K2CO3 = CO2 + K2O

K_2CO_3 pearl ash ⟶ CO_2 carbon dioxide + K_2O potassium oxide

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

⟶ +

pearl ash ⟶ carbon dioxide + potassium oxide

Construct the equilibrium constant, K, expression for: K_2CO_3 ⟶ CO_2 + K_2O 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: K_2CO_3 ⟶ CO_2 + K_2O 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 K_2CO_3 | 1 | -1 CO_2 | 1 | 1 K_2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2CO_3 | 1 | -1 | ([K2CO3])^(-1) CO_2 | 1 | 1 | [CO2] K_2O | 1 | 1 | [K2O] 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 = ([K2CO3])^(-1) [CO2] [K2O] = ([CO2] [K2O])/([K2CO3])

Construct the rate of reaction expression for: K_2CO_3 ⟶ CO_2 + K_2O 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: K_2CO_3 ⟶ CO_2 + K_2O 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 K_2CO_3 | 1 | -1 CO_2 | 1 | 1 K_2O | 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 K_2CO_3 | 1 | -1 | -(Δ[K2CO3])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) K_2O | 1 | 1 | (Δ[K2O])/(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[K2CO3])/(Δt) = (Δ[CO2])/(Δt) = (Δ[K2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

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

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