CO2 + Na = C + Na2O

CO_2 carbon dioxide + Na sodium ⟶ C activated charcoal + Na_2O sodium oxide

Balance the chemical equation algebraically: CO_2 + Na ⟶ C + Na_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 + c_2 Na ⟶ c_3 C + c_4 Na_2O Set the number of atoms in the reactants equal to the number of atoms in the products for C, O and Na: C: | c_1 = c_3 O: | 2 c_1 = c_4 Na: | c_2 = 2 c_4 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 = 4 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CO_2 + 4 Na ⟶ C + 2 Na_2O

+ ⟶ +

carbon dioxide + sodium ⟶ activated charcoal + sodium oxide

Construct the equilibrium constant, K, expression for: CO_2 + Na ⟶ C + Na_2O 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: CO_2 + 4 Na ⟶ C + 2 Na_2O 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 CO_2 | 1 | -1 Na | 4 | -4 C | 1 | 1 Na_2O | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO_2 | 1 | -1 | ([CO2])^(-1) Na | 4 | -4 | ([Na])^(-4) C | 1 | 1 | [C] Na_2O | 2 | 2 | ([Na2O])^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 = ([CO2])^(-1) ([Na])^(-4) [C] ([Na2O])^2 = ([C] ([Na2O])^2)/([CO2] ([Na])^4)

Construct the rate of reaction expression for: CO_2 + Na ⟶ C + Na_2O 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: CO_2 + 4 Na ⟶ C + 2 Na_2O 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 CO_2 | 1 | -1 Na | 4 | -4 C | 1 | 1 Na_2O | 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 CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) Na | 4 | -4 | -1/4 (Δ[Na])/(Δt) C | 1 | 1 | (Δ[C])/(Δt) Na_2O | 2 | 2 | 1/2 (Δ[Na2O])/(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[CO2])/(Δt) = -1/4 (Δ[Na])/(Δt) = (Δ[C])/(Δt) = 1/2 (Δ[Na2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon dioxide | sodium | activated charcoal | sodium oxide formula | CO_2 | Na | C | Na_2O name | carbon dioxide | sodium | activated charcoal | sodium oxide IUPAC name | carbon dioxide | sodium | carbon | disodium oxygen(-2) anion