CO2 + BaO = BaCO3

CO_2 carbon dioxide + BaO barium oxide ⟶ BaCO_3 barium carbonate

Balance the chemical equation algebraically: CO_2 + BaO ⟶ BaCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 + c_2 BaO ⟶ c_3 BaCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, O and Ba: C: | c_1 = c_3 O: | 2 c_1 + c_2 = 3 c_3 Ba: | 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: | | CO_2 + BaO ⟶ BaCO_3

+ ⟶

carbon dioxide + barium oxide ⟶ barium carbonate

| carbon dioxide | barium oxide | barium carbonate molecular enthalpy | -393.5 kJ/mol | -548 kJ/mol | -1213 kJ/mol total enthalpy | -393.5 kJ/mol | -548 kJ/mol | -1213 kJ/mol | H_initial = -941.5 kJ/mol | | H_final = -1213 kJ/mol ΔH_rxn^0 | -1213 kJ/mol - -941.5 kJ/mol = -271.5 kJ/mol (exothermic) | |

| carbon dioxide | barium oxide | barium carbonate molecular free energy | -394.4 kJ/mol | -520.3 kJ/mol | -1134 kJ/mol total free energy | -394.4 kJ/mol | -520.3 kJ/mol | -1134 kJ/mol | G_initial = -914.7 kJ/mol | | G_final = -1134 kJ/mol ΔG_rxn^0 | -1134 kJ/mol - -914.7 kJ/mol = -219.7 kJ/mol (exergonic) | |

| carbon dioxide | barium oxide | barium carbonate molecular entropy | 214 J/(mol K) | 70 J/(mol K) | 112 J/(mol K) total entropy | 214 J/(mol K) | 70 J/(mol K) | 112 J/(mol K) | S_initial = 284 J/(mol K) | | S_final = 112 J/(mol K) ΔS_rxn^0 | 112 J/(mol K) - 284 J/(mol K) = -172 J/(mol K) (exoentropic) | |

Construct the equilibrium constant, K, expression for: CO_2 + BaO ⟶ 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: CO_2 + BaO ⟶ 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 CO_2 | 1 | -1 BaO | 1 | -1 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 CO_2 | 1 | -1 | ([CO2])^(-1) BaO | 1 | -1 | ([BaO])^(-1) 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 = ([CO2])^(-1) ([BaO])^(-1) [BaCO3] = ([BaCO3])/([CO2] [BaO])

Construct the rate of reaction expression for: CO_2 + BaO ⟶ 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: CO_2 + BaO ⟶ 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 CO_2 | 1 | -1 BaO | 1 | -1 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 CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) BaO | 1 | -1 | -(Δ[BaO])/(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[CO2])/(Δt) = -(Δ[BaO])/(Δt) = (Δ[BaCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon dioxide | barium oxide | barium carbonate formula | CO_2 | BaO | BaCO_3 Hill formula | CO_2 | BaO | CBaO_3 name | carbon dioxide | barium oxide | barium carbonate IUPAC name | carbon dioxide | oxobarium | barium(+2) cation carbonate

| carbon dioxide | barium oxide | barium carbonate molar mass | 44.009 g/mol | 153.326 g/mol | 197.33 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) melting point | -56.56 °C (at triple point) | 1920 °C | 1350 °C boiling point | -78.5 °C (at sublimation point) | | density | 0.00184212 g/cm^3 (at 20 °C) | 5.72 g/cm^3 | 3.89 g/cm^3 solubility in water | | | insoluble dynamic viscosity | 1.491×10^-5 Pa s (at 25 °C) | | odor | odorless | | odorless