Ba(OH)2 + H2CO3 = H2O + BaCO3

Ba(OH)_2 barium hydroxide + H_2CO_3 carbonic acid ⟶ H_2O water + BaCO_3 barium carbonate

Balance the chemical equation algebraically: Ba(OH)_2 + H_2CO_3 ⟶ H_2O + BaCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ba(OH)_2 + c_2 H_2CO_3 ⟶ c_3 H_2O + c_4 BaCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Ba, H, O and C: Ba: | c_1 = c_4 H: | 2 c_1 + 2 c_2 = 2 c_3 O: | 2 c_1 + 3 c_2 = c_3 + 3 c_4 C: | c_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 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Ba(OH)_2 + H_2CO_3 ⟶ 2 H_2O + BaCO_3

+ ⟶ +

barium hydroxide + carbonic acid ⟶ water + barium carbonate

Construct the equilibrium constant, K, expression for: Ba(OH)_2 + H_2CO_3 ⟶ H_2O + BaCO_3 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: Ba(OH)_2 + H_2CO_3 ⟶ 2 H_2O + BaCO_3 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 Ba(OH)_2 | 1 | -1 H_2CO_3 | 1 | -1 H_2O | 2 | 2 BaCO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ba(OH)_2 | 1 | -1 | ([Ba(OH)2])^(-1) H_2CO_3 | 1 | -1 | ([H2CO3])^(-1) H_2O | 2 | 2 | ([H2O])^2 BaCO_3 | 1 | 1 | [BaCO3] 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 = ([Ba(OH)2])^(-1) ([H2CO3])^(-1) ([H2O])^2 [BaCO3] = (([H2O])^2 [BaCO3])/([Ba(OH)2] [H2CO3])

Construct the rate of reaction expression for: Ba(OH)_2 + H_2CO_3 ⟶ H_2O + BaCO_3 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: Ba(OH)_2 + H_2CO_3 ⟶ 2 H_2O + BaCO_3 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 Ba(OH)_2 | 1 | -1 H_2CO_3 | 1 | -1 H_2O | 2 | 2 BaCO_3 | 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 Ba(OH)_2 | 1 | -1 | -(Δ[Ba(OH)2])/(Δt) H_2CO_3 | 1 | -1 | -(Δ[H2CO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) BaCO_3 | 1 | 1 | (Δ[BaCO3])/(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[Ba(OH)2])/(Δt) = -(Δ[H2CO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[BaCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| barium hydroxide | carbonic acid | water | barium carbonate formula | Ba(OH)_2 | H_2CO_3 | H_2O | BaCO_3 Hill formula | BaH_2O_2 | CH_2O_3 | H_2O | CBaO_3 name | barium hydroxide | carbonic acid | water | barium carbonate IUPAC name | barium(+2) cation dihydroxide | carbonic acid | water | barium(+2) cation carbonate