HCl + NaMnO4 = H2O + Cl2 + NaCl + MnCl2

HCl hydrogen chloride + NaMnO_4 sodium permanganate ⟶ H_2O water + Cl_2 chlorine + NaCl sodium chloride + MnCl_2 manganese(II) chloride

Balance the chemical equation algebraically: HCl + NaMnO_4 ⟶ H_2O + Cl_2 + NaCl + MnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 NaMnO_4 ⟶ c_3 H_2O + c_4 Cl_2 + c_5 NaCl + c_6 MnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Mn, Na and O: Cl: | c_1 = 2 c_4 + c_5 + 2 c_6 H: | c_1 = 2 c_3 Mn: | c_2 = c_6 Na: | c_2 = c_5 O: | 4 c_2 = c_3 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 = 8 c_2 = 1 c_3 = 4 c_4 = 5/2 c_5 = 1 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 16 c_2 = 2 c_3 = 8 c_4 = 5 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 HCl + 2 NaMnO_4 ⟶ 8 H_2O + 5 Cl_2 + 2 NaCl + 2 MnCl_2

+ ⟶ + + +

hydrogen chloride + sodium permanganate ⟶ water + chlorine + sodium chloride + manganese(II) chloride

Construct the equilibrium constant, K, expression for: HCl + NaMnO_4 ⟶ H_2O + Cl_2 + NaCl + MnCl_2 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: 16 HCl + 2 NaMnO_4 ⟶ 8 H_2O + 5 Cl_2 + 2 NaCl + 2 MnCl_2 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 | 16 | -16 NaMnO_4 | 2 | -2 H_2O | 8 | 8 Cl_2 | 5 | 5 NaCl | 2 | 2 MnCl_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 16 | -16 | ([HCl])^(-16) NaMnO_4 | 2 | -2 | ([NaMnO4])^(-2) H_2O | 8 | 8 | ([H2O])^8 Cl_2 | 5 | 5 | ([Cl2])^5 NaCl | 2 | 2 | ([NaCl])^2 MnCl_2 | 2 | 2 | ([MnCl2])^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])^(-16) ([NaMnO4])^(-2) ([H2O])^8 ([Cl2])^5 ([NaCl])^2 ([MnCl2])^2 = (([H2O])^8 ([Cl2])^5 ([NaCl])^2 ([MnCl2])^2)/(([HCl])^16 ([NaMnO4])^2)

Construct the rate of reaction expression for: HCl + NaMnO_4 ⟶ H_2O + Cl_2 + NaCl + MnCl_2 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: 16 HCl + 2 NaMnO_4 ⟶ 8 H_2O + 5 Cl_2 + 2 NaCl + 2 MnCl_2 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 | 16 | -16 NaMnO_4 | 2 | -2 H_2O | 8 | 8 Cl_2 | 5 | 5 NaCl | 2 | 2 MnCl_2 | 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 | 16 | -16 | -1/16 (Δ[HCl])/(Δt) NaMnO_4 | 2 | -2 | -1/2 (Δ[NaMnO4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) Cl_2 | 5 | 5 | 1/5 (Δ[Cl2])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) MnCl_2 | 2 | 2 | 1/2 (Δ[MnCl2])/(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 = -1/16 (Δ[HCl])/(Δt) = -1/2 (Δ[NaMnO4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/5 (Δ[Cl2])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = 1/2 (Δ[MnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | sodium permanganate | water | chlorine | sodium chloride | manganese(II) chloride formula | HCl | NaMnO_4 | H_2O | Cl_2 | NaCl | MnCl_2 Hill formula | ClH | MnNaO_4 | H_2O | Cl_2 | ClNa | Cl_2Mn name | hydrogen chloride | sodium permanganate | water | chlorine | sodium chloride | manganese(II) chloride IUPAC name | hydrogen chloride | sodium permanganate | water | molecular chlorine | sodium chloride | dichloromanganese