HNO3 + Li2CO3 = H2O + CO2 + LiNO3

HNO_3 nitric acid + Li_2CO_3 lithium carbonate ⟶ H_2O water + CO_2 carbon dioxide + LiNO_3 lithium nitrate

Balance the chemical equation algebraically: HNO_3 + Li_2CO_3 ⟶ H_2O + CO_2 + LiNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Li_2CO_3 ⟶ c_3 H_2O + c_4 CO_2 + c_5 LiNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, C and Li: H: | c_1 = 2 c_3 N: | c_1 = c_5 O: | 3 c_1 + 3 c_2 = c_3 + 2 c_4 + 3 c_5 C: | c_2 = c_4 Li: | 2 c_2 = c_5 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 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + Li_2CO_3 ⟶ H_2O + CO_2 + 2 LiNO_3

+ ⟶ + +

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

| nitric acid | lithium carbonate | water | carbon dioxide | lithium nitrate molecular free energy | -80.7 kJ/mol | -1132 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -381.1 kJ/mol total free energy | -161.4 kJ/mol | -1132 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -762.2 kJ/mol | G_initial = -1294 kJ/mol | | G_final = -1394 kJ/mol | | ΔG_rxn^0 | -1394 kJ/mol - -1294 kJ/mol = -100.2 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: HNO_3 + Li_2CO_3 ⟶ H_2O + CO_2 + LiNO_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: 2 HNO_3 + Li_2CO_3 ⟶ H_2O + CO_2 + 2 LiNO_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 HNO_3 | 2 | -2 Li_2CO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 LiNO_3 | 2 | 2 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) Li_2CO_3 | 1 | -1 | ([Li2CO3])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] LiNO_3 | 2 | 2 | ([LiNO3])^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) ([Li2CO3])^(-1) [H2O] [CO2] ([LiNO3])^2 = ([H2O] [CO2] ([LiNO3])^2)/(([HNO3])^2 [Li2CO3])

Construct the rate of reaction expression for: HNO_3 + Li_2CO_3 ⟶ H_2O + CO_2 + LiNO_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: 2 HNO_3 + Li_2CO_3 ⟶ H_2O + CO_2 + 2 LiNO_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 HNO_3 | 2 | -2 Li_2CO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 LiNO_3 | 2 | 2 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) Li_2CO_3 | 1 | -1 | -(Δ[Li2CO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) LiNO_3 | 2 | 2 | 1/2 (Δ[LiNO3])/(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[Li2CO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[LiNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | lithium carbonate | water | carbon dioxide | lithium nitrate formula | HNO_3 | Li_2CO_3 | H_2O | CO_2 | LiNO_3 Hill formula | HNO_3 | CLi_2O_3 | H_2O | CO_2 | LiNO_3 name | nitric acid | lithium carbonate | water | carbon dioxide | lithium nitrate IUPAC name | nitric acid | dilithium carbonate | water | carbon dioxide | lithium nitrate

| nitric acid | lithium carbonate | water | carbon dioxide | lithium nitrate molar mass | 63.012 g/mol | 73.9 g/mol | 18.015 g/mol | 44.009 g/mol | 68.94 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -41.6 °C | 618 °C | 0 °C | -56.56 °C (at triple point) | 264 °C boiling point | 83 °C | | 99.9839 °C | -78.5 °C (at sublimation point) | density | 1.5129 g/cm^3 | 2.11 g/cm^3 | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | solubility in water | miscible | | | | surface tension | | | 0.0728 N/m | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless |