Ag + O3 = O2 + Ag2O

Ag silver + O_3 ozone ⟶ O_2 oxygen + Ag_2O silver(I) oxide

Balance the chemical equation algebraically: Ag + O_3 ⟶ O_2 + Ag_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ag + c_2 O_3 ⟶ c_3 O_2 + c_4 Ag_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Ag and O: Ag: | c_1 = 2 c_4 O: | 3 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_2 = 1 c_3 = 3/2 - c_1/4 c_4 = c_1/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Ag + O_3 ⟶ O_2 + Ag_2O

+ ⟶ +

silver + ozone ⟶ oxygen + silver(I) oxide

Construct the equilibrium constant, K, expression for: Ag + O_3 ⟶ O_2 + 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: 2 Ag + O_3 ⟶ O_2 + 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 Ag | 2 | -2 O_3 | 1 | -1 O_2 | 1 | 1 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 Ag | 2 | -2 | ([Ag])^(-2) O_3 | 1 | -1 | ([O3])^(-1) O_2 | 1 | 1 | [O2] 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 = ([Ag])^(-2) ([O3])^(-1) [O2] [Ag2O] = ([O2] [Ag2O])/(([Ag])^2 [O3])

Construct the rate of reaction expression for: Ag + O_3 ⟶ O_2 + 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: 2 Ag + O_3 ⟶ O_2 + 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 Ag | 2 | -2 O_3 | 1 | -1 O_2 | 1 | 1 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 Ag | 2 | -2 | -1/2 (Δ[Ag])/(Δt) O_3 | 1 | -1 | -(Δ[O3])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(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 = -1/2 (Δ[Ag])/(Δt) = -(Δ[O3])/(Δt) = (Δ[O2])/(Δt) = (Δ[Ag2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silver | ozone | oxygen | silver(I) oxide formula | Ag | O_3 | O_2 | Ag_2O Hill formula | Ag | O_3 | O_2 | Ag_2O_1 name | silver | ozone | oxygen | silver(I) oxide IUPAC name | silver | ozone | molecular oxygen |

| silver | ozone | oxygen | silver(I) oxide molar mass | 107.8682 g/mol | 47.997 g/mol | 31.998 g/mol | 231.7 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | melting point | 960 °C | -192.2 °C | -218 °C | boiling point | 2212 °C | -111.9 °C | -183 °C | density | 10.49 g/cm^3 | 0.001962 g/cm^3 (at 25 °C) | 0.001429 g/cm^3 (at 0 °C) | solubility in water | insoluble | | | surface tension | | | 0.01347 N/m | dynamic viscosity | | | 2.055×10^-5 Pa s (at 25 °C) | odor | | | odorless |