AgNO3 + Pb = Ag + PbNO3

AgNO_3 silver nitrate + Pb lead ⟶ Ag silver + PbNO3

Balance the chemical equation algebraically: AgNO_3 + Pb ⟶ Ag + PbNO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AgNO_3 + c_2 Pb ⟶ c_3 Ag + c_4 PbNO3 Set the number of atoms in the reactants equal to the number of atoms in the products for Ag, N, O and Pb: Ag: | c_1 = c_3 N: | c_1 = c_4 O: | 3 c_1 = 3 c_4 Pb: | 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | AgNO_3 + Pb ⟶ Ag + PbNO3

+ ⟶ + PbNO3

silver nitrate + lead ⟶ silver + PbNO3

Construct the equilibrium constant, K, expression for: AgNO_3 + Pb ⟶ Ag + PbNO3 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: AgNO_3 + Pb ⟶ Ag + PbNO3 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 AgNO_3 | 1 | -1 Pb | 1 | -1 Ag | 1 | 1 PbNO3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AgNO_3 | 1 | -1 | ([AgNO3])^(-1) Pb | 1 | -1 | ([Pb])^(-1) Ag | 1 | 1 | [Ag] PbNO3 | 1 | 1 | [PbNO3] 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 = ([AgNO3])^(-1) ([Pb])^(-1) [Ag] [PbNO3] = ([Ag] [PbNO3])/([AgNO3] [Pb])

Construct the rate of reaction expression for: AgNO_3 + Pb ⟶ Ag + PbNO3 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: AgNO_3 + Pb ⟶ Ag + PbNO3 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 AgNO_3 | 1 | -1 Pb | 1 | -1 Ag | 1 | 1 PbNO3 | 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 AgNO_3 | 1 | -1 | -(Δ[AgNO3])/(Δt) Pb | 1 | -1 | -(Δ[Pb])/(Δt) Ag | 1 | 1 | (Δ[Ag])/(Δt) PbNO3 | 1 | 1 | (Δ[PbNO3])/(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[AgNO3])/(Δt) = -(Δ[Pb])/(Δt) = (Δ[Ag])/(Δt) = (Δ[PbNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silver nitrate | lead | silver | PbNO3 formula | AgNO_3 | Pb | Ag | PbNO3 Hill formula | AgNO_3 | Pb | Ag | NO3Pb name | silver nitrate | lead | silver |

| silver nitrate | lead | silver | PbNO3 molar mass | 169.87 g/mol | 207.2 g/mol | 107.8682 g/mol | 269.2 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 212 °C | 327.4 °C | 960 °C | boiling point | | 1740 °C | 2212 °C | density | | 11.34 g/cm^3 | 10.49 g/cm^3 | solubility in water | soluble | insoluble | insoluble | dynamic viscosity | | 0.00183 Pa s (at 38 °C) | | odor | odorless | | |