HCl + KMnO4 + KSCN = H2O + CO2 + SO2 + KCl + NO + MnCl2

HCl hydrogen chloride + KMnO_4 potassium permanganate + KSCN potassium thiocyanate ⟶ H_2O water + CO_2 carbon dioxide + SO_2 sulfur dioxide + KCl potassium chloride + NO nitric oxide + MnCl_2 manganese(II) chloride

Balance the chemical equation algebraically: HCl + KMnO_4 + KSCN ⟶ H_2O + CO_2 + SO_2 + KCl + NO + MnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 KMnO_4 + c_3 KSCN ⟶ c_4 H_2O + c_5 CO_2 + c_6 SO_2 + c_7 KCl + c_8 NO + c_9 MnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, Mn, O, C, N and S: Cl: | c_1 = c_7 + 2 c_9 H: | c_1 = 2 c_4 K: | c_2 + c_3 = c_7 Mn: | c_2 = c_9 O: | 4 c_2 = c_4 + 2 c_5 + 2 c_6 + c_8 C: | c_3 = c_5 N: | c_3 = c_8 S: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 38/5 c_2 = 11/5 c_3 = 1 c_4 = 19/5 c_5 = 1 c_6 = 1 c_7 = 16/5 c_8 = 1 c_9 = 11/5 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 38 c_2 = 11 c_3 = 5 c_4 = 19 c_5 = 5 c_6 = 5 c_7 = 16 c_8 = 5 c_9 = 11 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 38 HCl + 11 KMnO_4 + 5 KSCN ⟶ 19 H_2O + 5 CO_2 + 5 SO_2 + 16 KCl + 5 NO + 11 MnCl_2

hydrogen chloride + potassium permanganate + potassium thiocyanate ⟶ water + carbon dioxide + sulfur dioxide + potassium chloride + nitric oxide + manganese(II) chloride

Construct the equilibrium constant, K, expression for: HCl + KMnO_4 + KSCN ⟶ H_2O + CO_2 + SO_2 + KCl + NO + 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: 38 HCl + 11 KMnO_4 + 5 KSCN ⟶ 19 H_2O + 5 CO_2 + 5 SO_2 + 16 KCl + 5 NO + 11 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 | 38 | -38 KMnO_4 | 11 | -11 KSCN | 5 | -5 H_2O | 19 | 19 CO_2 | 5 | 5 SO_2 | 5 | 5 KCl | 16 | 16 NO | 5 | 5 MnCl_2 | 11 | 11 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 38 | -38 | ([HCl])^(-38) KMnO_4 | 11 | -11 | ([KMnO4])^(-11) KSCN | 5 | -5 | ([KSCN])^(-5) H_2O | 19 | 19 | ([H2O])^19 CO_2 | 5 | 5 | ([CO2])^5 SO_2 | 5 | 5 | ([SO2])^5 KCl | 16 | 16 | ([KCl])^16 NO | 5 | 5 | ([NO])^5 MnCl_2 | 11 | 11 | ([MnCl2])^11 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])^(-38) ([KMnO4])^(-11) ([KSCN])^(-5) ([H2O])^19 ([CO2])^5 ([SO2])^5 ([KCl])^16 ([NO])^5 ([MnCl2])^11 = (([H2O])^19 ([CO2])^5 ([SO2])^5 ([KCl])^16 ([NO])^5 ([MnCl2])^11)/(([HCl])^38 ([KMnO4])^11 ([KSCN])^5)

Construct the rate of reaction expression for: HCl + KMnO_4 + KSCN ⟶ H_2O + CO_2 + SO_2 + KCl + NO + 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: 38 HCl + 11 KMnO_4 + 5 KSCN ⟶ 19 H_2O + 5 CO_2 + 5 SO_2 + 16 KCl + 5 NO + 11 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 | 38 | -38 KMnO_4 | 11 | -11 KSCN | 5 | -5 H_2O | 19 | 19 CO_2 | 5 | 5 SO_2 | 5 | 5 KCl | 16 | 16 NO | 5 | 5 MnCl_2 | 11 | 11 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 | 38 | -38 | -1/38 (Δ[HCl])/(Δt) KMnO_4 | 11 | -11 | -1/11 (Δ[KMnO4])/(Δt) KSCN | 5 | -5 | -1/5 (Δ[KSCN])/(Δt) H_2O | 19 | 19 | 1/19 (Δ[H2O])/(Δt) CO_2 | 5 | 5 | 1/5 (Δ[CO2])/(Δt) SO_2 | 5 | 5 | 1/5 (Δ[SO2])/(Δt) KCl | 16 | 16 | 1/16 (Δ[KCl])/(Δt) NO | 5 | 5 | 1/5 (Δ[NO])/(Δt) MnCl_2 | 11 | 11 | 1/11 (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 = -1/38 (Δ[HCl])/(Δt) = -1/11 (Δ[KMnO4])/(Δt) = -1/5 (Δ[KSCN])/(Δt) = 1/19 (Δ[H2O])/(Δt) = 1/5 (Δ[CO2])/(Δt) = 1/5 (Δ[SO2])/(Δt) = 1/16 (Δ[KCl])/(Δt) = 1/5 (Δ[NO])/(Δt) = 1/11 (Δ[MnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium permanganate | potassium thiocyanate | water | carbon dioxide | sulfur dioxide | potassium chloride | nitric oxide | manganese(II) chloride formula | HCl | KMnO_4 | KSCN | H_2O | CO_2 | SO_2 | KCl | NO | MnCl_2 Hill formula | ClH | KMnO_4 | CKNS | H_2O | CO_2 | O_2S | ClK | NO | Cl_2Mn name | hydrogen chloride | potassium permanganate | potassium thiocyanate | water | carbon dioxide | sulfur dioxide | potassium chloride | nitric oxide | manganese(II) chloride IUPAC name | hydrogen chloride | potassium permanganate | potassium isothiocyanate | water | carbon dioxide | sulfur dioxide | potassium chloride | nitric oxide | dichloromanganese