I2 + KHCO3 + As4O6 = H2O + CO2 + KI + As4O10

I_2 iodine + KHCO_3 potassium bicarbonate + As4O6 ⟶ H_2O water + CO_2 carbon dioxide + KI potassium iodide + As4O10

Balance the chemical equation algebraically: I_2 + KHCO_3 + As4O6 ⟶ H_2O + CO_2 + KI + As4O10 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 I_2 + c_2 KHCO_3 + c_3 As4O6 ⟶ c_4 H_2O + c_5 CO_2 + c_6 KI + c_7 As4O10 Set the number of atoms in the reactants equal to the number of atoms in the products for I, C, H, K, O and As: I: | 2 c_1 = c_6 C: | c_2 = c_5 H: | c_2 = 2 c_4 K: | c_2 = c_6 O: | 3 c_2 + 6 c_3 = c_4 + 2 c_5 + 10 c_7 As: | 4 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 8 c_3 = 1 c_4 = 4 c_5 = 8 c_6 = 8 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 I_2 + 8 KHCO_3 + As4O6 ⟶ 4 H_2O + 8 CO_2 + 8 KI + As4O10

+ + As4O6 ⟶ + + + As4O10

iodine + potassium bicarbonate + As4O6 ⟶ water + carbon dioxide + potassium iodide + As4O10

Construct the equilibrium constant, K, expression for: I_2 + KHCO_3 + As4O6 ⟶ H_2O + CO_2 + KI + As4O10 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: 4 I_2 + 8 KHCO_3 + As4O6 ⟶ 4 H_2O + 8 CO_2 + 8 KI + As4O10 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 I_2 | 4 | -4 KHCO_3 | 8 | -8 As4O6 | 1 | -1 H_2O | 4 | 4 CO_2 | 8 | 8 KI | 8 | 8 As4O10 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression I_2 | 4 | -4 | ([I2])^(-4) KHCO_3 | 8 | -8 | ([KHCO3])^(-8) As4O6 | 1 | -1 | ([As4O6])^(-1) H_2O | 4 | 4 | ([H2O])^4 CO_2 | 8 | 8 | ([CO2])^8 KI | 8 | 8 | ([KI])^8 As4O10 | 1 | 1 | [As4O10] 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 = ([I2])^(-4) ([KHCO3])^(-8) ([As4O6])^(-1) ([H2O])^4 ([CO2])^8 ([KI])^8 [As4O10] = (([H2O])^4 ([CO2])^8 ([KI])^8 [As4O10])/(([I2])^4 ([KHCO3])^8 [As4O6])

Construct the rate of reaction expression for: I_2 + KHCO_3 + As4O6 ⟶ H_2O + CO_2 + KI + As4O10 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: 4 I_2 + 8 KHCO_3 + As4O6 ⟶ 4 H_2O + 8 CO_2 + 8 KI + As4O10 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 I_2 | 4 | -4 KHCO_3 | 8 | -8 As4O6 | 1 | -1 H_2O | 4 | 4 CO_2 | 8 | 8 KI | 8 | 8 As4O10 | 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 I_2 | 4 | -4 | -1/4 (Δ[I2])/(Δt) KHCO_3 | 8 | -8 | -1/8 (Δ[KHCO3])/(Δt) As4O6 | 1 | -1 | -(Δ[As4O6])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) CO_2 | 8 | 8 | 1/8 (Δ[CO2])/(Δt) KI | 8 | 8 | 1/8 (Δ[KI])/(Δt) As4O10 | 1 | 1 | (Δ[As4O10])/(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 = -1/4 (Δ[I2])/(Δt) = -1/8 (Δ[KHCO3])/(Δt) = -(Δ[As4O6])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/8 (Δ[CO2])/(Δt) = 1/8 (Δ[KI])/(Δt) = (Δ[As4O10])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iodine | potassium bicarbonate | As4O6 | water | carbon dioxide | potassium iodide | As4O10 formula | I_2 | KHCO_3 | As4O6 | H_2O | CO_2 | KI | As4O10 Hill formula | I_2 | CHKO_3 | As4O6 | H_2O | CO_2 | IK | As4O10 name | iodine | potassium bicarbonate | | water | carbon dioxide | potassium iodide | IUPAC name | molecular iodine | potassium hydrogen carbonate | | water | carbon dioxide | potassium iodide |