H2O + AgNO3 = HNO3 + Ag2O

H_2O water + AgNO_3 silver nitrate ⟶ HNO_3 nitric acid + Ag_2O silver(I) oxide

Balance the chemical equation algebraically: H_2O + AgNO_3 ⟶ HNO_3 + Ag_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AgNO_3 ⟶ c_3 HNO_3 + c_4 Ag_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ag and N: H: | 2 c_1 = c_3 O: | c_1 + 3 c_2 = 3 c_3 + c_4 Ag: | c_2 = 2 c_4 N: | c_2 = c_3 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: | | H_2O + 2 AgNO_3 ⟶ 2 HNO_3 + Ag_2O

+ ⟶ +

water + silver nitrate ⟶ nitric acid + silver(I) oxide

Construct the equilibrium constant, K, expression for: H_2O + AgNO_3 ⟶ HNO_3 + Ag_2O 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 + 2 AgNO_3 ⟶ 2 HNO_3 + Ag_2O 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 AgNO_3 | 2 | -2 HNO_3 | 2 | 2 Ag_2O | 1 | 1 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) AgNO_3 | 2 | -2 | ([AgNO3])^(-2) HNO_3 | 2 | 2 | ([HNO3])^2 Ag_2O | 1 | 1 | [Ag2O] 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) ([AgNO3])^(-2) ([HNO3])^2 [Ag2O] = (([HNO3])^2 [Ag2O])/([H2O] ([AgNO3])^2)

Construct the rate of reaction expression for: H_2O + AgNO_3 ⟶ HNO_3 + Ag_2O 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 + 2 AgNO_3 ⟶ 2 HNO_3 + Ag_2O 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 AgNO_3 | 2 | -2 HNO_3 | 2 | 2 Ag_2O | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) AgNO_3 | 2 | -2 | -1/2 (Δ[AgNO3])/(Δt) HNO_3 | 2 | 2 | 1/2 (Δ[HNO3])/(Δt) Ag_2O | 1 | 1 | (Δ[Ag2O])/(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) = -1/2 (Δ[AgNO3])/(Δt) = 1/2 (Δ[HNO3])/(Δt) = (Δ[Ag2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | silver nitrate | nitric acid | silver(I) oxide formula | H_2O | AgNO_3 | HNO_3 | Ag_2O Hill formula | H_2O | AgNO_3 | HNO_3 | Ag_2O_1 name | water | silver nitrate | nitric acid | silver(I) oxide

| water | silver nitrate | nitric acid | silver(I) oxide molar mass | 18.015 g/mol | 169.87 g/mol | 63.012 g/mol | 231.7 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | melting point | 0 °C | 212 °C | -41.6 °C | boiling point | 99.9839 °C | | 83 °C | density | 1 g/cm^3 | | 1.5129 g/cm^3 | solubility in water | | soluble | miscible | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 7.6×10^-4 Pa s (at 25 °C) | odor | odorless | odorless | |