HCl + MnCl2 + K3PO4 = H2O + KMnO4 + KCl + PCl3

HCl hydrogen chloride + MnCl_2 manganese(II) chloride + K3PO4 ⟶ H_2O water + KMnO_4 potassium permanganate + KCl potassium chloride + PCl_3 phosphorus trichloride

Balance the chemical equation algebraically: HCl + MnCl_2 + K3PO4 ⟶ H_2O + KMnO_4 + KCl + PCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 MnCl_2 + c_3 K3PO4 ⟶ c_4 H_2O + c_5 KMnO_4 + c_6 KCl + c_7 PCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Mn, K, P and O: Cl: | c_1 + 2 c_2 = c_6 + 3 c_7 H: | c_1 = 2 c_4 Mn: | c_2 = c_5 K: | 3 c_3 = c_5 + c_6 P: | c_3 = c_7 O: | 4 c_3 = c_4 + 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 12 c_2 = 1 c_3 = 5/2 c_4 = 6 c_5 = 1 c_6 = 13/2 c_7 = 5/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 24 c_2 = 2 c_3 = 5 c_4 = 12 c_5 = 2 c_6 = 13 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 24 HCl + 2 MnCl_2 + 5 K3PO4 ⟶ 12 H_2O + 2 KMnO_4 + 13 KCl + 5 PCl_3

+ + K3PO4 ⟶ + + +

hydrogen chloride + manganese(II) chloride + K3PO4 ⟶ water + potassium permanganate + potassium chloride + phosphorus trichloride

Construct the equilibrium constant, K, expression for: HCl + MnCl_2 + K3PO4 ⟶ H_2O + KMnO_4 + KCl + PCl_3 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: 24 HCl + 2 MnCl_2 + 5 K3PO4 ⟶ 12 H_2O + 2 KMnO_4 + 13 KCl + 5 PCl_3 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 | 24 | -24 MnCl_2 | 2 | -2 K3PO4 | 5 | -5 H_2O | 12 | 12 KMnO_4 | 2 | 2 KCl | 13 | 13 PCl_3 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 24 | -24 | ([HCl])^(-24) MnCl_2 | 2 | -2 | ([MnCl2])^(-2) K3PO4 | 5 | -5 | ([K3PO4])^(-5) H_2O | 12 | 12 | ([H2O])^12 KMnO_4 | 2 | 2 | ([KMnO4])^2 KCl | 13 | 13 | ([KCl])^13 PCl_3 | 5 | 5 | ([PCl3])^5 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])^(-24) ([MnCl2])^(-2) ([K3PO4])^(-5) ([H2O])^12 ([KMnO4])^2 ([KCl])^13 ([PCl3])^5 = (([H2O])^12 ([KMnO4])^2 ([KCl])^13 ([PCl3])^5)/(([HCl])^24 ([MnCl2])^2 ([K3PO4])^5)

Construct the rate of reaction expression for: HCl + MnCl_2 + K3PO4 ⟶ H_2O + KMnO_4 + KCl + PCl_3 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: 24 HCl + 2 MnCl_2 + 5 K3PO4 ⟶ 12 H_2O + 2 KMnO_4 + 13 KCl + 5 PCl_3 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 | 24 | -24 MnCl_2 | 2 | -2 K3PO4 | 5 | -5 H_2O | 12 | 12 KMnO_4 | 2 | 2 KCl | 13 | 13 PCl_3 | 5 | 5 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 | 24 | -24 | -1/24 (Δ[HCl])/(Δt) MnCl_2 | 2 | -2 | -1/2 (Δ[MnCl2])/(Δt) K3PO4 | 5 | -5 | -1/5 (Δ[K3PO4])/(Δt) H_2O | 12 | 12 | 1/12 (Δ[H2O])/(Δt) KMnO_4 | 2 | 2 | 1/2 (Δ[KMnO4])/(Δt) KCl | 13 | 13 | 1/13 (Δ[KCl])/(Δt) PCl_3 | 5 | 5 | 1/5 (Δ[PCl3])/(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 = -1/24 (Δ[HCl])/(Δt) = -1/2 (Δ[MnCl2])/(Δt) = -1/5 (Δ[K3PO4])/(Δt) = 1/12 (Δ[H2O])/(Δt) = 1/2 (Δ[KMnO4])/(Δt) = 1/13 (Δ[KCl])/(Δt) = 1/5 (Δ[PCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | manganese(II) chloride | K3PO4 | water | potassium permanganate | potassium chloride | phosphorus trichloride formula | HCl | MnCl_2 | K3PO4 | H_2O | KMnO_4 | KCl | PCl_3 Hill formula | ClH | Cl_2Mn | K3O4P | H_2O | KMnO_4 | ClK | Cl_3P name | hydrogen chloride | manganese(II) chloride | | water | potassium permanganate | potassium chloride | phosphorus trichloride IUPAC name | hydrogen chloride | dichloromanganese | | water | potassium permanganate | potassium chloride | trichlorophosphane