HCl + KBrO3 + SbCl3 = H2O + KBr + SbCl5

HCl hydrogen chloride + KBrO_3 potassium bromate + SbCl_3 antimony(III) chloride ⟶ H_2O water + KBr potassium bromide + SbCl_5 antimony pentachloride

Balance the chemical equation algebraically: HCl + KBrO_3 + SbCl_3 ⟶ H_2O + KBr + SbCl_5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 KBrO_3 + c_3 SbCl_3 ⟶ c_4 H_2O + c_5 KBr + c_6 SbCl_5 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Br, K, O and Sb: Cl: | c_1 + 3 c_3 = 5 c_6 H: | c_1 = 2 c_4 Br: | c_2 = c_5 K: | c_2 = c_5 O: | 3 c_2 = c_4 Sb: | 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 HCl + KBrO_3 + 3 SbCl_3 ⟶ 3 H_2O + KBr + 3 SbCl_5

+ + ⟶ + +

hydrogen chloride + potassium bromate + antimony(III) chloride ⟶ water + potassium bromide + antimony pentachloride

Construct the equilibrium constant, K, expression for: HCl + KBrO_3 + SbCl_3 ⟶ H_2O + KBr + SbCl_5 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 HCl + KBrO_3 + 3 SbCl_3 ⟶ 3 H_2O + KBr + 3 SbCl_5 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 HCl | 6 | -6 KBrO_3 | 1 | -1 SbCl_3 | 3 | -3 H_2O | 3 | 3 KBr | 1 | 1 SbCl_5 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) KBrO_3 | 1 | -1 | ([KBrO3])^(-1) SbCl_3 | 3 | -3 | ([SbCl3])^(-3) H_2O | 3 | 3 | ([H2O])^3 KBr | 1 | 1 | [KBr] SbCl_5 | 3 | 3 | ([SbCl5])^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 = ([HCl])^(-6) ([KBrO3])^(-1) ([SbCl3])^(-3) ([H2O])^3 [KBr] ([SbCl5])^3 = (([H2O])^3 [KBr] ([SbCl5])^3)/(([HCl])^6 [KBrO3] ([SbCl3])^3)

Construct the rate of reaction expression for: HCl + KBrO_3 + SbCl_3 ⟶ H_2O + KBr + SbCl_5 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 HCl + KBrO_3 + 3 SbCl_3 ⟶ 3 H_2O + KBr + 3 SbCl_5 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 HCl | 6 | -6 KBrO_3 | 1 | -1 SbCl_3 | 3 | -3 H_2O | 3 | 3 KBr | 1 | 1 SbCl_5 | 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 HCl | 6 | -6 | -1/6 (Δ[HCl])/(Δt) KBrO_3 | 1 | -1 | -(Δ[KBrO3])/(Δt) SbCl_3 | 3 | -3 | -1/3 (Δ[SbCl3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) KBr | 1 | 1 | (Δ[KBr])/(Δt) SbCl_5 | 3 | 3 | 1/3 (Δ[SbCl5])/(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[HCl])/(Δt) = -(Δ[KBrO3])/(Δt) = -1/3 (Δ[SbCl3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[KBr])/(Δt) = 1/3 (Δ[SbCl5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium bromate | antimony(III) chloride | water | potassium bromide | antimony pentachloride formula | HCl | KBrO_3 | SbCl_3 | H_2O | KBr | SbCl_5 Hill formula | ClH | BrKO_3 | Cl_3Sb | H_2O | BrK | Cl_5Sb name | hydrogen chloride | potassium bromate | antimony(III) chloride | water | potassium bromide | antimony pentachloride IUPAC name | hydrogen chloride | potassium bromate | trichlorostibane | water | potassium bromide | pentachlorostiborane