Ca(OH)2 + Ca(HCO3)2 = H2O + CaCO3

Input interpretation

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Ca(OH)_2 calcium hydroxide + Ca(HCO3)2 ⟶ H_2O water + CaCO_3 calcium carbonate

Balanced equation

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Balance the chemical equation algebraically: Ca(OH)_2 + Ca(HCO3)2 ⟶ H_2O + CaCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca(OH)_2 + c_2 Ca(HCO3)2 ⟶ c_3 H_2O + c_4 CaCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, H, O and C: Ca: | c_1 + c_2 = c_4 H: | 2 c_1 + 2 c_2 = 2 c_3 O: | 2 c_1 + 6 c_2 = c_3 + 3 c_4 C: | 2 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 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Ca(OH)_2 + Ca(HCO3)2 ⟶ 2 H_2O + 2 CaCO_3

+ Ca(HCO3)2 ⟶ +

Names

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calcium hydroxide + Ca(HCO3)2 ⟶ water + calcium carbonate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Ca(OH)_2 + Ca(HCO3)2 ⟶ H_2O + CaCO_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: Ca(OH)_2 + Ca(HCO3)2 ⟶ 2 H_2O + 2 CaCO_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 Ca(OH)_2 | 1 | -1 Ca(HCO3)2 | 1 | -1 H_2O | 2 | 2 CaCO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca(OH)_2 | 1 | -1 | ([Ca(OH)2])^(-1) Ca(HCO3)2 | 1 | -1 | ([Ca(HCO3)2])^(-1) H_2O | 2 | 2 | ([H2O])^2 CaCO_3 | 2 | 2 | ([CaCO3])^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 = ([Ca(OH)2])^(-1) ([Ca(HCO3)2])^(-1) ([H2O])^2 ([CaCO3])^2 = (([H2O])^2 ([CaCO3])^2)/([Ca(OH)2] [Ca(HCO3)2])

Rate of reaction

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Construct the rate of reaction expression for: Ca(OH)_2 + Ca(HCO3)2 ⟶ H_2O + CaCO_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: Ca(OH)_2 + Ca(HCO3)2 ⟶ 2 H_2O + 2 CaCO_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 Ca(OH)_2 | 1 | -1 Ca(HCO3)2 | 1 | -1 H_2O | 2 | 2 CaCO_3 | 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 Ca(OH)_2 | 1 | -1 | -(Δ[Ca(OH)2])/(Δt) Ca(HCO3)2 | 1 | -1 | -(Δ[Ca(HCO3)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CaCO_3 | 2 | 2 | 1/2 (Δ[CaCO3])/(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[Ca(OH)2])/(Δt) = -(Δ[Ca(HCO3)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[CaCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)