CaCO3 = CO2 + CaO

CaCO_3 (calcium carbonate) ⟶ CO_2 (carbon dioxide) + CaO (lime)

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

⟶ +

calcium carbonate ⟶ carbon dioxide + lime

| calcium carbonate | carbon dioxide | lime molecular enthalpy | -1208 kJ/mol | -393.5 kJ/mol | -634.9 kJ/mol total enthalpy | -1208 kJ/mol | -393.5 kJ/mol | -634.9 kJ/mol | H_initial = -1208 kJ/mol | H_final = -1028 kJ/mol | ΔH_rxn^0 | -1028 kJ/mol - -1208 kJ/mol = 179.2 kJ/mol (endothermic) | |

| calcium carbonate | carbon dioxide | lime molecular free energy | -1129 kJ/mol | -394.4 kJ/mol | -603.3 kJ/mol total free energy | -1129 kJ/mol | -394.4 kJ/mol | -603.3 kJ/mol | G_initial = -1129 kJ/mol | G_final = -997.7 kJ/mol | ΔG_rxn^0 | -997.7 kJ/mol - -1129 kJ/mol = 131.4 kJ/mol (endergonic) | |

| calcium carbonate | carbon dioxide | lime molecular entropy | 91.7 J/(mol K) | 214 J/(mol K) | 40 J/(mol K) total entropy | 91.7 J/(mol K) | 214 J/(mol K) | 40 J/(mol K) | S_initial = 91.7 J/(mol K) | S_final = 254 J/(mol K) | ΔS_rxn^0 | 254 J/(mol K) - 91.7 J/(mol K) = 162.3 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: CaCO_3 ⟶ CO_2 + CaO 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: CaCO_3 ⟶ CO_2 + CaO 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 CaCO_3 | 1 | -1 CO_2 | 1 | 1 CaO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CaCO_3 | 1 | -1 | ([CaCO3])^(-1) CO_2 | 1 | 1 | [CO2] CaO | 1 | 1 | [CaO] 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 = ([CaCO3])^(-1) [CO2] [CaO] = ([CO2] [CaO])/([CaCO3])

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

| calcium carbonate | carbon dioxide | lime formula | CaCO_3 | CO_2 | CaO Hill formula | CCaO_3 | CO_2 | CaO name | calcium carbonate | carbon dioxide | lime

| calcium carbonate | carbon dioxide | lime molar mass | 100.09 g/mol | 44.009 g/mol | 56.077 g/mol phase | solid (at STP) | gas (at STP) | solid (at STP) melting point | 1340 °C | -56.56 °C (at triple point) | 2580 °C boiling point | | -78.5 °C (at sublimation point) | 2850 °C density | 2.71 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 3.3 g/cm^3 solubility in water | insoluble | | reacts dynamic viscosity | | 1.491×10^-5 Pa s (at 25 °C) | odor | | odorless |