HNO3 + KCl + PbO2 = H2O + Cl2 + KNO3 + Pb(NO3)2

HNO_3 nitric acid + KCl potassium chloride + PbO_2 lead dioxide ⟶ H_2O water + Cl_2 chlorine + KNO_3 potassium nitrate + Pb(NO_3)_2 lead(II) nitrate

Balance the chemical equation algebraically: HNO_3 + KCl + PbO_2 ⟶ H_2O + Cl_2 + KNO_3 + Pb(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 KCl + c_3 PbO_2 ⟶ c_4 H_2O + c_5 Cl_2 + c_6 KNO_3 + c_7 Pb(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Cl, K and Pb: H: | c_1 = 2 c_4 N: | c_1 = c_6 + 2 c_7 O: | 3 c_1 + 2 c_3 = c_4 + 3 c_6 + 6 c_7 Cl: | c_2 = 2 c_5 K: | c_2 = c_6 Pb: | 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 = 4 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_3 + 2 KCl + PbO_2 ⟶ 2 H_2O + Cl_2 + 2 KNO_3 + Pb(NO_3)_2

+ + ⟶ + + +

nitric acid + potassium chloride + lead dioxide ⟶ water + chlorine + potassium nitrate + lead(II) nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + KCl + PbO_2 ⟶ H_2O + Cl_2 + KNO_3 + Pb(NO_3)_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: 4 HNO_3 + 2 KCl + PbO_2 ⟶ 2 H_2O + Cl_2 + 2 KNO_3 + Pb(NO_3)_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 HNO_3 | 4 | -4 KCl | 2 | -2 PbO_2 | 1 | -1 H_2O | 2 | 2 Cl_2 | 1 | 1 KNO_3 | 2 | 2 Pb(NO_3)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 4 | -4 | ([HNO3])^(-4) KCl | 2 | -2 | ([KCl])^(-2) PbO_2 | 1 | -1 | ([PbO2])^(-1) H_2O | 2 | 2 | ([H2O])^2 Cl_2 | 1 | 1 | [Cl2] KNO_3 | 2 | 2 | ([KNO3])^2 Pb(NO_3)_2 | 1 | 1 | [Pb(NO3)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 = ([HNO3])^(-4) ([KCl])^(-2) ([PbO2])^(-1) ([H2O])^2 [Cl2] ([KNO3])^2 [Pb(NO3)2] = (([H2O])^2 [Cl2] ([KNO3])^2 [Pb(NO3)2])/(([HNO3])^4 ([KCl])^2 [PbO2])

Construct the rate of reaction expression for: HNO_3 + KCl + PbO_2 ⟶ H_2O + Cl_2 + KNO_3 + Pb(NO_3)_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: 4 HNO_3 + 2 KCl + PbO_2 ⟶ 2 H_2O + Cl_2 + 2 KNO_3 + Pb(NO_3)_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 HNO_3 | 4 | -4 KCl | 2 | -2 PbO_2 | 1 | -1 H_2O | 2 | 2 Cl_2 | 1 | 1 KNO_3 | 2 | 2 Pb(NO_3)_2 | 1 | 1 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 HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) KCl | 2 | -2 | -1/2 (Δ[KCl])/(Δt) PbO_2 | 1 | -1 | -(Δ[PbO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Cl_2 | 1 | 1 | (Δ[Cl2])/(Δt) KNO_3 | 2 | 2 | 1/2 (Δ[KNO3])/(Δt) Pb(NO_3)_2 | 1 | 1 | (Δ[Pb(NO3)2])/(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 = -1/4 (Δ[HNO3])/(Δt) = -1/2 (Δ[KCl])/(Δt) = -(Δ[PbO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[Cl2])/(Δt) = 1/2 (Δ[KNO3])/(Δt) = (Δ[Pb(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | potassium chloride | lead dioxide | water | chlorine | potassium nitrate | lead(II) nitrate formula | HNO_3 | KCl | PbO_2 | H_2O | Cl_2 | KNO_3 | Pb(NO_3)_2 Hill formula | HNO_3 | ClK | O_2Pb | H_2O | Cl_2 | KNO_3 | N_2O_6Pb name | nitric acid | potassium chloride | lead dioxide | water | chlorine | potassium nitrate | lead(II) nitrate IUPAC name | nitric acid | potassium chloride | | water | molecular chlorine | potassium nitrate | plumbous dinitrate

| nitric acid | potassium chloride | lead dioxide | water | chlorine | potassium nitrate | lead(II) nitrate molar mass | 63.012 g/mol | 74.55 g/mol | 239.2 g/mol | 18.015 g/mol | 70.9 g/mol | 101.1 g/mol | 331.2 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | -41.6 °C | 770 °C | 290 °C | 0 °C | -101 °C | 334 °C | 470 °C boiling point | 83 °C | 1420 °C | | 99.9839 °C | -34 °C | | density | 1.5129 g/cm^3 | 1.98 g/cm^3 | 9.58 g/cm^3 | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | | solubility in water | miscible | soluble | insoluble | | | soluble | surface tension | | | | 0.0728 N/m | | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | odorless | | odorless | | odorless | odorless