Pb(NO3)2 + Li = Pb + Li(NO3)

Pb(NO_3)_2 lead(II) nitrate + Li lithium ⟶ Pb lead + LiNO_3 lithium nitrate

Balance the chemical equation algebraically: Pb(NO_3)_2 + Li ⟶ Pb + LiNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Pb(NO_3)_2 + c_2 Li ⟶ c_3 Pb + c_4 LiNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for N, O, Pb and Li: N: | 2 c_1 = c_4 O: | 6 c_1 = 3 c_4 Pb: | c_1 = c_3 Li: | c_2 = c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Pb(NO_3)_2 + 2 Li ⟶ Pb + 2 LiNO_3

+ ⟶ +

lead(II) nitrate + lithium ⟶ lead + lithium nitrate

| lead(II) nitrate | lithium | lead | lithium nitrate molecular enthalpy | -451.9 kJ/mol | 0 kJ/mol | 0 kJ/mol | -483.1 kJ/mol total enthalpy | -451.9 kJ/mol | 0 kJ/mol | 0 kJ/mol | -966.2 kJ/mol | H_initial = -451.9 kJ/mol | | H_final = -966.2 kJ/mol | ΔH_rxn^0 | -966.2 kJ/mol - -451.9 kJ/mol = -514.3 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: Pb(NO_3)_2 + Li ⟶ Pb + LiNO_3 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: Pb(NO_3)_2 + 2 Li ⟶ Pb + 2 LiNO_3 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 | 1 | -1 Li | 2 | -2 Pb | 1 | 1 LiNO_3 | 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 | 1 | -1 | ([Pb(NO3)2])^(-1) Li | 2 | -2 | ([Li])^(-2) Pb | 1 | 1 | [Pb] LiNO_3 | 2 | 2 | ([LiNO3])^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])^(-1) ([Li])^(-2) [Pb] ([LiNO3])^2 = ([Pb] ([LiNO3])^2)/([Pb(NO3)2] ([Li])^2)

Construct the rate of reaction expression for: Pb(NO_3)_2 + Li ⟶ Pb + LiNO_3 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: Pb(NO_3)_2 + 2 Li ⟶ Pb + 2 LiNO_3 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 | 1 | -1 Li | 2 | -2 Pb | 1 | 1 LiNO_3 | 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 | 1 | -1 | -(Δ[Pb(NO3)2])/(Δt) Li | 2 | -2 | -1/2 (Δ[Li])/(Δt) Pb | 1 | 1 | (Δ[Pb])/(Δt) LiNO_3 | 2 | 2 | 1/2 (Δ[LiNO3])/(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 = -(Δ[Pb(NO3)2])/(Δt) = -1/2 (Δ[Li])/(Δt) = (Δ[Pb])/(Δt) = 1/2 (Δ[LiNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| lead(II) nitrate | lithium | lead | lithium nitrate formula | Pb(NO_3)_2 | Li | Pb | LiNO_3 Hill formula | N_2O_6Pb | Li | Pb | LiNO_3 name | lead(II) nitrate | lithium | lead | lithium nitrate IUPAC name | plumbous dinitrate | lithium | lead | lithium nitrate

| lead(II) nitrate | lithium | lead | lithium nitrate molar mass | 331.2 g/mol | 6.94 g/mol | 207.2 g/mol | 68.94 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 470 °C | 180 °C | 327.4 °C | 264 °C boiling point | | 1342 °C | 1740 °C | density | | 0.534 g/cm^3 | 11.34 g/cm^3 | solubility in water | | decomposes | insoluble | surface tension | | 0.3975 N/m | | dynamic viscosity | | | 0.00183 Pa s (at 38 °C) | odor | odorless | | |