Na2CO3 + Co(NO3)2 = NaNO3 + CoCO3

Na_2CO_3 soda ash + CoN_2O_6 cobaltous nitrate ⟶ NaNO_3 sodium nitrate + CoCO_3 cobaltous carbonate

Balance the chemical equation algebraically: Na_2CO_3 + CoN_2O_6 ⟶ NaNO_3 + CoCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2CO_3 + c_2 CoN_2O_6 ⟶ c_3 NaNO_3 + c_4 CoCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Na, O, Co and N: C: | c_1 = c_4 Na: | 2 c_1 = c_3 O: | 3 c_1 + 6 c_2 = 3 c_3 + 3 c_4 Co: | 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: | | Na_2CO_3 + CoN_2O_6 ⟶ 2 NaNO_3 + CoCO_3

+ ⟶ +

soda ash + cobaltous nitrate ⟶ sodium nitrate + cobaltous carbonate

Construct the equilibrium constant, K, expression for: Na_2CO_3 + CoN_2O_6 ⟶ NaNO_3 + CoCO_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: Na_2CO_3 + CoN_2O_6 ⟶ 2 NaNO_3 + CoCO_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 Na_2CO_3 | 1 | -1 CoN_2O_6 | 1 | -1 NaNO_3 | 2 | 2 CoCO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2CO_3 | 1 | -1 | ([Na2CO3])^(-1) CoN_2O_6 | 1 | -1 | ([CoN2O6])^(-1) NaNO_3 | 2 | 2 | ([NaNO3])^2 CoCO_3 | 1 | 1 | [CoCO3] 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 = ([Na2CO3])^(-1) ([CoN2O6])^(-1) ([NaNO3])^2 [CoCO3] = (([NaNO3])^2 [CoCO3])/([Na2CO3] [CoN2O6])

Construct the rate of reaction expression for: Na_2CO_3 + CoN_2O_6 ⟶ NaNO_3 + CoCO_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: Na_2CO_3 + CoN_2O_6 ⟶ 2 NaNO_3 + CoCO_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 Na_2CO_3 | 1 | -1 CoN_2O_6 | 1 | -1 NaNO_3 | 2 | 2 CoCO_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 Na_2CO_3 | 1 | -1 | -(Δ[Na2CO3])/(Δt) CoN_2O_6 | 1 | -1 | -(Δ[CoN2O6])/(Δt) NaNO_3 | 2 | 2 | 1/2 (Δ[NaNO3])/(Δt) CoCO_3 | 1 | 1 | (Δ[CoCO3])/(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[Na2CO3])/(Δt) = -(Δ[CoN2O6])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) = (Δ[CoCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| soda ash | cobaltous nitrate | sodium nitrate | cobaltous carbonate formula | Na_2CO_3 | CoN_2O_6 | NaNO_3 | CoCO_3 Hill formula | CNa_2O_3 | CoN_2O_6 | NNaO_3 | CCoO_3 name | soda ash | cobaltous nitrate | sodium nitrate | cobaltous carbonate IUPAC name | disodium carbonate | cobalt(+2) cation dinitrate | sodium nitrate | cobalt(+2) cation carbonate

| soda ash | cobaltous nitrate | sodium nitrate | cobaltous carbonate molar mass | 105.99 g/mol | 182.94 g/mol | 84.994 g/mol | 118.94 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 851 °C | 55 °C | 306 °C | boiling point | 1600 °C | | | density | | 2.49 g/cm^3 | 2.26 g/cm^3 | 4.13 g/cm^3 solubility in water | soluble | soluble | soluble | dynamic viscosity | 0.00355 Pa s (at 900 °C) | | 0.003 Pa s (at 250 °C) |