H2O + CO2 + K2CO3 = KHCO3

H_2O water + CO_2 carbon dioxide + K_2CO_3 pearl ash ⟶ KHCO_3 potassium bicarbonate

Balance the chemical equation algebraically: H_2O + CO_2 + K_2CO_3 ⟶ KHCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CO_2 + c_3 K_2CO_3 ⟶ c_4 KHCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, C and K: H: | 2 c_1 = c_4 O: | c_1 + 2 c_2 + 3 c_3 = 3 c_4 C: | c_2 + c_3 = c_4 K: | 2 c_3 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + CO_2 + K_2CO_3 ⟶ 2 KHCO_3

+ + ⟶

water + carbon dioxide + pearl ash ⟶ potassium bicarbonate

| water | carbon dioxide | pearl ash | potassium bicarbonate molecular enthalpy | -285.8 kJ/mol | -393.5 kJ/mol | -1151 kJ/mol | -963.2 kJ/mol total enthalpy | -285.8 kJ/mol | -393.5 kJ/mol | -1151 kJ/mol | -1926 kJ/mol | H_initial = -1830 kJ/mol | | | H_final = -1926 kJ/mol ΔH_rxn^0 | -1926 kJ/mol - -1830 kJ/mol = -96.07 kJ/mol (exothermic) | | |

| water | carbon dioxide | pearl ash | potassium bicarbonate molecular free energy | -237.1 kJ/mol | -394.4 kJ/mol | -1064 kJ/mol | -863.5 kJ/mol total free energy | -237.1 kJ/mol | -394.4 kJ/mol | -1064 kJ/mol | -1727 kJ/mol | G_initial = -1695 kJ/mol | | | G_final = -1727 kJ/mol ΔG_rxn^0 | -1727 kJ/mol - -1695 kJ/mol = -32 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: H_2O + CO_2 + K_2CO_3 ⟶ KHCO_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: H_2O + CO_2 + K_2CO_3 ⟶ 2 KHCO_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 H_2O | 1 | -1 CO_2 | 1 | -1 K_2CO_3 | 1 | -1 KHCO_3 | 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 | 1 | -1 | ([H2O])^(-1) CO_2 | 1 | -1 | ([CO2])^(-1) K_2CO_3 | 1 | -1 | ([K2CO3])^(-1) KHCO_3 | 2 | 2 | ([KHCO3])^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])^(-1) ([CO2])^(-1) ([K2CO3])^(-1) ([KHCO3])^2 = ([KHCO3])^2/([H2O] [CO2] [K2CO3])

Construct the rate of reaction expression for: H_2O + CO_2 + K_2CO_3 ⟶ KHCO_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: H_2O + CO_2 + K_2CO_3 ⟶ 2 KHCO_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 H_2O | 1 | -1 CO_2 | 1 | -1 K_2CO_3 | 1 | -1 KHCO_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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) K_2CO_3 | 1 | -1 | -(Δ[K2CO3])/(Δt) KHCO_3 | 2 | 2 | 1/2 (Δ[KHCO3])/(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[H2O])/(Δt) = -(Δ[CO2])/(Δt) = -(Δ[K2CO3])/(Δt) = 1/2 (Δ[KHCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | carbon dioxide | pearl ash | potassium bicarbonate formula | H_2O | CO_2 | K_2CO_3 | KHCO_3 Hill formula | H_2O | CO_2 | CK_2O_3 | CHKO_3 name | water | carbon dioxide | pearl ash | potassium bicarbonate IUPAC name | water | carbon dioxide | dipotassium carbonate | potassium hydrogen carbonate

| water | carbon dioxide | pearl ash | potassium bicarbonate molar mass | 18.015 g/mol | 44.009 g/mol | 138.2 g/mol | 100.11 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | -56.56 °C (at triple point) | 891 °C | 292 °C boiling point | 99.9839 °C | -78.5 °C (at sublimation point) | | density | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 2.43 g/cm^3 | 2.17 g/cm^3 solubility in water | | | soluble | soluble surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | | odor | odorless | odorless | | odorless