CO2 + Ba(OH)2 = Ba(HCO3)2

CO_2 carbon dioxide + Ba(OH)_2 barium hydroxide ⟶ Ba(HCO3)2

Balance the chemical equation algebraically: CO_2 + Ba(OH)_2 ⟶ Ba(HCO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 + c_2 Ba(OH)_2 ⟶ c_3 Ba(HCO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for C, O, Ba and H: C: | c_1 = 2 c_3 O: | 2 c_1 + 2 c_2 = 6 c_3 Ba: | c_2 = c_3 H: | 2 c_2 = 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 CO_2 + Ba(OH)_2 ⟶ Ba(HCO3)2

+ ⟶ Ba(HCO3)2

carbon dioxide + barium hydroxide ⟶ Ba(HCO3)2

Construct the equilibrium constant, K, expression for: CO_2 + Ba(OH)_2 ⟶ Ba(HCO3)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: 2 CO_2 + Ba(OH)_2 ⟶ Ba(HCO3)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 CO_2 | 2 | -2 Ba(OH)_2 | 1 | -1 Ba(HCO3)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO_2 | 2 | -2 | ([CO2])^(-2) Ba(OH)_2 | 1 | -1 | ([Ba(OH)2])^(-1) Ba(HCO3)2 | 1 | 1 | [Ba(HCO3)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])^(-2) ([Ba(OH)2])^(-1) [Ba(HCO3)2] = ([Ba(HCO3)2])/(([CO2])^2 [Ba(OH)2])

Construct the rate of reaction expression for: CO_2 + Ba(OH)_2 ⟶ Ba(HCO3)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: 2 CO_2 + Ba(OH)_2 ⟶ Ba(HCO3)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 CO_2 | 2 | -2 Ba(OH)_2 | 1 | -1 Ba(HCO3)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 CO_2 | 2 | -2 | -1/2 (Δ[CO2])/(Δt) Ba(OH)_2 | 1 | -1 | -(Δ[Ba(OH)2])/(Δt) Ba(HCO3)2 | 1 | 1 | (Δ[Ba(HCO3)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 = -1/2 (Δ[CO2])/(Δt) = -(Δ[Ba(OH)2])/(Δt) = (Δ[Ba(HCO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon dioxide | barium hydroxide | Ba(HCO3)2 formula | CO_2 | Ba(OH)_2 | Ba(HCO3)2 Hill formula | CO_2 | BaH_2O_2 | C2H2BaO6 name | carbon dioxide | barium hydroxide | IUPAC name | carbon dioxide | barium(+2) cation dihydroxide |

| carbon dioxide | barium hydroxide | Ba(HCO3)2 molar mass | 44.009 g/mol | 171.34 g/mol | 259.36 g/mol phase | gas (at STP) | solid (at STP) | melting point | -56.56 °C (at triple point) | 300 °C | boiling point | -78.5 °C (at sublimation point) | | density | 0.00184212 g/cm^3 (at 20 °C) | 2.2 g/cm^3 | dynamic viscosity | 1.491×10^-5 Pa s (at 25 °C) | | odor | odorless | |