H2O + C + BaCO3 = CO + Ba(OH)2

H_2O water + C activated charcoal + BaCO_3 barium carbonate ⟶ CO carbon monoxide + Ba(OH)_2 barium hydroxide

Balance the chemical equation algebraically: H_2O + C + BaCO_3 ⟶ CO + Ba(OH)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 C + c_3 BaCO_3 ⟶ c_4 CO + c_5 Ba(OH)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, C and Ba: H: | 2 c_1 = 2 c_5 O: | c_1 + 3 c_3 = c_4 + 2 c_5 C: | c_2 + c_3 = c_4 Ba: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + C + BaCO_3 ⟶ 2 CO + Ba(OH)_2

+ + ⟶ +

water + activated charcoal + barium carbonate ⟶ carbon monoxide + barium hydroxide

Construct the equilibrium constant, K, expression for: H_2O + C + BaCO_3 ⟶ CO + Ba(OH)_2 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: H_2O + C + BaCO_3 ⟶ 2 CO + Ba(OH)_2 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 H_2O | 1 | -1 C | 1 | -1 BaCO_3 | 1 | -1 CO | 2 | 2 Ba(OH)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) C | 1 | -1 | ([C])^(-1) BaCO_3 | 1 | -1 | ([BaCO3])^(-1) CO | 2 | 2 | ([CO])^2 Ba(OH)_2 | 1 | 1 | [Ba(OH)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 = ([H2O])^(-1) ([C])^(-1) ([BaCO3])^(-1) ([CO])^2 [Ba(OH)2] = (([CO])^2 [Ba(OH)2])/([H2O] [C] [BaCO3])

Construct the rate of reaction expression for: H_2O + C + BaCO_3 ⟶ CO + Ba(OH)_2 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: H_2O + C + BaCO_3 ⟶ 2 CO + Ba(OH)_2 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 H_2O | 1 | -1 C | 1 | -1 BaCO_3 | 1 | -1 CO | 2 | 2 Ba(OH)_2 | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) BaCO_3 | 1 | -1 | -(Δ[BaCO3])/(Δt) CO | 2 | 2 | 1/2 (Δ[CO])/(Δt) Ba(OH)_2 | 1 | 1 | (Δ[Ba(OH)2])/(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[H2O])/(Δt) = -(Δ[C])/(Δt) = -(Δ[BaCO3])/(Δt) = 1/2 (Δ[CO])/(Δt) = (Δ[Ba(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | activated charcoal | barium carbonate | carbon monoxide | barium hydroxide formula | H_2O | C | BaCO_3 | CO | Ba(OH)_2 Hill formula | H_2O | C | CBaO_3 | CO | BaH_2O_2 name | water | activated charcoal | barium carbonate | carbon monoxide | barium hydroxide IUPAC name | water | carbon | barium(+2) cation carbonate | carbon monoxide | barium(+2) cation dihydroxide