HCl + MnCl2 + NaBiO3 = H2O + NaCl + BiCl3 + NaMnO4

HCl hydrogen chloride + MnCl_2 manganese(II) chloride + NaBiO_3 sodium bismuthate ⟶ H_2O water + NaCl sodium chloride + BiCl_3 bismuth chloride + NaMnO_4 sodium permanganate

Balance the chemical equation algebraically: HCl + MnCl_2 + NaBiO_3 ⟶ H_2O + NaCl + BiCl_3 + NaMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 MnCl_2 + c_3 NaBiO_3 ⟶ c_4 H_2O + c_5 NaCl + c_6 BiCl_3 + c_7 NaMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Mn, Bi, Na and O: Cl: | c_1 + 2 c_2 = c_5 + 3 c_6 H: | c_1 = 2 c_4 Mn: | c_2 = c_7 Bi: | c_3 = c_6 Na: | c_3 = c_5 + c_7 O: | 3 c_3 = c_4 + 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7 c_2 = 1 c_3 = 5/2 c_4 = 7/2 c_5 = 3/2 c_6 = 5/2 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 14 c_2 = 2 c_3 = 5 c_4 = 7 c_5 = 3 c_6 = 5 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HCl + 2 MnCl_2 + 5 NaBiO_3 ⟶ 7 H_2O + 3 NaCl + 5 BiCl_3 + 2 NaMnO_4

+ + ⟶ + + +

hydrogen chloride + manganese(II) chloride + sodium bismuthate ⟶ water + sodium chloride + bismuth chloride + sodium permanganate

Construct the equilibrium constant, K, expression for: HCl + MnCl_2 + NaBiO_3 ⟶ H_2O + NaCl + BiCl_3 + NaMnO_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: 14 HCl + 2 MnCl_2 + 5 NaBiO_3 ⟶ 7 H_2O + 3 NaCl + 5 BiCl_3 + 2 NaMnO_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 HCl | 14 | -14 MnCl_2 | 2 | -2 NaBiO_3 | 5 | -5 H_2O | 7 | 7 NaCl | 3 | 3 BiCl_3 | 5 | 5 NaMnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 14 | -14 | ([HCl])^(-14) MnCl_2 | 2 | -2 | ([MnCl2])^(-2) NaBiO_3 | 5 | -5 | ([NaBiO3])^(-5) H_2O | 7 | 7 | ([H2O])^7 NaCl | 3 | 3 | ([NaCl])^3 BiCl_3 | 5 | 5 | ([BiCl3])^5 NaMnO_4 | 2 | 2 | ([NaMnO4])^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 = ([HCl])^(-14) ([MnCl2])^(-2) ([NaBiO3])^(-5) ([H2O])^7 ([NaCl])^3 ([BiCl3])^5 ([NaMnO4])^2 = (([H2O])^7 ([NaCl])^3 ([BiCl3])^5 ([NaMnO4])^2)/(([HCl])^14 ([MnCl2])^2 ([NaBiO3])^5)

Construct the rate of reaction expression for: HCl + MnCl_2 + NaBiO_3 ⟶ H_2O + NaCl + BiCl_3 + NaMnO_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: 14 HCl + 2 MnCl_2 + 5 NaBiO_3 ⟶ 7 H_2O + 3 NaCl + 5 BiCl_3 + 2 NaMnO_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 HCl | 14 | -14 MnCl_2 | 2 | -2 NaBiO_3 | 5 | -5 H_2O | 7 | 7 NaCl | 3 | 3 BiCl_3 | 5 | 5 NaMnO_4 | 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 HCl | 14 | -14 | -1/14 (Δ[HCl])/(Δt) MnCl_2 | 2 | -2 | -1/2 (Δ[MnCl2])/(Δt) NaBiO_3 | 5 | -5 | -1/5 (Δ[NaBiO3])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) NaCl | 3 | 3 | 1/3 (Δ[NaCl])/(Δt) BiCl_3 | 5 | 5 | 1/5 (Δ[BiCl3])/(Δt) NaMnO_4 | 2 | 2 | 1/2 (Δ[NaMnO4])/(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 = -1/14 (Δ[HCl])/(Δt) = -1/2 (Δ[MnCl2])/(Δt) = -1/5 (Δ[NaBiO3])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/3 (Δ[NaCl])/(Δt) = 1/5 (Δ[BiCl3])/(Δt) = 1/2 (Δ[NaMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | manganese(II) chloride | sodium bismuthate | water | sodium chloride | bismuth chloride | sodium permanganate formula | HCl | MnCl_2 | NaBiO_3 | H_2O | NaCl | BiCl_3 | NaMnO_4 Hill formula | ClH | Cl_2Mn | BiNaO_3 | H_2O | ClNa | BiCl_3 | MnNaO_4 name | hydrogen chloride | manganese(II) chloride | sodium bismuthate | water | sodium chloride | bismuth chloride | sodium permanganate IUPAC name | hydrogen chloride | dichloromanganese | sodium oxido-dioxobismuth | water | sodium chloride | trichlorobismuthane | sodium permanganate