AgNO3 + K2CO3 = AgCO3 + K2NO3

AgNO_3 silver nitrate + K_2CO_3 pearl ash ⟶ AgCO3 + K2NO3

Balance the chemical equation algebraically: AgNO_3 + K_2CO_3 ⟶ AgCO3 + K2NO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AgNO_3 + c_2 K_2CO_3 ⟶ c_3 AgCO3 + c_4 K2NO3 Set the number of atoms in the reactants equal to the number of atoms in the products for Ag, N, O, C and K: Ag: | c_1 = c_3 N: | c_1 = c_4 O: | 3 c_1 + 3 c_2 = 3 c_3 + 3 c_4 C: | c_2 = c_3 K: | 2 c_2 = 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: | | AgNO_3 + K_2CO_3 ⟶ AgCO3 + K2NO3

+ ⟶ AgCO3 + K2NO3

silver nitrate + pearl ash ⟶ AgCO3 + K2NO3

Construct the equilibrium constant, K, expression for: AgNO_3 + K_2CO_3 ⟶ AgCO3 + 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: AgNO_3 + K_2CO_3 ⟶ AgCO3 + 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 AgNO_3 | 1 | -1 K_2CO_3 | 1 | -1 AgCO3 | 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 AgNO_3 | 1 | -1 | ([AgNO3])^(-1) K_2CO_3 | 1 | -1 | ([K2CO3])^(-1) AgCO3 | 1 | 1 | [AgCO3] 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 = ([AgNO3])^(-1) ([K2CO3])^(-1) [AgCO3] [K2NO3] = ([AgCO3] [K2NO3])/([AgNO3] [K2CO3])

Construct the rate of reaction expression for: AgNO_3 + K_2CO_3 ⟶ AgCO3 + 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: AgNO_3 + K_2CO_3 ⟶ AgCO3 + 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 AgNO_3 | 1 | -1 K_2CO_3 | 1 | -1 AgCO3 | 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 AgNO_3 | 1 | -1 | -(Δ[AgNO3])/(Δt) K_2CO_3 | 1 | -1 | -(Δ[K2CO3])/(Δt) AgCO3 | 1 | 1 | (Δ[AgCO3])/(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[AgNO3])/(Δt) = -(Δ[K2CO3])/(Δt) = (Δ[AgCO3])/(Δt) = (Δ[K2NO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silver nitrate | pearl ash | AgCO3 | K2NO3 formula | AgNO_3 | K_2CO_3 | AgCO3 | K2NO3 Hill formula | AgNO_3 | CK_2O_3 | CAgO3 | K2NO3 name | silver nitrate | pearl ash | | IUPAC name | silver nitrate | dipotassium carbonate | |

| silver nitrate | pearl ash | AgCO3 | K2NO3 molar mass | 169.87 g/mol | 138.2 g/mol | 167.88 g/mol | 140.2 g/mol phase | solid (at STP) | solid (at STP) | | melting point | 212 °C | 891 °C | | density | | 2.43 g/cm^3 | | solubility in water | soluble | soluble | | odor | odorless | | |