SO2 + Na2CO3 + AuCl3 = CO2 + NaCl + Na2SO4 + Au

SO_2 sulfur dioxide + Na_2CO_3 soda ash + AuCl_3 gold(III) chloride ⟶ CO_2 carbon dioxide + NaCl sodium chloride + Na_2SO_4 sodium sulfate + Au gold

Balance the chemical equation algebraically: SO_2 + Na_2CO_3 + AuCl_3 ⟶ CO_2 + NaCl + Na_2SO_4 + Au Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 Na_2CO_3 + c_3 AuCl_3 ⟶ c_4 CO_2 + c_5 NaCl + c_6 Na_2SO_4 + c_7 Au Set the number of atoms in the reactants equal to the number of atoms in the products for O, S, C, Na, Au and Cl: O: | 2 c_1 + 3 c_2 = 2 c_4 + 4 c_6 S: | c_1 = c_6 C: | c_2 = c_4 Na: | 2 c_2 = c_5 + 2 c_6 Au: | c_3 = c_7 Cl: | 3 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 = 3/2 c_2 = 3 c_3 = 1 c_4 = 3 c_5 = 3 c_6 = 3/2 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 6 c_3 = 2 c_4 = 6 c_5 = 6 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 SO_2 + 6 Na_2CO_3 + 2 AuCl_3 ⟶ 6 CO_2 + 6 NaCl + 3 Na_2SO_4 + 2 Au

+ + ⟶ + + +

sulfur dioxide + soda ash + gold(III) chloride ⟶ carbon dioxide + sodium chloride + sodium sulfate + gold

Construct the equilibrium constant, K, expression for: SO_2 + Na_2CO_3 + AuCl_3 ⟶ CO_2 + NaCl + Na_2SO_4 + Au 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: 3 SO_2 + 6 Na_2CO_3 + 2 AuCl_3 ⟶ 6 CO_2 + 6 NaCl + 3 Na_2SO_4 + 2 Au 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 SO_2 | 3 | -3 Na_2CO_3 | 6 | -6 AuCl_3 | 2 | -2 CO_2 | 6 | 6 NaCl | 6 | 6 Na_2SO_4 | 3 | 3 Au | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 3 | -3 | ([SO2])^(-3) Na_2CO_3 | 6 | -6 | ([Na2CO3])^(-6) AuCl_3 | 2 | -2 | ([AuCl3])^(-2) CO_2 | 6 | 6 | ([CO2])^6 NaCl | 6 | 6 | ([NaCl])^6 Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 Au | 2 | 2 | ([Au])^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 = ([SO2])^(-3) ([Na2CO3])^(-6) ([AuCl3])^(-2) ([CO2])^6 ([NaCl])^6 ([Na2SO4])^3 ([Au])^2 = (([CO2])^6 ([NaCl])^6 ([Na2SO4])^3 ([Au])^2)/(([SO2])^3 ([Na2CO3])^6 ([AuCl3])^2)

Construct the rate of reaction expression for: SO_2 + Na_2CO_3 + AuCl_3 ⟶ CO_2 + NaCl + Na_2SO_4 + Au 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: 3 SO_2 + 6 Na_2CO_3 + 2 AuCl_3 ⟶ 6 CO_2 + 6 NaCl + 3 Na_2SO_4 + 2 Au 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 SO_2 | 3 | -3 Na_2CO_3 | 6 | -6 AuCl_3 | 2 | -2 CO_2 | 6 | 6 NaCl | 6 | 6 Na_2SO_4 | 3 | 3 Au | 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 SO_2 | 3 | -3 | -1/3 (Δ[SO2])/(Δt) Na_2CO_3 | 6 | -6 | -1/6 (Δ[Na2CO3])/(Δt) AuCl_3 | 2 | -2 | -1/2 (Δ[AuCl3])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(Δt) NaCl | 6 | 6 | 1/6 (Δ[NaCl])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) Au | 2 | 2 | 1/2 (Δ[Au])/(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 = -1/3 (Δ[SO2])/(Δt) = -1/6 (Δ[Na2CO3])/(Δt) = -1/2 (Δ[AuCl3])/(Δt) = 1/6 (Δ[CO2])/(Δt) = 1/6 (Δ[NaCl])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[Au])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | soda ash | gold(III) chloride | carbon dioxide | sodium chloride | sodium sulfate | gold formula | SO_2 | Na_2CO_3 | AuCl_3 | CO_2 | NaCl | Na_2SO_4 | Au Hill formula | O_2S | CNa_2O_3 | AuCl_3 | CO_2 | ClNa | Na_2O_4S | Au name | sulfur dioxide | soda ash | gold(III) chloride | carbon dioxide | sodium chloride | sodium sulfate | gold IUPAC name | sulfur dioxide | disodium carbonate | trichlorogold | carbon dioxide | sodium chloride | disodium sulfate | gold