K2CO3 + Zn(NO3)2 = KNO3 + ZnCO3

K_2CO_3 pearl ash + Zn(NO3)2 ⟶ KNO_3 potassium nitrate + ZnCO_3 zinc carbonate

Balance the chemical equation algebraically: K_2CO_3 + Zn(NO3)2 ⟶ KNO_3 + ZnCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2CO_3 + c_2 Zn(NO3)2 ⟶ c_3 KNO_3 + c_4 ZnCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, K, O, Zn and N: C: | c_1 = c_4 K: | 2 c_1 = c_3 O: | 3 c_1 + 6 c_2 = 3 c_3 + 3 c_4 Zn: | c_2 = c_4 N: | 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 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | K_2CO_3 + Zn(NO3)2 ⟶ 2 KNO_3 + ZnCO_3

+ Zn(NO3)2 ⟶ +

pearl ash + Zn(NO3)2 ⟶ potassium nitrate + zinc carbonate

Construct the equilibrium constant, K, expression for: K_2CO_3 + Zn(NO3)2 ⟶ KNO_3 + ZnCO_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: K_2CO_3 + Zn(NO3)2 ⟶ 2 KNO_3 + ZnCO_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 K_2CO_3 | 1 | -1 Zn(NO3)2 | 1 | -1 KNO_3 | 2 | 2 ZnCO_3 | 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) Zn(NO3)2 | 1 | -1 | ([Zn(NO3)2])^(-1) KNO_3 | 2 | 2 | ([KNO3])^2 ZnCO_3 | 1 | 1 | [ZnCO3] 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) ([Zn(NO3)2])^(-1) ([KNO3])^2 [ZnCO3] = (([KNO3])^2 [ZnCO3])/([K2CO3] [Zn(NO3)2])

Construct the rate of reaction expression for: K_2CO_3 + Zn(NO3)2 ⟶ KNO_3 + ZnCO_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: K_2CO_3 + Zn(NO3)2 ⟶ 2 KNO_3 + ZnCO_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 K_2CO_3 | 1 | -1 Zn(NO3)2 | 1 | -1 KNO_3 | 2 | 2 ZnCO_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 K_2CO_3 | 1 | -1 | -(Δ[K2CO3])/(Δt) Zn(NO3)2 | 1 | -1 | -(Δ[Zn(NO3)2])/(Δt) KNO_3 | 2 | 2 | 1/2 (Δ[KNO3])/(Δt) ZnCO_3 | 1 | 1 | (Δ[ZnCO3])/(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[Zn(NO3)2])/(Δt) = 1/2 (Δ[KNO3])/(Δt) = (Δ[ZnCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| pearl ash | Zn(NO3)2 | potassium nitrate | zinc carbonate formula | K_2CO_3 | Zn(NO3)2 | KNO_3 | ZnCO_3 Hill formula | CK_2O_3 | N2O6Zn | KNO_3 | CO_3Zn name | pearl ash | | potassium nitrate | zinc carbonate IUPAC name | dipotassium carbonate | | potassium nitrate | zinc carbonate

| pearl ash | Zn(NO3)2 | potassium nitrate | zinc carbonate molar mass | 138.2 g/mol | 189.4 g/mol | 101.1 g/mol | 125.4 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 891 °C | | 334 °C | density | 2.43 g/cm^3 | | | 4.3476 g/cm^3 solubility in water | soluble | | soluble | insoluble odor | | | odorless |