Na2SO4 + C = CO2 + Na2S

Na_2SO_4 (sodium sulfate) + C (activated charcoal) ⟶ CO_2 (carbon dioxide) + Na_2S (sodium sulfide)

Balance the chemical equation algebraically: Na_2SO_4 + C ⟶ CO_2 + Na_2S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2SO_4 + c_2 C ⟶ c_3 CO_2 + c_4 Na_2S Set the number of atoms in the reactants equal to the number of atoms in the products for Na, O, S and C: Na: | 2 c_1 = 2 c_4 O: | 4 c_1 = 2 c_3 S: | c_1 = c_4 C: | c_2 = c_3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Na_2SO_4 + 2 C ⟶ 2 CO_2 + Na_2S

+ ⟶ +

sodium sulfate + activated charcoal ⟶ carbon dioxide + sodium sulfide

Construct the equilibrium constant, K, expression for: Na_2SO_4 + C ⟶ CO_2 + Na_2S 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: Na_2SO_4 + 2 C ⟶ 2 CO_2 + Na_2S 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 Na_2SO_4 | 1 | -1 C | 2 | -2 CO_2 | 2 | 2 Na_2S | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2SO_4 | 1 | -1 | ([Na2SO4])^(-1) C | 2 | -2 | ([C])^(-2) CO_2 | 2 | 2 | ([CO2])^2 Na_2S | 1 | 1 | [Na2S] 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 = ([Na2SO4])^(-1) ([C])^(-2) ([CO2])^2 [Na2S] = (([CO2])^2 [Na2S])/([Na2SO4] ([C])^2)

Construct the rate of reaction expression for: Na_2SO_4 + C ⟶ CO_2 + Na_2S 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: Na_2SO_4 + 2 C ⟶ 2 CO_2 + Na_2S 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 Na_2SO_4 | 1 | -1 C | 2 | -2 CO_2 | 2 | 2 Na_2S | 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 Na_2SO_4 | 1 | -1 | -(Δ[Na2SO4])/(Δt) C | 2 | -2 | -1/2 (Δ[C])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) Na_2S | 1 | 1 | (Δ[Na2S])/(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 = -(Δ[Na2SO4])/(Δt) = -1/2 (Δ[C])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[Na2S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium sulfate | activated charcoal | carbon dioxide | sodium sulfide formula | Na_2SO_4 | C | CO_2 | Na_2S Hill formula | Na_2O_4S | C | CO_2 | Na_2S_1 name | sodium sulfate | activated charcoal | carbon dioxide | sodium sulfide IUPAC name | disodium sulfate | carbon | carbon dioxide |

| sodium sulfate | activated charcoal | carbon dioxide | sodium sulfide molar mass | 142.04 g/mol | 12.011 g/mol | 44.009 g/mol | 78.04 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 884 °C | 3550 °C | -56.56 °C (at triple point) | 1172 °C boiling point | 1429 °C | 4027 °C | -78.5 °C (at sublimation point) | density | 2.68 g/cm^3 | 2.26 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 1.856 g/cm^3 solubility in water | soluble | insoluble | | dynamic viscosity | | | 1.491×10^-5 Pa s (at 25 °C) | odor | | | odorless |