C + Na2CO3 = CO + Na

C activated charcoal + Na_2CO_3 soda ash ⟶ CO carbon monoxide + Na sodium

Balance the chemical equation algebraically: C + Na_2CO_3 ⟶ CO + Na Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Na_2CO_3 ⟶ c_3 CO + c_4 Na Set the number of atoms in the reactants equal to the number of atoms in the products for C, Na and O: C: | c_1 + c_2 = c_3 Na: | 2 c_2 = c_4 O: | 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 C + Na_2CO_3 ⟶ 3 CO + 2 Na

+ ⟶ +

activated charcoal + soda ash ⟶ carbon monoxide + sodium

Construct the equilibrium constant, K, expression for: C + Na_2CO_3 ⟶ CO + Na 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 C + Na_2CO_3 ⟶ 3 CO + 2 Na 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 C | 2 | -2 Na_2CO_3 | 1 | -1 CO | 3 | 3 Na | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 2 | -2 | ([C])^(-2) Na_2CO_3 | 1 | -1 | ([Na2CO3])^(-1) CO | 3 | 3 | ([CO])^3 Na | 2 | 2 | ([Na])^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 = ([C])^(-2) ([Na2CO3])^(-1) ([CO])^3 ([Na])^2 = (([CO])^3 ([Na])^2)/(([C])^2 [Na2CO3])

Construct the rate of reaction expression for: C + Na_2CO_3 ⟶ CO + Na 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 C + Na_2CO_3 ⟶ 3 CO + 2 Na 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 C | 2 | -2 Na_2CO_3 | 1 | -1 CO | 3 | 3 Na | 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 C | 2 | -2 | -1/2 (Δ[C])/(Δt) Na_2CO_3 | 1 | -1 | -(Δ[Na2CO3])/(Δt) CO | 3 | 3 | 1/3 (Δ[CO])/(Δt) Na | 2 | 2 | 1/2 (Δ[Na])/(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[C])/(Δt) = -(Δ[Na2CO3])/(Δt) = 1/3 (Δ[CO])/(Δt) = 1/2 (Δ[Na])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | soda ash | carbon monoxide | sodium formula | C | Na_2CO_3 | CO | Na Hill formula | C | CNa_2O_3 | CO | Na name | activated charcoal | soda ash | carbon monoxide | sodium IUPAC name | carbon | disodium carbonate | carbon monoxide | sodium