HNO3 + PbO2 + MoS2 = H2O + Pb(NO3)2 + PbSO4 + H2MoO4

HNO_3 nitric acid + PbO_2 lead dioxide + MoS_2 molybdenum disulfide ⟶ H_2O water + Pb(NO_3)_2 lead(II) nitrate + PbSO_4 lead(II) sulfate + H_2MoO_4 molybdic acid

Balance the chemical equation algebraically: HNO_3 + PbO_2 + MoS_2 ⟶ H_2O + Pb(NO_3)_2 + PbSO_4 + H_2MoO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 PbO_2 + c_3 MoS_2 ⟶ c_4 H_2O + c_5 Pb(NO_3)_2 + c_6 PbSO_4 + c_7 H_2MoO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Pb, Mo and S: H: | c_1 = 2 c_4 + 2 c_7 N: | c_1 = 2 c_5 O: | 3 c_1 + 2 c_2 = c_4 + 6 c_5 + 4 c_6 + 4 c_7 Pb: | c_2 = c_5 + c_6 Mo: | c_3 = c_7 S: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 14 c_2 = 9 c_3 = 1 c_4 = 6 c_5 = 7 c_6 = 2 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HNO_3 + 9 PbO_2 + MoS_2 ⟶ 6 H_2O + 7 Pb(NO_3)_2 + 2 PbSO_4 + H_2MoO_4

+ + ⟶ + + +

nitric acid + lead dioxide + molybdenum disulfide ⟶ water + lead(II) nitrate + lead(II) sulfate + molybdic acid

Construct the equilibrium constant, K, expression for: HNO_3 + PbO_2 + MoS_2 ⟶ H_2O + Pb(NO_3)_2 + PbSO_4 + H_2MoO_4 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: 14 HNO_3 + 9 PbO_2 + MoS_2 ⟶ 6 H_2O + 7 Pb(NO_3)_2 + 2 PbSO_4 + H_2MoO_4 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 | 14 | -14 PbO_2 | 9 | -9 MoS_2 | 1 | -1 H_2O | 6 | 6 Pb(NO_3)_2 | 7 | 7 PbSO_4 | 2 | 2 H_2MoO_4 | 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 | 14 | -14 | ([HNO3])^(-14) PbO_2 | 9 | -9 | ([PbO2])^(-9) MoS_2 | 1 | -1 | ([MoS2])^(-1) H_2O | 6 | 6 | ([H2O])^6 Pb(NO_3)_2 | 7 | 7 | ([Pb(NO3)2])^7 PbSO_4 | 2 | 2 | ([PbSO4])^2 H_2MoO_4 | 1 | 1 | [H2MoO4] 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])^(-14) ([PbO2])^(-9) ([MoS2])^(-1) ([H2O])^6 ([Pb(NO3)2])^7 ([PbSO4])^2 [H2MoO4] = (([H2O])^6 ([Pb(NO3)2])^7 ([PbSO4])^2 [H2MoO4])/(([HNO3])^14 ([PbO2])^9 [MoS2])

Construct the rate of reaction expression for: HNO_3 + PbO_2 + MoS_2 ⟶ H_2O + Pb(NO_3)_2 + PbSO_4 + H_2MoO_4 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: 14 HNO_3 + 9 PbO_2 + MoS_2 ⟶ 6 H_2O + 7 Pb(NO_3)_2 + 2 PbSO_4 + H_2MoO_4 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 | 14 | -14 PbO_2 | 9 | -9 MoS_2 | 1 | -1 H_2O | 6 | 6 Pb(NO_3)_2 | 7 | 7 PbSO_4 | 2 | 2 H_2MoO_4 | 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 | 14 | -14 | -1/14 (Δ[HNO3])/(Δt) PbO_2 | 9 | -9 | -1/9 (Δ[PbO2])/(Δt) MoS_2 | 1 | -1 | -(Δ[MoS2])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) Pb(NO_3)_2 | 7 | 7 | 1/7 (Δ[Pb(NO3)2])/(Δt) PbSO_4 | 2 | 2 | 1/2 (Δ[PbSO4])/(Δt) H_2MoO_4 | 1 | 1 | (Δ[H2MoO4])/(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 = -1/14 (Δ[HNO3])/(Δt) = -1/9 (Δ[PbO2])/(Δt) = -(Δ[MoS2])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/7 (Δ[Pb(NO3)2])/(Δt) = 1/2 (Δ[PbSO4])/(Δt) = (Δ[H2MoO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | lead dioxide | molybdenum disulfide | water | lead(II) nitrate | lead(II) sulfate | molybdic acid formula | HNO_3 | PbO_2 | MoS_2 | H_2O | Pb(NO_3)_2 | PbSO_4 | H_2MoO_4 Hill formula | HNO_3 | O_2Pb | MoS_2 | H_2O | N_2O_6Pb | O_4PbS | H_2MoO_4 name | nitric acid | lead dioxide | molybdenum disulfide | water | lead(II) nitrate | lead(II) sulfate | molybdic acid IUPAC name | nitric acid | | dithioxomolybdenum | water | plumbous dinitrate | | dihydroxy-dioxo-molybdenum

| nitric acid | lead dioxide | molybdenum disulfide | water | lead(II) nitrate | lead(II) sulfate | molybdic acid molar mass | 63.012 g/mol | 239.2 g/mol | 160.1 g/mol | 18.015 g/mol | 331.2 g/mol | 303.3 g/mol | 162 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | -41.6 °C | 290 °C | 2375 °C | 0 °C | 470 °C | 1087 °C | 300 °C boiling point | 83 °C | | | 99.9839 °C | | | density | 1.5129 g/cm^3 | 9.58 g/cm^3 | 5.06 g/cm^3 | 1 g/cm^3 | | 6.29 g/cm^3 | 3.1 g/cm^3 solubility in water | miscible | insoluble | insoluble | | | slightly 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 | |