) = 1/2 (Δ[K3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | iodine | arsenic trioxide | water | potassium iodide | K3AsO4 formula | KOH | I_2 | As_2O_3 | H_2O | KI | K3AsO4 Hill formula | HKO | I_2 | As_2O_3 | H_2O | IK | AsK3O4 name | potassium hydroxide | iodine | arsenic trioxide | water | potassium iodide | IUPAC name | potassium hydroxide | molecular iodine | 2, 4, 5-trioxa-1, 3-diarsabicyclo[1.1.1]pentane | water | potassium iodide |

| potassium hydroxide | iodine | arsenic trioxide | water | potassium iodide | K3AsO4 molar mass | 56.105 g/mol | 253.80894 g/mol | 197.84 g/mol | 18.015 g/mol | 166.0028 g/mol | 256.212 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | melting point | 406 °C | 113 °C | 312 °C | 0 °C | 681 °C | boiling point | 1327 °C | 184 °C | 465 °C | 99.9839 °C | 1330 °C | density | 2.044 g/cm^3 | 4.94 g/cm^3 | 4.15 g/cm^3 | 1 g/cm^3 | 3.123 g/cm^3 | solubility in water | soluble | | | | | surface tension | | | | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | 0.00227 Pa s (at 116 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 0.0010227 Pa s (at 732.9 °C) | odor | | | | odorless | |