H2O + CO2 + CaCO3 = Ca(HCO3)2

H_2O (water) + CO_2 (carbon dioxide) + CaCO_3 (calcium carbonate) ⟶ Ca(HCO3)2

Balance the chemical equation algebraically: H_2O + CO_2 + CaCO_3 ⟶ Ca(HCO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CO_2 + c_3 CaCO_3 ⟶ c_4 Ca(HCO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, C and Ca: H: | 2 c_1 = 2 c_4 O: | c_1 + 2 c_2 + 3 c_3 = 6 c_4 C: | c_2 + c_3 = 2 c_4 Ca: | c_3 = 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 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + CO_2 + CaCO_3 ⟶ Ca(HCO3)2

+ + ⟶ Ca(HCO3)2

water + carbon dioxide + calcium carbonate ⟶ Ca(HCO3)2

Construct the equilibrium constant, K, expression for: H_2O + CO_2 + CaCO_3 ⟶ Ca(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: H_2O + CO_2 + CaCO_3 ⟶ Ca(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 H_2O | 1 | -1 CO_2 | 1 | -1 CaCO_3 | 1 | -1 Ca(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 H_2O | 1 | -1 | ([H2O])^(-1) CO_2 | 1 | -1 | ([CO2])^(-1) CaCO_3 | 1 | -1 | ([CaCO3])^(-1) Ca(HCO3)2 | 1 | 1 | [Ca(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 = ([H2O])^(-1) ([CO2])^(-1) ([CaCO3])^(-1) [Ca(HCO3)2] = ([Ca(HCO3)2])/([H2O] [CO2] [CaCO3])

Construct the rate of reaction expression for: H_2O + CO_2 + CaCO_3 ⟶ Ca(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: H_2O + CO_2 + CaCO_3 ⟶ Ca(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 H_2O | 1 | -1 CO_2 | 1 | -1 CaCO_3 | 1 | -1 Ca(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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) CaCO_3 | 1 | -1 | -(Δ[CaCO3])/(Δt) Ca(HCO3)2 | 1 | 1 | (Δ[Ca(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 = -(Δ[H2O])/(Δt) = -(Δ[CO2])/(Δt) = -(Δ[CaCO3])/(Δt) = (Δ[Ca(HCO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | carbon dioxide | calcium carbonate | Ca(HCO3)2 formula | H_2O | CO_2 | CaCO_3 | Ca(HCO3)2 Hill formula | H_2O | CO_2 | CCaO_3 | C2H2CaO6 name | water | carbon dioxide | calcium carbonate |

| water | carbon dioxide | calcium carbonate | Ca(HCO3)2 molar mass | 18.015 g/mol | 44.009 g/mol | 100.09 g/mol | 162.11 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | melting point | 0 °C | -56.56 °C (at triple point) | 1340 °C | boiling point | 99.9839 °C | -78.5 °C (at sublimation point) | | density | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 2.71 g/cm^3 | solubility in water | | | insoluble | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | | odor | odorless | odorless | |