HCl + PbO2 + KCN = H2O + CO2 + KCl + NO + PbCl2

HCl hydrogen chloride + PbO_2 lead dioxide + KCN potassium cyanide ⟶ H_2O water + CO_2 carbon dioxide + KCl potassium chloride + NO nitric oxide + PbCl_2 lead(II) chloride

Balance the chemical equation algebraically: HCl + PbO_2 + KCN ⟶ H_2O + CO_2 + KCl + NO + PbCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 PbO_2 + c_3 KCN ⟶ c_4 H_2O + c_5 CO_2 + c_6 KCl + c_7 NO + c_8 PbCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, O, Pb, C, K and N: Cl: | c_1 = c_6 + 2 c_8 H: | c_1 = 2 c_4 O: | 2 c_2 = c_4 + 2 c_5 + c_7 Pb: | c_2 = c_8 C: | c_3 = c_5 K: | c_3 = c_6 N: | c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 7/2 c_3 = 1 c_4 = 4 c_5 = 1 c_6 = 1 c_7 = 1 c_8 = 7/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 16 c_2 = 7 c_3 = 2 c_4 = 8 c_5 = 2 c_6 = 2 c_7 = 2 c_8 = 7 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 HCl + 7 PbO_2 + 2 KCN ⟶ 8 H_2O + 2 CO_2 + 2 KCl + 2 NO + 7 PbCl_2

+ + ⟶ + + + +

hydrogen chloride + lead dioxide + potassium cyanide ⟶ water + carbon dioxide + potassium chloride + nitric oxide + lead(II) chloride

Construct the equilibrium constant, K, expression for: HCl + PbO_2 + KCN ⟶ H_2O + CO_2 + KCl + NO + PbCl_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 + 7 PbO_2 + 2 KCN ⟶ 8 H_2O + 2 CO_2 + 2 KCl + 2 NO + 7 PbCl_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 PbO_2 | 7 | -7 KCN | 2 | -2 H_2O | 8 | 8 CO_2 | 2 | 2 KCl | 2 | 2 NO | 2 | 2 PbCl_2 | 7 | 7 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) PbO_2 | 7 | -7 | ([PbO2])^(-7) KCN | 2 | -2 | ([KCN])^(-2) H_2O | 8 | 8 | ([H2O])^8 CO_2 | 2 | 2 | ([CO2])^2 KCl | 2 | 2 | ([KCl])^2 NO | 2 | 2 | ([NO])^2 PbCl_2 | 7 | 7 | ([PbCl2])^7 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) ([PbO2])^(-7) ([KCN])^(-2) ([H2O])^8 ([CO2])^2 ([KCl])^2 ([NO])^2 ([PbCl2])^7 = (([H2O])^8 ([CO2])^2 ([KCl])^2 ([NO])^2 ([PbCl2])^7)/(([HCl])^16 ([PbO2])^7 ([KCN])^2)

Construct the rate of reaction expression for: HCl + PbO_2 + KCN ⟶ H_2O + CO_2 + KCl + NO + PbCl_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 + 7 PbO_2 + 2 KCN ⟶ 8 H_2O + 2 CO_2 + 2 KCl + 2 NO + 7 PbCl_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 PbO_2 | 7 | -7 KCN | 2 | -2 H_2O | 8 | 8 CO_2 | 2 | 2 KCl | 2 | 2 NO | 2 | 2 PbCl_2 | 7 | 7 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) PbO_2 | 7 | -7 | -1/7 (Δ[PbO2])/(Δt) KCN | 2 | -2 | -1/2 (Δ[KCN])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) NO | 2 | 2 | 1/2 (Δ[NO])/(Δt) PbCl_2 | 7 | 7 | 1/7 (Δ[PbCl2])/(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) = -1/7 (Δ[PbO2])/(Δt) = -1/2 (Δ[KCN])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[NO])/(Δt) = 1/7 (Δ[PbCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | lead dioxide | potassium cyanide | water | carbon dioxide | potassium chloride | nitric oxide | lead(II) chloride formula | HCl | PbO_2 | KCN | H_2O | CO_2 | KCl | NO | PbCl_2 Hill formula | ClH | O_2Pb | CKN | H_2O | CO_2 | ClK | NO | Cl_2Pb name | hydrogen chloride | lead dioxide | potassium cyanide | water | carbon dioxide | potassium chloride | nitric oxide | lead(II) chloride IUPAC name | hydrogen chloride | | potassium cyanide | water | carbon dioxide | potassium chloride | nitric oxide | dichlorolead