H2O + Ca(CO3) = CaO + H2CO3

H_2O water + CaCO_3 calcium carbonate ⟶ CaO lime + H_2CO_3 carbonic acid

Balance the chemical equation algebraically: H_2O + CaCO_3 ⟶ CaO + H_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CaCO_3 ⟶ c_3 CaO + c_4 H_2CO_3 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 + 3 c_2 = c_3 + 3 c_4 C: | c_2 = c_4 Ca: | c_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_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 + CaCO_3 ⟶ CaO + H_2CO_3

+ ⟶ +

water + calcium carbonate ⟶ lime + carbonic acid

Construct the equilibrium constant, K, expression for: H_2O + CaCO_3 ⟶ CaO + H_2CO_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: H_2O + CaCO_3 ⟶ CaO + H_2CO_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 H_2O | 1 | -1 CaCO_3 | 1 | -1 CaO | 1 | 1 H_2CO_3 | 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) CaCO_3 | 1 | -1 | ([CaCO3])^(-1) CaO | 1 | 1 | [CaO] H_2CO_3 | 1 | 1 | [H2CO3] 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) ([CaCO3])^(-1) [CaO] [H2CO3] = ([CaO] [H2CO3])/([H2O] [CaCO3])

Construct the rate of reaction expression for: H_2O + CaCO_3 ⟶ CaO + H_2CO_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: H_2O + CaCO_3 ⟶ CaO + H_2CO_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 H_2O | 1 | -1 CaCO_3 | 1 | -1 CaO | 1 | 1 H_2CO_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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) CaCO_3 | 1 | -1 | -(Δ[CaCO3])/(Δt) CaO | 1 | 1 | (Δ[CaO])/(Δt) H_2CO_3 | 1 | 1 | (Δ[H2CO3])/(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[CaCO3])/(Δt) = (Δ[CaO])/(Δt) = (Δ[H2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | calcium carbonate | lime | carbonic acid formula | H_2O | CaCO_3 | CaO | H_2CO_3 Hill formula | H_2O | CCaO_3 | CaO | CH_2O_3 name | water | calcium carbonate | lime | carbonic acid

| water | calcium carbonate | lime | carbonic acid molar mass | 18.015 g/mol | 100.09 g/mol | 56.077 g/mol | 62.024 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | 0 °C | 1340 °C | 2580 °C | boiling point | 99.9839 °C | | 2850 °C | density | 1 g/cm^3 | 2.71 g/cm^3 | 3.3 g/cm^3 | solubility in water | | insoluble | reacts | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | | |