KOH + KClO3 + PoO2 = H2O + KCl + K2PoO4

KOH potassium hydroxide + KClO_3 potassium chlorate + PoO_2 polonium(IV) oxide ⟶ H_2O water + KCl potassium chloride + K2PoO4

Balance the chemical equation algebraically: KOH + KClO_3 + PoO_2 ⟶ H_2O + KCl + K2PoO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KClO_3 + c_3 PoO_2 ⟶ c_4 H_2O + c_5 KCl + c_6 K2PoO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cl and Po: H: | c_1 = 2 c_4 K: | c_1 + c_2 = c_5 + 2 c_6 O: | c_1 + 3 c_2 + 2 c_3 = c_4 + 4 c_6 Cl: | c_2 = c_5 Po: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 3 c_4 = 3 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 KOH + KClO_3 + 3 PoO_2 ⟶ 3 H_2O + KCl + 3 K2PoO4

+ + PoO_2 ⟶ + + K2PoO4

potassium hydroxide + potassium chlorate + polonium(IV) oxide ⟶ water + potassium chloride + K2PoO4

Construct the equilibrium constant, K, expression for: KOH + KClO_3 + PoO_2 ⟶ H_2O + KCl + K2PoO4 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: 6 KOH + KClO_3 + 3 PoO_2 ⟶ 3 H_2O + KCl + 3 K2PoO4 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 | 6 | -6 KClO_3 | 1 | -1 PoO_2 | 3 | -3 H_2O | 3 | 3 KCl | 1 | 1 K2PoO4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 6 | -6 | ([KOH])^(-6) KClO_3 | 1 | -1 | ([KClO3])^(-1) PoO_2 | 3 | -3 | ([PoO2])^(-3) H_2O | 3 | 3 | ([H2O])^3 KCl | 1 | 1 | [KCl] K2PoO4 | 3 | 3 | ([K2PoO4])^3 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])^(-6) ([KClO3])^(-1) ([PoO2])^(-3) ([H2O])^3 [KCl] ([K2PoO4])^3 = (([H2O])^3 [KCl] ([K2PoO4])^3)/(([KOH])^6 [KClO3] ([PoO2])^3)

Construct the rate of reaction expression for: KOH + KClO_3 + PoO_2 ⟶ H_2O + KCl + K2PoO4 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: 6 KOH + KClO_3 + 3 PoO_2 ⟶ 3 H_2O + KCl + 3 K2PoO4 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 | 6 | -6 KClO_3 | 1 | -1 PoO_2 | 3 | -3 H_2O | 3 | 3 KCl | 1 | 1 K2PoO4 | 3 | 3 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 | 6 | -6 | -1/6 (Δ[KOH])/(Δt) KClO_3 | 1 | -1 | -(Δ[KClO3])/(Δt) PoO_2 | 3 | -3 | -1/3 (Δ[PoO2])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(Δt) K2PoO4 | 3 | 3 | 1/3 (Δ[K2PoO4])/(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 = -1/6 (Δ[KOH])/(Δt) = -(Δ[KClO3])/(Δt) = -1/3 (Δ[PoO2])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[KCl])/(Δt) = 1/3 (Δ[K2PoO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium chlorate | polonium(IV) oxide | water | potassium chloride | K2PoO4 formula | KOH | KClO_3 | PoO_2 | H_2O | KCl | K2PoO4 Hill formula | HKO | ClKO_3 | O_2Po_1 | H_2O | ClK | K2O4Po name | potassium hydroxide | potassium chlorate | polonium(IV) oxide | water | potassium chloride |