Pb(NO3)2 = O2 + PbO + N2O4

Pb(NO_3)_2 lead(II) nitrate ⟶ O_2 oxygen + PbO lead monoxide + N_2O_4 dinitrogen tetroxide

Balance the chemical equation algebraically: Pb(NO_3)_2 ⟶ O_2 + PbO + N_2O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Pb(NO_3)_2 ⟶ c_2 O_2 + c_3 PbO + c_4 N_2O_4 Set the number of atoms in the reactants equal to the number of atoms in the products for N, O and Pb: N: | 2 c_1 = 2 c_4 O: | 6 c_1 = 2 c_2 + c_3 + 4 c_4 Pb: | c_1 = c_3 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 = 2 c_2 = 1 c_3 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Pb(NO_3)_2 ⟶ O_2 + 2 PbO + 2 N_2O_4

⟶ + +

lead(II) nitrate ⟶ oxygen + lead monoxide + dinitrogen tetroxide

Construct the equilibrium constant, K, expression for: Pb(NO_3)_2 ⟶ O_2 + PbO + N_2O_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: 2 Pb(NO_3)_2 ⟶ O_2 + 2 PbO + 2 N_2O_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 Pb(NO_3)_2 | 2 | -2 O_2 | 1 | 1 PbO | 2 | 2 N_2O_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Pb(NO_3)_2 | 2 | -2 | ([Pb(NO3)2])^(-2) O_2 | 1 | 1 | [O2] PbO | 2 | 2 | ([PbO])^2 N_2O_4 | 2 | 2 | ([N2O4])^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 = ([Pb(NO3)2])^(-2) [O2] ([PbO])^2 ([N2O4])^2 = ([O2] ([PbO])^2 ([N2O4])^2)/([Pb(NO3)2])^2

Construct the rate of reaction expression for: Pb(NO_3)_2 ⟶ O_2 + PbO + N_2O_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: 2 Pb(NO_3)_2 ⟶ O_2 + 2 PbO + 2 N_2O_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 Pb(NO_3)_2 | 2 | -2 O_2 | 1 | 1 PbO | 2 | 2 N_2O_4 | 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 Pb(NO_3)_2 | 2 | -2 | -1/2 (Δ[Pb(NO3)2])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) PbO | 2 | 2 | 1/2 (Δ[PbO])/(Δt) N_2O_4 | 2 | 2 | 1/2 (Δ[N2O4])/(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 = -1/2 (Δ[Pb(NO3)2])/(Δt) = (Δ[O2])/(Δt) = 1/2 (Δ[PbO])/(Δt) = 1/2 (Δ[N2O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| lead(II) nitrate | oxygen | lead monoxide | dinitrogen tetroxide formula | Pb(NO_3)_2 | O_2 | PbO | N_2O_4 Hill formula | N_2O_6Pb | O_2 | OPb | N_2O_4 name | lead(II) nitrate | oxygen | lead monoxide | dinitrogen tetroxide IUPAC name | plumbous dinitrate | molecular oxygen | |

| lead(II) nitrate | oxygen | lead monoxide | dinitrogen tetroxide molar mass | 331.2 g/mol | 31.998 g/mol | 223.2 g/mol | 92.01 g/mol phase | solid (at STP) | gas (at STP) | solid (at STP) | gas (at STP) melting point | 470 °C | -218 °C | 886 °C | -15 °C boiling point | | -183 °C | 1470 °C | 21.2 °C density | | 0.001429 g/cm^3 (at 0 °C) | 9.5 g/cm^3 | 1.45 g/cm^3 (at 20 °C) solubility in water | | | insoluble | reacts surface tension | | 0.01347 N/m | | 0.0275 N/m dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | 1.45×10^-4 Pa s (at 1000 °C) | 4.18×10^-4 Pa s (at 20 °C) odor | odorless | odorless | |