CO2 + K2O = K2CO3

CO_2 carbon dioxide + K_2O potassium oxide ⟶ K_2CO_3 pearl ash

Balance the chemical equation algebraically: CO_2 + K_2O ⟶ K_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 + c_2 K_2O ⟶ c_3 K_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, O and K: C: | c_1 = c_3 O: | 2 c_1 + c_2 = 3 c_3 K: | 2 c_2 = 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 + K_2O ⟶ K_2CO_3

+ ⟶

carbon dioxide + potassium oxide ⟶ pearl ash

Construct the equilibrium constant, K, expression for: CO_2 + K_2O ⟶ K_2CO_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 + K_2O ⟶ K_2CO_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 K_2O | 1 | -1 K_2CO_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) K_2O | 1 | -1 | ([K2O])^(-1) K_2CO_3 | 1 | 1 | [K2CO3] 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) ([K2O])^(-1) [K2CO3] = ([K2CO3])/([CO2] [K2O])

Construct the rate of reaction expression for: CO_2 + K_2O ⟶ K_2CO_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 + K_2O ⟶ K_2CO_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 K_2O | 1 | -1 K_2CO_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) K_2O | 1 | -1 | -(Δ[K2O])/(Δt) K_2CO_3 | 1 | 1 | (Δ[K2CO3])/(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[K2O])/(Δt) = (Δ[K2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon dioxide | potassium oxide | pearl ash formula | CO_2 | K_2O | K_2CO_3 Hill formula | CO_2 | K_2O | CK_2O_3 name | carbon dioxide | potassium oxide | pearl ash IUPAC name | carbon dioxide | dipotassium oxygen(2-) | dipotassium carbonate

| carbon dioxide | potassium oxide | pearl ash molar mass | 44.009 g/mol | 94.196 g/mol | 138.2 g/mol phase | gas (at STP) | | solid (at STP) melting point | -56.56 °C (at triple point) | | 891 °C boiling point | -78.5 °C (at sublimation point) | | density | 0.00184212 g/cm^3 (at 20 °C) | | 2.43 g/cm^3 solubility in water | | | soluble dynamic viscosity | 1.491×10^-5 Pa s (at 25 °C) | | odor | odorless | |