K2CO3 + BaNO3 = BaCO3 + K2NO3

K_2CO_3 pearl ash + BaNO3 ⟶ BaCO_3 barium carbonate + K2NO3

Balance the chemical equation algebraically: K_2CO_3 + BaNO3 ⟶ BaCO_3 + K2NO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2CO_3 + c_2 BaNO3 ⟶ c_3 BaCO_3 + c_4 K2NO3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, K, O, Ba and N: C: | c_1 = c_3 K: | 2 c_1 = 2 c_4 O: | 3 c_1 + 3 c_2 = 3 c_3 + 3 c_4 Ba: | c_2 = c_3 N: | c_2 = 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | K_2CO_3 + BaNO3 ⟶ BaCO_3 + K2NO3

+ BaNO3 ⟶ + K2NO3

pearl ash + BaNO3 ⟶ barium carbonate + K2NO3

Construct the equilibrium constant, K, expression for: K_2CO_3 + BaNO3 ⟶ BaCO_3 + K2NO3 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 + BaNO3 ⟶ BaCO_3 + K2NO3 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 BaNO3 | 1 | -1 BaCO_3 | 1 | 1 K2NO3 | 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) BaNO3 | 1 | -1 | ([BaNO3])^(-1) BaCO_3 | 1 | 1 | [BaCO3] K2NO3 | 1 | 1 | [K2NO3] 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) ([BaNO3])^(-1) [BaCO3] [K2NO3] = ([BaCO3] [K2NO3])/([K2CO3] [BaNO3])

Construct the rate of reaction expression for: K_2CO_3 + BaNO3 ⟶ BaCO_3 + K2NO3 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 + BaNO3 ⟶ BaCO_3 + K2NO3 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 BaNO3 | 1 | -1 BaCO_3 | 1 | 1 K2NO3 | 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) BaNO3 | 1 | -1 | -(Δ[BaNO3])/(Δt) BaCO_3 | 1 | 1 | (Δ[BaCO3])/(Δt) K2NO3 | 1 | 1 | (Δ[K2NO3])/(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[BaNO3])/(Δt) = (Δ[BaCO3])/(Δt) = (Δ[K2NO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| pearl ash | BaNO3 | barium carbonate | K2NO3 formula | K_2CO_3 | BaNO3 | BaCO_3 | K2NO3 Hill formula | CK_2O_3 | BaNO3 | CBaO_3 | K2NO3 name | pearl ash | | barium carbonate | IUPAC name | dipotassium carbonate | | barium(+2) cation carbonate |

| pearl ash | BaNO3 | barium carbonate | K2NO3 molar mass | 138.2 g/mol | 199.33 g/mol | 197.33 g/mol | 140.2 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 891 °C | | 1350 °C | density | 2.43 g/cm^3 | | 3.89 g/cm^3 | solubility in water | soluble | | insoluble | odor | | | odorless |