H2O + NH3 + AgNO3 + Sb2O3 = Ag + NH4NO3 + Sb2O5

H_2O water + NH_3 ammonia + AgNO_3 silver nitrate + Sb_2O_3 antimony trioxide ⟶ Ag silver + NH_4NO_3 ammonium nitrate + Sb_2O_5 antimony pentoxide

Balance the chemical equation algebraically: H_2O + NH_3 + AgNO_3 + Sb_2O_3 ⟶ Ag + NH_4NO_3 + Sb_2O_5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 + c_3 AgNO_3 + c_4 Sb_2O_3 ⟶ c_5 Ag + c_6 NH_4NO_3 + c_7 Sb_2O_5 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N, Ag and Sb: H: | 2 c_1 + 3 c_2 = 4 c_6 O: | c_1 + 3 c_3 + 3 c_4 = 3 c_6 + 5 c_7 N: | c_2 + c_3 = 2 c_6 Ag: | c_3 = c_5 Sb: | 2 c_4 = 2 c_7 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_2 = 1 c_3 = c_1 + 1/2 c_4 = (5 c_1)/4 - 3/8 c_5 = c_1 + 1/2 c_6 = c_1/2 + 3/4 c_7 = (5 c_1)/4 - 3/8 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_2 = 2 c_3 = c_1 + 1 c_4 = (5 c_1)/4 - 3/4 c_5 = c_1 + 1 c_6 = c_1/2 + 3/2 c_7 = (5 c_1)/4 - 3/4 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 4 c_4 = 3 c_5 = 4 c_6 = 3 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 NH_3 + 4 AgNO_3 + 3 Sb_2O_3 ⟶ 4 Ag + 3 NH_4NO_3 + 3 Sb_2O_5

+ + + ⟶ + +

water + ammonia + silver nitrate + antimony trioxide ⟶ silver + ammonium nitrate + antimony pentoxide

Construct the equilibrium constant, K, expression for: H_2O + NH_3 + AgNO_3 + Sb_2O_3 ⟶ Ag + NH_4NO_3 + Sb_2O_5 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: 3 H_2O + 2 NH_3 + 4 AgNO_3 + 3 Sb_2O_3 ⟶ 4 Ag + 3 NH_4NO_3 + 3 Sb_2O_5 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 H_2O | 3 | -3 NH_3 | 2 | -2 AgNO_3 | 4 | -4 Sb_2O_3 | 3 | -3 Ag | 4 | 4 NH_4NO_3 | 3 | 3 Sb_2O_5 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) NH_3 | 2 | -2 | ([NH3])^(-2) AgNO_3 | 4 | -4 | ([AgNO3])^(-4) Sb_2O_3 | 3 | -3 | ([Sb2O3])^(-3) Ag | 4 | 4 | ([Ag])^4 NH_4NO_3 | 3 | 3 | ([NH4NO3])^3 Sb_2O_5 | 3 | 3 | ([Sb2O5])^3 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 = ([H2O])^(-3) ([NH3])^(-2) ([AgNO3])^(-4) ([Sb2O3])^(-3) ([Ag])^4 ([NH4NO3])^3 ([Sb2O5])^3 = (([Ag])^4 ([NH4NO3])^3 ([Sb2O5])^3)/(([H2O])^3 ([NH3])^2 ([AgNO3])^4 ([Sb2O3])^3)

Construct the rate of reaction expression for: H_2O + NH_3 + AgNO_3 + Sb_2O_3 ⟶ Ag + NH_4NO_3 + Sb_2O_5 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: 3 H_2O + 2 NH_3 + 4 AgNO_3 + 3 Sb_2O_3 ⟶ 4 Ag + 3 NH_4NO_3 + 3 Sb_2O_5 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 H_2O | 3 | -3 NH_3 | 2 | -2 AgNO_3 | 4 | -4 Sb_2O_3 | 3 | -3 Ag | 4 | 4 NH_4NO_3 | 3 | 3 Sb_2O_5 | 3 | 3 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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) AgNO_3 | 4 | -4 | -1/4 (Δ[AgNO3])/(Δt) Sb_2O_3 | 3 | -3 | -1/3 (Δ[Sb2O3])/(Δt) Ag | 4 | 4 | 1/4 (Δ[Ag])/(Δt) NH_4NO_3 | 3 | 3 | 1/3 (Δ[NH4NO3])/(Δt) Sb_2O_5 | 3 | 3 | 1/3 (Δ[Sb2O5])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[NH3])/(Δt) = -1/4 (Δ[AgNO3])/(Δt) = -1/3 (Δ[Sb2O3])/(Δt) = 1/4 (Δ[Ag])/(Δt) = 1/3 (Δ[NH4NO3])/(Δt) = 1/3 (Δ[Sb2O5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | ammonia | silver nitrate | antimony trioxide | silver | ammonium nitrate | antimony pentoxide formula | H_2O | NH_3 | AgNO_3 | Sb_2O_3 | Ag | NH_4NO_3 | Sb_2O_5 Hill formula | H_2O | H_3N | AgNO_3 | O_3Sb_2 | Ag | H_4N_2O_3 | O_5Sb_2 name | water | ammonia | silver nitrate | antimony trioxide | silver | ammonium nitrate | antimony pentoxide IUPAC name | water | ammonia | silver nitrate | oxo-oxostibanyloxystibane | silver | |