HCl + KMnO4 + Na2C2O4 = H2O + CO2 + NaCl + KCl + MnCl2

HCl hydrogen chloride + KMnO_4 potassium permanganate + Na_2C_2O_4 sodium oxalate ⟶ H_2O water + CO_2 carbon dioxide + NaCl sodium chloride + KCl potassium chloride + MnCl_2 manganese(II) chloride

Balance the chemical equation algebraically: HCl + KMnO_4 + Na_2C_2O_4 ⟶ H_2O + CO_2 + NaCl + KCl + MnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 KMnO_4 + c_3 Na_2C_2O_4 ⟶ c_4 H_2O + c_5 CO_2 + c_6 NaCl + c_7 KCl + c_8 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 and Na: Cl: | c_1 = c_6 + c_7 + 2 c_8 H: | c_1 = 2 c_4 K: | c_2 = c_7 Mn: | c_2 = c_8 O: | 4 c_2 + 4 c_3 = c_4 + 2 c_5 C: | 2 c_3 = c_5 Na: | 2 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 = 8 c_2 = 1 c_3 = 5/2 c_4 = 4 c_5 = 5 c_6 = 5 c_7 = 1 c_8 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 16 c_2 = 2 c_3 = 5 c_4 = 8 c_5 = 10 c_6 = 10 c_7 = 2 c_8 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 HCl + 2 KMnO_4 + 5 Na_2C_2O_4 ⟶ 8 H_2O + 10 CO_2 + 10 NaCl + 2 KCl + 2 MnCl_2

+ + ⟶ + + + +

hydrogen chloride + potassium permanganate + sodium oxalate ⟶ water + carbon dioxide + sodium chloride + potassium chloride + manganese(II) chloride

Construct the equilibrium constant, K, expression for: HCl + KMnO_4 + Na_2C_2O_4 ⟶ H_2O + CO_2 + NaCl + KCl + 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 KMnO_4 + 5 Na_2C_2O_4 ⟶ 8 H_2O + 10 CO_2 + 10 NaCl + 2 KCl + 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 KMnO_4 | 2 | -2 Na_2C_2O_4 | 5 | -5 H_2O | 8 | 8 CO_2 | 10 | 10 NaCl | 10 | 10 KCl | 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) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) Na_2C_2O_4 | 5 | -5 | ([Na2C2O4])^(-5) H_2O | 8 | 8 | ([H2O])^8 CO_2 | 10 | 10 | ([CO2])^10 NaCl | 10 | 10 | ([NaCl])^10 KCl | 2 | 2 | ([KCl])^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) ([KMnO4])^(-2) ([Na2C2O4])^(-5) ([H2O])^8 ([CO2])^10 ([NaCl])^10 ([KCl])^2 ([MnCl2])^2 = (([H2O])^8 ([CO2])^10 ([NaCl])^10 ([KCl])^2 ([MnCl2])^2)/(([HCl])^16 ([KMnO4])^2 ([Na2C2O4])^5)

Construct the rate of reaction expression for: HCl + KMnO_4 + Na_2C_2O_4 ⟶ H_2O + CO_2 + NaCl + KCl + 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 KMnO_4 + 5 Na_2C_2O_4 ⟶ 8 H_2O + 10 CO_2 + 10 NaCl + 2 KCl + 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 KMnO_4 | 2 | -2 Na_2C_2O_4 | 5 | -5 H_2O | 8 | 8 CO_2 | 10 | 10 NaCl | 10 | 10 KCl | 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) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) Na_2C_2O_4 | 5 | -5 | -1/5 (Δ[Na2C2O4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) CO_2 | 10 | 10 | 1/10 (Δ[CO2])/(Δt) NaCl | 10 | 10 | 1/10 (Δ[NaCl])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(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[KMnO4])/(Δt) = -1/5 (Δ[Na2C2O4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/10 (Δ[CO2])/(Δt) = 1/10 (Δ[NaCl])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[MnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium permanganate | sodium oxalate | water | carbon dioxide | sodium chloride | potassium chloride | manganese(II) chloride formula | HCl | KMnO_4 | Na_2C_2O_4 | H_2O | CO_2 | NaCl | KCl | MnCl_2 Hill formula | ClH | KMnO_4 | Na_2C_2O_4 | H_2O | CO_2 | ClNa | ClK | Cl_2Mn name | hydrogen chloride | potassium permanganate | sodium oxalate | water | carbon dioxide | sodium chloride | potassium chloride | manganese(II) chloride IUPAC name | hydrogen chloride | potassium permanganate | disodium oxalate | water | carbon dioxide | sodium chloride | potassium chloride | dichloromanganese