Ca + (COO)2Na2 = Na + (COO)2Ca2

Ca calcium + Na_2C_2O_4 sodium oxalate ⟶ Na sodium + (COO)2Ca2

Balance the chemical equation algebraically: Ca + Na_2C_2O_4 ⟶ Na + (COO)2Ca2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca + c_2 Na_2C_2O_4 ⟶ c_3 Na + c_4 (COO)2Ca2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, C, Na and O: Ca: | c_1 = 2 c_4 C: | 2 c_2 = 2 c_4 Na: | 2 c_2 = c_3 O: | 4 c_2 = 4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Ca + Na_2C_2O_4 ⟶ 2 Na + (COO)2Ca2

+ ⟶ + (COO)2Ca2

calcium + sodium oxalate ⟶ sodium + (COO)2Ca2

Construct the equilibrium constant, K, expression for: Ca + Na_2C_2O_4 ⟶ Na + (COO)2Ca2 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: 2 Ca + Na_2C_2O_4 ⟶ 2 Na + (COO)2Ca2 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 Ca | 2 | -2 Na_2C_2O_4 | 1 | -1 Na | 2 | 2 (COO)2Ca2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca | 2 | -2 | ([Ca])^(-2) Na_2C_2O_4 | 1 | -1 | ([Na2C2O4])^(-1) Na | 2 | 2 | ([Na])^2 (COO)2Ca2 | 1 | 1 | [(COO)2Ca2] 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 = ([Ca])^(-2) ([Na2C2O4])^(-1) ([Na])^2 [(COO)2Ca2] = (([Na])^2 [(COO)2Ca2])/(([Ca])^2 [Na2C2O4])

Construct the rate of reaction expression for: Ca + Na_2C_2O_4 ⟶ Na + (COO)2Ca2 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: 2 Ca + Na_2C_2O_4 ⟶ 2 Na + (COO)2Ca2 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 Ca | 2 | -2 Na_2C_2O_4 | 1 | -1 Na | 2 | 2 (COO)2Ca2 | 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 Ca | 2 | -2 | -1/2 (Δ[Ca])/(Δt) Na_2C_2O_4 | 1 | -1 | -(Δ[Na2C2O4])/(Δt) Na | 2 | 2 | 1/2 (Δ[Na])/(Δt) (COO)2Ca2 | 1 | 1 | (Δ[(COO)2Ca2])/(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 = -1/2 (Δ[Ca])/(Δt) = -(Δ[Na2C2O4])/(Δt) = 1/2 (Δ[Na])/(Δt) = (Δ[(COO)2Ca2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium | sodium oxalate | sodium | (COO)2Ca2 formula | Ca | Na_2C_2O_4 | Na | (COO)2Ca2 Hill formula | Ca | Na_2C_2O_4 | Na | C2Ca2O4 name | calcium | sodium oxalate | sodium | IUPAC name | calcium | disodium oxalate | sodium |

| calcium | sodium oxalate | sodium | (COO)2Ca2 molar mass | 40.078 g/mol | 134 g/mol | 22.98976928 g/mol | 168.17 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 850 °C | 260 °C | 97.8 °C | boiling point | 1484 °C | | 883 °C | density | 1.54 g/cm^3 | 2.27 g/cm^3 | 0.968 g/cm^3 | solubility in water | decomposes | | decomposes | dynamic viscosity | | | 1.413×10^-5 Pa s (at 527 °C) |