NaNO3 + Na2CO3 + As2S3 = CO2 + Na2SO4 + NaNO2 + Na3AsO4

NaNO_3 sodium nitrate + Na_2CO_3 soda ash + As_2S_3 arsenic(III) sulfide ⟶ CO_2 carbon dioxide + Na_2SO_4 sodium sulfate + NaNO_2 sodium nitrite + AsNa_3O_4 arsenic acid, trisodium salt

Balance the chemical equation algebraically: NaNO_3 + Na_2CO_3 + As_2S_3 ⟶ CO_2 + Na_2SO_4 + NaNO_2 + AsNa_3O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaNO_3 + c_2 Na_2CO_3 + c_3 As_2S_3 ⟶ c_4 CO_2 + c_5 Na_2SO_4 + c_6 NaNO_2 + c_7 AsNa_3O_4 Set the number of atoms in the reactants equal to the number of atoms in the products for N, Na, O, C, As and S: N: | c_1 = c_6 Na: | c_1 + 2 c_2 = 2 c_5 + c_6 + 3 c_7 O: | 3 c_1 + 3 c_2 = 2 c_4 + 4 c_5 + 2 c_6 + 4 c_7 C: | c_2 = c_4 As: | 2 c_3 = c_7 S: | 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 = 14 c_2 = 6 c_3 = 1 c_4 = 6 c_5 = 3 c_6 = 14 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 NaNO_3 + 6 Na_2CO_3 + As_2S_3 ⟶ 6 CO_2 + 3 Na_2SO_4 + 14 NaNO_2 + 2 AsNa_3O_4

+ + ⟶ + + +

sodium nitrate + soda ash + arsenic(III) sulfide ⟶ carbon dioxide + sodium sulfate + sodium nitrite + arsenic acid, trisodium salt

Construct the equilibrium constant, K, expression for: NaNO_3 + Na_2CO_3 + As_2S_3 ⟶ CO_2 + Na_2SO_4 + NaNO_2 + AsNa_3O_4 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: 14 NaNO_3 + 6 Na_2CO_3 + As_2S_3 ⟶ 6 CO_2 + 3 Na_2SO_4 + 14 NaNO_2 + 2 AsNa_3O_4 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 NaNO_3 | 14 | -14 Na_2CO_3 | 6 | -6 As_2S_3 | 1 | -1 CO_2 | 6 | 6 Na_2SO_4 | 3 | 3 NaNO_2 | 14 | 14 AsNa_3O_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaNO_3 | 14 | -14 | ([NaNO3])^(-14) Na_2CO_3 | 6 | -6 | ([Na2CO3])^(-6) As_2S_3 | 1 | -1 | ([As2S3])^(-1) CO_2 | 6 | 6 | ([CO2])^6 Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 NaNO_2 | 14 | 14 | ([NaNO2])^14 AsNa_3O_4 | 2 | 2 | ([AsNa3O4])^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 = ([NaNO3])^(-14) ([Na2CO3])^(-6) ([As2S3])^(-1) ([CO2])^6 ([Na2SO4])^3 ([NaNO2])^14 ([AsNa3O4])^2 = (([CO2])^6 ([Na2SO4])^3 ([NaNO2])^14 ([AsNa3O4])^2)/(([NaNO3])^14 ([Na2CO3])^6 [As2S3])

Construct the rate of reaction expression for: NaNO_3 + Na_2CO_3 + As_2S_3 ⟶ CO_2 + Na_2SO_4 + NaNO_2 + AsNa_3O_4 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: 14 NaNO_3 + 6 Na_2CO_3 + As_2S_3 ⟶ 6 CO_2 + 3 Na_2SO_4 + 14 NaNO_2 + 2 AsNa_3O_4 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 NaNO_3 | 14 | -14 Na_2CO_3 | 6 | -6 As_2S_3 | 1 | -1 CO_2 | 6 | 6 Na_2SO_4 | 3 | 3 NaNO_2 | 14 | 14 AsNa_3O_4 | 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 NaNO_3 | 14 | -14 | -1/14 (Δ[NaNO3])/(Δt) Na_2CO_3 | 6 | -6 | -1/6 (Δ[Na2CO3])/(Δt) As_2S_3 | 1 | -1 | -(Δ[As2S3])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) NaNO_2 | 14 | 14 | 1/14 (Δ[NaNO2])/(Δt) AsNa_3O_4 | 2 | 2 | 1/2 (Δ[AsNa3O4])/(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 = -1/14 (Δ[NaNO3])/(Δt) = -1/6 (Δ[Na2CO3])/(Δt) = -(Δ[As2S3])/(Δt) = 1/6 (Δ[CO2])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/14 (Δ[NaNO2])/(Δt) = 1/2 (Δ[AsNa3O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium nitrate | soda ash | arsenic(III) sulfide | carbon dioxide | sodium sulfate | sodium nitrite | arsenic acid, trisodium salt formula | NaNO_3 | Na_2CO_3 | As_2S_3 | CO_2 | Na_2SO_4 | NaNO_2 | AsNa_3O_4 Hill formula | NNaO_3 | CNa_2O_3 | As_2S_3 | CO_2 | Na_2O_4S | NNaO_2 | AsNa_3O_4 name | sodium nitrate | soda ash | arsenic(III) sulfide | carbon dioxide | sodium sulfate | sodium nitrite | arsenic acid, trisodium salt IUPAC name | sodium nitrate | disodium carbonate | | carbon dioxide | disodium sulfate | sodium nitrite |