KOH + I2 + AsH3 = H2O + KI + K2AsO4

KOH potassium hydroxide + I_2 iodine + AsH_3 arsine ⟶ H_2O water + KI potassium iodide + K2AsO4

Balance the chemical equation algebraically: KOH + I_2 + AsH_3 ⟶ H_2O + KI + K2AsO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 I_2 + c_3 AsH_3 ⟶ c_4 H_2O + c_5 KI + c_6 K2AsO4 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 + 3 c_3 = 2 c_4 K: | c_1 = c_5 + 2 c_6 O: | c_1 = c_4 + 4 c_6 I: | 2 c_2 = c_5 As: | 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 = 11 c_2 = 9/2 c_3 = 1 c_4 = 7 c_5 = 9 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 22 c_2 = 9 c_3 = 2 c_4 = 14 c_5 = 18 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 22 KOH + 9 I_2 + 2 AsH_3 ⟶ 14 H_2O + 18 KI + 2 K2AsO4

+ + ⟶ + + K2AsO4

potassium hydroxide + iodine + arsine ⟶ water + potassium iodide + K2AsO4

Construct the equilibrium constant, K, expression for: KOH + I_2 + AsH_3 ⟶ H_2O + KI + K2AsO4 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: 22 KOH + 9 I_2 + 2 AsH_3 ⟶ 14 H_2O + 18 KI + 2 K2AsO4 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 | 22 | -22 I_2 | 9 | -9 AsH_3 | 2 | -2 H_2O | 14 | 14 KI | 18 | 18 K2AsO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 22 | -22 | ([KOH])^(-22) I_2 | 9 | -9 | ([I2])^(-9) AsH_3 | 2 | -2 | ([AsH3])^(-2) H_2O | 14 | 14 | ([H2O])^14 KI | 18 | 18 | ([KI])^18 K2AsO4 | 2 | 2 | ([K2AsO4])^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])^(-22) ([I2])^(-9) ([AsH3])^(-2) ([H2O])^14 ([KI])^18 ([K2AsO4])^2 = (([H2O])^14 ([KI])^18 ([K2AsO4])^2)/(([KOH])^22 ([I2])^9 ([AsH3])^2)

Construct the rate of reaction expression for: KOH + I_2 + AsH_3 ⟶ H_2O + KI + K2AsO4 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: 22 KOH + 9 I_2 + 2 AsH_3 ⟶ 14 H_2O + 18 KI + 2 K2AsO4 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 | 22 | -22 I_2 | 9 | -9 AsH_3 | 2 | -2 H_2O | 14 | 14 KI | 18 | 18 K2AsO4 | 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 | 22 | -22 | -1/22 (Δ[KOH])/(Δt) I_2 | 9 | -9 | -1/9 (Δ[I2])/(Δt) AsH_3 | 2 | -2 | -1/2 (Δ[AsH3])/(Δt) H_2O | 14 | 14 | 1/14 (Δ[H2O])/(Δt) KI | 18 | 18 | 1/18 (Δ[KI])/(Δt) K2AsO4 | 2 | 2 | 1/2 (Δ[K2AsO4])/(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 = -1/22 (Δ[KOH])/(Δt) = -1/9 (Δ[I2])/(Δt) = -1/2 (Δ[AsH3])/(Δt) = 1/14 (Δ[H2O])/(Δt) = 1/18 (Δ[KI])/(Δt) = 1/2 (Δ[K2AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | iodine | arsine | water | potassium iodide | K2AsO4 formula | KOH | I_2 | AsH_3 | H_2O | KI | K2AsO4 Hill formula | HKO | I_2 | AsH_3 | H_2O | IK | AsK2O4 name | potassium hydroxide | iodine | arsine | water | potassium iodide | IUPAC name | potassium hydroxide | molecular iodine | arsane | water | potassium iodide |

| potassium hydroxide | iodine | arsine | water | potassium iodide | K2AsO4 molar mass | 56.105 g/mol | 253.80894 g/mol | 77.946 g/mol | 18.015 g/mol | 166.0028 g/mol | 217.11 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) | melting point | 406 °C | 113 °C | -111.2 °C | 0 °C | 681 °C | boiling point | 1327 °C | 184 °C | -62.5 °C | 99.9839 °C | 1330 °C | density | 2.044 g/cm^3 | 4.94 g/cm^3 | 0.003186 g/cm^3 (at 25 °C) | 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) | 1.47×10^-5 Pa s (at 0 °C) | 8.9×10^-4 Pa s (at 25 °C) | 0.0010227 Pa s (at 732.9 °C) | odor | | | | odorless | |