Al + AgNO3 = Ag + Al(NO3)2

Al aluminum + AgNO_3 silver nitrate ⟶ Ag silver + Al(NO3)2

Balance the chemical equation algebraically: Al + AgNO_3 ⟶ Ag + Al(NO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 AgNO_3 ⟶ c_3 Ag + c_4 Al(NO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Ag, N and O: Al: | c_1 = c_4 Ag: | 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: | | Al + 2 AgNO_3 ⟶ 2 Ag + Al(NO3)2

+ ⟶ + Al(NO3)2

aluminum + silver nitrate ⟶ silver + Al(NO3)2

Construct the equilibrium constant, K, expression for: Al + AgNO_3 ⟶ Ag + Al(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: Al + 2 AgNO_3 ⟶ 2 Ag + Al(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 Al | 1 | -1 AgNO_3 | 2 | -2 Ag | 2 | 2 Al(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 Al | 1 | -1 | ([Al])^(-1) AgNO_3 | 2 | -2 | ([AgNO3])^(-2) Ag | 2 | 2 | ([Ag])^2 Al(NO3)2 | 1 | 1 | [Al(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 = ([Al])^(-1) ([AgNO3])^(-2) ([Ag])^2 [Al(NO3)2] = (([Ag])^2 [Al(NO3)2])/([Al] ([AgNO3])^2)

Construct the rate of reaction expression for: Al + AgNO_3 ⟶ Ag + Al(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: Al + 2 AgNO_3 ⟶ 2 Ag + Al(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 Al | 1 | -1 AgNO_3 | 2 | -2 Ag | 2 | 2 Al(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 Al | 1 | -1 | -(Δ[Al])/(Δt) AgNO_3 | 2 | -2 | -1/2 (Δ[AgNO3])/(Δt) Ag | 2 | 2 | 1/2 (Δ[Ag])/(Δt) Al(NO3)2 | 1 | 1 | (Δ[Al(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[Al])/(Δt) = -1/2 (Δ[AgNO3])/(Δt) = 1/2 (Δ[Ag])/(Δt) = (Δ[Al(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | silver nitrate | silver | Al(NO3)2 formula | Al | AgNO_3 | Ag | Al(NO3)2 Hill formula | Al | AgNO_3 | Ag | AlN2O6 name | aluminum | silver nitrate | silver |

| aluminum | silver nitrate | silver | Al(NO3)2 molar mass | 26.9815385 g/mol | 169.87 g/mol | 107.8682 g/mol | 150.99 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 660.4 °C | 212 °C | 960 °C | boiling point | 2460 °C | | 2212 °C | density | 2.7 g/cm^3 | | 10.49 g/cm^3 | solubility in water | insoluble | soluble | insoluble | surface tension | 0.817 N/m | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | | odor | odorless | odorless | |