KOH + AgNO3 + Na2SO3 = H2O + Na2SO4 + KNO3 + Ag

KOH potassium hydroxide + AgNO_3 silver nitrate + Na_2SO_3 sodium sulfite ⟶ H_2O water + Na_2SO_4 sodium sulfate + KNO_3 potassium nitrate + Ag silver

Balance the chemical equation algebraically: KOH + AgNO_3 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + KNO_3 + Ag Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 AgNO_3 + c_3 Na_2SO_3 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 KNO_3 + c_7 Ag Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Ag, N, Na and S: H: | c_1 = 2 c_4 K: | c_1 = c_6 O: | c_1 + 3 c_2 + 3 c_3 = c_4 + 4 c_5 + 3 c_6 Ag: | c_2 = c_7 N: | c_2 = c_6 Na: | 2 c_3 = 2 c_5 S: | c_3 = c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + 2 AgNO_3 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + 2 KNO_3 + 2 Ag

+ + ⟶ + + +

potassium hydroxide + silver nitrate + sodium sulfite ⟶ water + sodium sulfate + potassium nitrate + silver

| potassium hydroxide | silver nitrate | sodium sulfite | water | sodium sulfate | potassium nitrate | silver molecular enthalpy | -424.6 kJ/mol | -124.4 kJ/mol | -1101 kJ/mol | -285.8 kJ/mol | -1387 kJ/mol | -494.6 kJ/mol | 0 kJ/mol total enthalpy | -849.2 kJ/mol | -248.8 kJ/mol | -1101 kJ/mol | -285.8 kJ/mol | -1387 kJ/mol | -989.2 kJ/mol | 0 kJ/mol | H_initial = -2199 kJ/mol | | | H_final = -2662 kJ/mol | | | ΔH_rxn^0 | -2662 kJ/mol - -2199 kJ/mol = -463.3 kJ/mol (exothermic) | | | | | |

Construct the equilibrium constant, K, expression for: KOH + AgNO_3 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + KNO_3 + Ag 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 KOH + 2 AgNO_3 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + 2 KNO_3 + 2 Ag 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 KOH | 2 | -2 AgNO_3 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 KNO_3 | 2 | 2 Ag | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) AgNO_3 | 2 | -2 | ([AgNO3])^(-2) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) H_2O | 1 | 1 | [H2O] Na_2SO_4 | 1 | 1 | [Na2SO4] KNO_3 | 2 | 2 | ([KNO3])^2 Ag | 2 | 2 | ([Ag])^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 = ([KOH])^(-2) ([AgNO3])^(-2) ([Na2SO3])^(-1) [H2O] [Na2SO4] ([KNO3])^2 ([Ag])^2 = ([H2O] [Na2SO4] ([KNO3])^2 ([Ag])^2)/(([KOH])^2 ([AgNO3])^2 [Na2SO3])

Construct the rate of reaction expression for: KOH + AgNO_3 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + KNO_3 + Ag 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 KOH + 2 AgNO_3 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + 2 KNO_3 + 2 Ag 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 KOH | 2 | -2 AgNO_3 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 KNO_3 | 2 | 2 Ag | 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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) AgNO_3 | 2 | -2 | -1/2 (Δ[AgNO3])/(Δt) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) KNO_3 | 2 | 2 | 1/2 (Δ[KNO3])/(Δt) Ag | 2 | 2 | 1/2 (Δ[Ag])/(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[KOH])/(Δt) = -1/2 (Δ[AgNO3])/(Δt) = -(Δ[Na2SO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Na2SO4])/(Δt) = 1/2 (Δ[KNO3])/(Δt) = 1/2 (Δ[Ag])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | silver nitrate | sodium sulfite | water | sodium sulfate | potassium nitrate | silver formula | KOH | AgNO_3 | Na_2SO_3 | H_2O | Na_2SO_4 | KNO_3 | Ag Hill formula | HKO | AgNO_3 | Na_2O_3S | H_2O | Na_2O_4S | KNO_3 | Ag name | potassium hydroxide | silver nitrate | sodium sulfite | water | sodium sulfate | potassium nitrate | silver IUPAC name | potassium hydroxide | silver nitrate | disodium sulfite | water | disodium sulfate | potassium nitrate | silver