H2O + CO2 + Li = H2 + LiHCO3

H_2O water + CO_2 carbon dioxide + Li lithium ⟶ H_2 hydrogen + LiHCO3

Balance the chemical equation algebraically: H_2O + CO_2 + Li ⟶ H_2 + LiHCO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CO_2 + c_3 Li ⟶ c_4 H_2 + c_5 LiHCO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, C and Li: H: | 2 c_1 = 2 c_4 + c_5 O: | c_1 + 2 c_2 = 3 c_5 C: | c_2 = c_5 Li: | c_3 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 CO_2 + 2 Li ⟶ H_2 + 2 LiHCO3

+ + ⟶ + LiHCO3

water + carbon dioxide + lithium ⟶ hydrogen + LiHCO3

Construct the equilibrium constant, K, expression for: H_2O + CO_2 + Li ⟶ H_2 + LiHCO3 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 H_2O + 2 CO_2 + 2 Li ⟶ H_2 + 2 LiHCO3 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 | 2 | -2 CO_2 | 2 | -2 Li | 2 | -2 H_2 | 1 | 1 LiHCO3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) CO_2 | 2 | -2 | ([CO2])^(-2) Li | 2 | -2 | ([Li])^(-2) H_2 | 1 | 1 | [H2] LiHCO3 | 2 | 2 | ([LiHCO3])^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 = ([H2O])^(-2) ([CO2])^(-2) ([Li])^(-2) [H2] ([LiHCO3])^2 = ([H2] ([LiHCO3])^2)/(([H2O])^2 ([CO2])^2 ([Li])^2)

Construct the rate of reaction expression for: H_2O + CO_2 + Li ⟶ H_2 + LiHCO3 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 H_2O + 2 CO_2 + 2 Li ⟶ H_2 + 2 LiHCO3 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 | 2 | -2 CO_2 | 2 | -2 Li | 2 | -2 H_2 | 1 | 1 LiHCO3 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) CO_2 | 2 | -2 | -1/2 (Δ[CO2])/(Δt) Li | 2 | -2 | -1/2 (Δ[Li])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) LiHCO3 | 2 | 2 | 1/2 (Δ[LiHCO3])/(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[H2O])/(Δt) = -1/2 (Δ[CO2])/(Δt) = -1/2 (Δ[Li])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[LiHCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | carbon dioxide | lithium | hydrogen | LiHCO3 formula | H_2O | CO_2 | Li | H_2 | LiHCO3 Hill formula | H_2O | CO_2 | Li | H_2 | CHLiO3 name | water | carbon dioxide | lithium | hydrogen | IUPAC name | water | carbon dioxide | lithium | molecular hydrogen |

| water | carbon dioxide | lithium | hydrogen | LiHCO3 molar mass | 18.015 g/mol | 44.009 g/mol | 6.94 g/mol | 2.016 g/mol | 67.96 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | -56.56 °C (at triple point) | 180 °C | -259.2 °C | boiling point | 99.9839 °C | -78.5 °C (at sublimation point) | 1342 °C | -252.8 °C | density | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 0.534 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | | | decomposes | | surface tension | 0.0728 N/m | | 0.3975 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | odorless | | odorless |