H2O + O2 + Ag + KCN = KOH + KAg(CN)2

H_2O water + O_2 oxygen + Ag silver + KCN potassium cyanide ⟶ KOH potassium hydroxide + KAg(CN)2

Balance the chemical equation algebraically: H_2O + O_2 + Ag + KCN ⟶ KOH + KAg(CN)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 Ag + c_4 KCN ⟶ c_5 KOH + c_6 KAg(CN)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ag, C, K and N: H: | 2 c_1 = c_5 O: | c_1 + 2 c_2 = c_5 Ag: | c_3 = c_6 C: | c_4 = 2 c_6 K: | c_4 = c_5 + c_6 N: | c_4 = 2 c_6 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_1 = 2 c_2 = 1 c_3 = 4 c_4 = 8 c_5 = 4 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + O_2 + 4 Ag + 8 KCN ⟶ 4 KOH + 4 KAg(CN)2

+ + + ⟶ + KAg(CN)2

water + oxygen + silver + potassium cyanide ⟶ potassium hydroxide + KAg(CN)2

Construct the equilibrium constant, K, expression for: H_2O + O_2 + Ag + KCN ⟶ KOH + KAg(CN)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: 2 H_2O + O_2 + 4 Ag + 8 KCN ⟶ 4 KOH + 4 KAg(CN)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 H_2O | 2 | -2 O_2 | 1 | -1 Ag | 4 | -4 KCN | 8 | -8 KOH | 4 | 4 KAg(CN)2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) O_2 | 1 | -1 | ([O2])^(-1) Ag | 4 | -4 | ([Ag])^(-4) KCN | 8 | -8 | ([KCN])^(-8) KOH | 4 | 4 | ([KOH])^4 KAg(CN)2 | 4 | 4 | ([KAg(CN)2])^4 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])^(-2) ([O2])^(-1) ([Ag])^(-4) ([KCN])^(-8) ([KOH])^4 ([KAg(CN)2])^4 = (([KOH])^4 ([KAg(CN)2])^4)/(([H2O])^2 [O2] ([Ag])^4 ([KCN])^8)

Construct the rate of reaction expression for: H_2O + O_2 + Ag + KCN ⟶ KOH + KAg(CN)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: 2 H_2O + O_2 + 4 Ag + 8 KCN ⟶ 4 KOH + 4 KAg(CN)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 H_2O | 2 | -2 O_2 | 1 | -1 Ag | 4 | -4 KCN | 8 | -8 KOH | 4 | 4 KAg(CN)2 | 4 | 4 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) Ag | 4 | -4 | -1/4 (Δ[Ag])/(Δt) KCN | 8 | -8 | -1/8 (Δ[KCN])/(Δt) KOH | 4 | 4 | 1/4 (Δ[KOH])/(Δt) KAg(CN)2 | 4 | 4 | 1/4 (Δ[KAg(CN)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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[O2])/(Δt) = -1/4 (Δ[Ag])/(Δt) = -1/8 (Δ[KCN])/(Δt) = 1/4 (Δ[KOH])/(Δt) = 1/4 (Δ[KAg(CN)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | oxygen | silver | potassium cyanide | potassium hydroxide | KAg(CN)2 formula | H_2O | O_2 | Ag | KCN | KOH | KAg(CN)2 Hill formula | H_2O | O_2 | Ag | CKN | HKO | C2AgKN2 name | water | oxygen | silver | potassium cyanide | potassium hydroxide | IUPAC name | water | molecular oxygen | silver | potassium cyanide | potassium hydroxide |

| water | oxygen | silver | potassium cyanide | potassium hydroxide | KAg(CN)2 molar mass | 18.015 g/mol | 31.998 g/mol | 107.8682 g/mol | 65.116 g/mol | 56.105 g/mol | 199.003 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | | solid (at STP) | melting point | 0 °C | -218 °C | 960 °C | | 406 °C | boiling point | 99.9839 °C | -183 °C | 2212 °C | | 1327 °C | density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 10.49 g/cm^3 | | 2.044 g/cm^3 | solubility in water | | | insoluble | | soluble | surface tension | 0.0728 N/m | 0.01347 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | | 0.001 Pa s (at 550 °C) | odor | odorless | odorless | | | |