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HNO3 + BaCO3 = H2O + CO2 + Ba(NO3)2

Input interpretation

HNO_3 nitric acid + BaCO_3 barium carbonate ⟶ H_2O water + CO_2 carbon dioxide + Ba(NO_3)_2 barium nitrate
HNO_3 nitric acid + BaCO_3 barium carbonate ⟶ H_2O water + CO_2 carbon dioxide + Ba(NO_3)_2 barium nitrate

Balanced equation

Balance the chemical equation algebraically: HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 BaCO_3 ⟶ c_3 H_2O + c_4 CO_2 + c_5 Ba(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Ba and C: H: | c_1 = 2 c_3 N: | c_1 = 2 c_5 O: | 3 c_1 + 3 c_2 = c_3 + 2 c_4 + 6 c_5 Ba: | c_2 = c_5 C: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_2
Balance the chemical equation algebraically: HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 BaCO_3 ⟶ c_3 H_2O + c_4 CO_2 + c_5 Ba(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Ba and C: H: | c_1 = 2 c_3 N: | c_1 = 2 c_5 O: | 3 c_1 + 3 c_2 = c_3 + 2 c_4 + 6 c_5 Ba: | c_2 = c_5 C: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_2

Structures

+ ⟶ + +
+ ⟶ + +

Names

nitric acid + barium carbonate ⟶ water + carbon dioxide + barium nitrate
nitric acid + barium carbonate ⟶ water + carbon dioxide + barium nitrate

Reaction thermodynamics

Gibbs free energy

| nitric acid | barium carbonate | water | carbon dioxide | barium nitrate molecular free energy | -80.7 kJ/mol | -1134 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -7926 kJ/mol total free energy | -161.4 kJ/mol | -1134 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -7926 kJ/mol | G_initial = -1296 kJ/mol | | G_final = -8558 kJ/mol | | ΔG_rxn^0 | -8558 kJ/mol - -1296 kJ/mol = -7262 kJ/mol (exergonic) | | | |
| nitric acid | barium carbonate | water | carbon dioxide | barium nitrate molecular free energy | -80.7 kJ/mol | -1134 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -7926 kJ/mol total free energy | -161.4 kJ/mol | -1134 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -7926 kJ/mol | G_initial = -1296 kJ/mol | | G_final = -8558 kJ/mol | | ΔG_rxn^0 | -8558 kJ/mol - -1296 kJ/mol = -7262 kJ/mol (exergonic) | | | |

Equilibrium constant

Construct the equilibrium constant, K, expression for: HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_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: 2 HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_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 HNO_3 | 2 | -2 BaCO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 Ba(NO_3)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 2 | -2 | ([HNO3])^(-2) BaCO_3 | 1 | -1 | ([BaCO3])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] Ba(NO_3)_2 | 1 | 1 | [Ba(NO3)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 = ([HNO3])^(-2) ([BaCO3])^(-1) [H2O] [CO2] [Ba(NO3)2] = ([H2O] [CO2] [Ba(NO3)2])/(([HNO3])^2 [BaCO3])
Construct the equilibrium constant, K, expression for: HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_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: 2 HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_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 HNO_3 | 2 | -2 BaCO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 Ba(NO_3)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 2 | -2 | ([HNO3])^(-2) BaCO_3 | 1 | -1 | ([BaCO3])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] Ba(NO_3)_2 | 1 | 1 | [Ba(NO3)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 = ([HNO3])^(-2) ([BaCO3])^(-1) [H2O] [CO2] [Ba(NO3)2] = ([H2O] [CO2] [Ba(NO3)2])/(([HNO3])^2 [BaCO3])

Rate of reaction

Construct the rate of reaction expression for: HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_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: 2 HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_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 HNO_3 | 2 | -2 BaCO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 Ba(NO_3)_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 HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) BaCO_3 | 1 | -1 | -(Δ[BaCO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) Ba(NO_3)_2 | 1 | 1 | (Δ[Ba(NO3)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 = -1/2 (Δ[HNO3])/(Δt) = -(Δ[BaCO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[Ba(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_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: 2 HNO_3 + BaCO_3 ⟶ H_2O + CO_2 + Ba(NO_3)_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 HNO_3 | 2 | -2 BaCO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 Ba(NO_3)_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 HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) BaCO_3 | 1 | -1 | -(Δ[BaCO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) Ba(NO_3)_2 | 1 | 1 | (Δ[Ba(NO3)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 = -1/2 (Δ[HNO3])/(Δt) = -(Δ[BaCO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[Ba(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitric acid | barium carbonate | water | carbon dioxide | barium nitrate formula | HNO_3 | BaCO_3 | H_2O | CO_2 | Ba(NO_3)_2 Hill formula | HNO_3 | CBaO_3 | H_2O | CO_2 | BaN_2O_6 name | nitric acid | barium carbonate | water | carbon dioxide | barium nitrate IUPAC name | nitric acid | barium(+2) cation carbonate | water | carbon dioxide | barium(+2) cation dinitrate
| nitric acid | barium carbonate | water | carbon dioxide | barium nitrate formula | HNO_3 | BaCO_3 | H_2O | CO_2 | Ba(NO_3)_2 Hill formula | HNO_3 | CBaO_3 | H_2O | CO_2 | BaN_2O_6 name | nitric acid | barium carbonate | water | carbon dioxide | barium nitrate IUPAC name | nitric acid | barium(+2) cation carbonate | water | carbon dioxide | barium(+2) cation dinitrate

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