H2O + NH3 + Ag2O = [Ag(NH3)2]OH

H_2O water + NH_3 ammonia + Ag_2O silver(I) oxide ⟶ Ag(NH3)2OH

Balance the chemical equation algebraically: H_2O + NH_3 + Ag_2O ⟶ Ag(NH3)2OH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 + c_3 Ag_2O ⟶ c_4 Ag(NH3)2OH Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N and Ag: H: | 2 c_1 + 3 c_2 = 7 c_4 O: | c_1 + c_3 = c_4 N: | c_2 = 2 c_4 Ag: | 2 c_3 = 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 = 4 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 4 NH_3 + Ag_2O ⟶ 2 Ag(NH3)2OH

+ + ⟶ Ag(NH3)2OH

water + ammonia + silver(I) oxide ⟶ Ag(NH3)2OH

Construct the equilibrium constant, K, expression for: H_2O + NH_3 + Ag_2O ⟶ Ag(NH3)2OH 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: H_2O + 4 NH_3 + Ag_2O ⟶ 2 Ag(NH3)2OH 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 | 1 | -1 NH_3 | 4 | -4 Ag_2O | 1 | -1 Ag(NH3)2OH | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) NH_3 | 4 | -4 | ([NH3])^(-4) Ag_2O | 1 | -1 | ([Ag2O])^(-1) Ag(NH3)2OH | 2 | 2 | ([Ag(NH3)2OH])^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 = ([H2O])^(-1) ([NH3])^(-4) ([Ag2O])^(-1) ([Ag(NH3)2OH])^2 = ([Ag(NH3)2OH])^2/([H2O] ([NH3])^4 [Ag2O])

Construct the rate of reaction expression for: H_2O + NH_3 + Ag_2O ⟶ Ag(NH3)2OH 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: H_2O + 4 NH_3 + Ag_2O ⟶ 2 Ag(NH3)2OH 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 | 1 | -1 NH_3 | 4 | -4 Ag_2O | 1 | -1 Ag(NH3)2OH | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) NH_3 | 4 | -4 | -1/4 (Δ[NH3])/(Δt) Ag_2O | 1 | -1 | -(Δ[Ag2O])/(Δt) Ag(NH3)2OH | 2 | 2 | 1/2 (Δ[Ag(NH3)2OH])/(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[H2O])/(Δt) = -1/4 (Δ[NH3])/(Δt) = -(Δ[Ag2O])/(Δt) = 1/2 (Δ[Ag(NH3)2OH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | ammonia | silver(I) oxide | Ag(NH3)2OH formula | H_2O | NH_3 | Ag_2O | Ag(NH3)2OH Hill formula | H_2O | H_3N | Ag_2O_1 | H7AgN2O name | water | ammonia | silver(I) oxide |

| water | ammonia | silver(I) oxide | Ag(NH3)2OH molar mass | 18.015 g/mol | 17.031 g/mol | 231.7 g/mol | 158.94 g/mol phase | liquid (at STP) | gas (at STP) | | melting point | 0 °C | -77.73 °C | | boiling point | 99.9839 °C | -33.33 °C | | density | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | | surface tension | 0.0728 N/m | 0.0234 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | | odor | odorless | | |