Zn + Pb(NO3) = Pb + Zn(NO3)2

Zn zinc + PbNO3 ⟶ Pb lead + Zn(NO3)2

Balance the chemical equation algebraically: Zn + PbNO3 ⟶ Pb + Zn(NO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Zn + c_2 PbNO3 ⟶ c_3 Pb + c_4 Zn(NO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Zn, Pb, N and O: Zn: | c_1 = c_4 Pb: | c_2 = c_3 N: | c_2 = 2 c_4 O: | 3 c_2 = 6 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 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Zn + 2 PbNO3 ⟶ 2 Pb + Zn(NO3)2

+ PbNO3 ⟶ + Zn(NO3)2

zinc + PbNO3 ⟶ lead + Zn(NO3)2

Construct the equilibrium constant, K, expression for: Zn + PbNO3 ⟶ Pb + Zn(NO3)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: Zn + 2 PbNO3 ⟶ 2 Pb + Zn(NO3)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 Zn | 1 | -1 PbNO3 | 2 | -2 Pb | 2 | 2 Zn(NO3)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Zn | 1 | -1 | ([Zn])^(-1) PbNO3 | 2 | -2 | ([PbNO3])^(-2) Pb | 2 | 2 | ([Pb])^2 Zn(NO3)2 | 1 | 1 | [Zn(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 = ([Zn])^(-1) ([PbNO3])^(-2) ([Pb])^2 [Zn(NO3)2] = (([Pb])^2 [Zn(NO3)2])/([Zn] ([PbNO3])^2)

Construct the rate of reaction expression for: Zn + PbNO3 ⟶ Pb + Zn(NO3)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: Zn + 2 PbNO3 ⟶ 2 Pb + Zn(NO3)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 Zn | 1 | -1 PbNO3 | 2 | -2 Pb | 2 | 2 Zn(NO3)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 Zn | 1 | -1 | -(Δ[Zn])/(Δt) PbNO3 | 2 | -2 | -1/2 (Δ[PbNO3])/(Δt) Pb | 2 | 2 | 1/2 (Δ[Pb])/(Δt) Zn(NO3)2 | 1 | 1 | (Δ[Zn(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 = -(Δ[Zn])/(Δt) = -1/2 (Δ[PbNO3])/(Δt) = 1/2 (Δ[Pb])/(Δt) = (Δ[Zn(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| zinc | PbNO3 | lead | Zn(NO3)2 formula | Zn | PbNO3 | Pb | Zn(NO3)2 Hill formula | Zn | NO3Pb | Pb | N2O6Zn name | zinc | | lead |

| zinc | PbNO3 | lead | Zn(NO3)2 molar mass | 65.38 g/mol | 269.2 g/mol | 207.2 g/mol | 189.4 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 420 °C | | 327.4 °C | boiling point | 907 °C | | 1740 °C | density | 7.14 g/cm^3 | | 11.34 g/cm^3 | solubility in water | insoluble | | insoluble | dynamic viscosity | | | 0.00183 Pa s (at 38 °C) | odor | odorless | | |