H2O + ReCl5 = HCl + ReO2 + HReO4

H_2O water + ReCl_5 rhenium(V) chloride ⟶ HCl hydrogen chloride + ReO_2 rhenium oxide + HReO_4 perrhenic acid

Balance the chemical equation algebraically: H_2O + ReCl_5 ⟶ HCl + ReO_2 + HReO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 ReCl_5 ⟶ c_3 HCl + c_4 ReO_2 + c_5 HReO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl and Re: H: | 2 c_1 = c_3 + c_5 O: | c_1 = 2 c_4 + 4 c_5 Cl: | 5 c_2 = c_3 Re: | c_2 = c_4 + 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 3 c_3 = 15 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2O + 3 ReCl_5 ⟶ 15 HCl + 2 ReO_2 + HReO_4

+ ⟶ + +

water + rhenium(V) chloride ⟶ hydrogen chloride + rhenium oxide + perrhenic acid

Construct the equilibrium constant, K, expression for: H_2O + ReCl_5 ⟶ HCl + ReO_2 + HReO_4 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: 8 H_2O + 3 ReCl_5 ⟶ 15 HCl + 2 ReO_2 + HReO_4 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 H_2O | 8 | -8 ReCl_5 | 3 | -3 HCl | 15 | 15 ReO_2 | 2 | 2 HReO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 8 | -8 | ([H2O])^(-8) ReCl_5 | 3 | -3 | ([ReCl5])^(-3) HCl | 15 | 15 | ([HCl])^15 ReO_2 | 2 | 2 | ([ReO2])^2 HReO_4 | 1 | 1 | [HReO4] 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 = ([H2O])^(-8) ([ReCl5])^(-3) ([HCl])^15 ([ReO2])^2 [HReO4] = (([HCl])^15 ([ReO2])^2 [HReO4])/(([H2O])^8 ([ReCl5])^3)

Construct the rate of reaction expression for: H_2O + ReCl_5 ⟶ HCl + ReO_2 + HReO_4 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: 8 H_2O + 3 ReCl_5 ⟶ 15 HCl + 2 ReO_2 + HReO_4 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 H_2O | 8 | -8 ReCl_5 | 3 | -3 HCl | 15 | 15 ReO_2 | 2 | 2 HReO_4 | 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 H_2O | 8 | -8 | -1/8 (Δ[H2O])/(Δt) ReCl_5 | 3 | -3 | -1/3 (Δ[ReCl5])/(Δt) HCl | 15 | 15 | 1/15 (Δ[HCl])/(Δt) ReO_2 | 2 | 2 | 1/2 (Δ[ReO2])/(Δt) HReO_4 | 1 | 1 | (Δ[HReO4])/(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 = -1/8 (Δ[H2O])/(Δt) = -1/3 (Δ[ReCl5])/(Δt) = 1/15 (Δ[HCl])/(Δt) = 1/2 (Δ[ReO2])/(Δt) = (Δ[HReO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | rhenium(V) chloride | hydrogen chloride | rhenium oxide | perrhenic acid formula | H_2O | ReCl_5 | HCl | ReO_2 | HReO_4 Hill formula | H_2O | Cl_5Re | ClH | O_2Re | HO_4Re name | water | rhenium(V) chloride | hydrogen chloride | rhenium oxide | perrhenic acid IUPAC name | water | pentachlororhenium | hydrogen chloride | dioxorhenium | hydroxy-trioxorhenium