H2SO4 + Na2CrO4 + Na2(COO)2 = H2O + CO2 + Na2SO4 + Cr2(SO4)3

H_2SO_4 sulfuric acid + Na_2CrO_4 sodium chromate + Na_2C_2O_4 sodium oxalate ⟶ H_2O water + CO_2 carbon dioxide + Na_2SO_4 sodium sulfate + Cr_2(SO_4)_3 chromium sulfate

Balance the chemical equation algebraically: H_2SO_4 + Na_2CrO_4 + Na_2C_2O_4 ⟶ H_2O + CO_2 + Na_2SO_4 + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Na_2CrO_4 + c_3 Na_2C_2O_4 ⟶ c_4 H_2O + c_5 CO_2 + c_6 Na_2SO_4 + c_7 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr, Na and C: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 4 c_3 = c_4 + 2 c_5 + 4 c_6 + 12 c_7 S: | c_1 = c_6 + 3 c_7 Cr: | c_2 = 2 c_7 Na: | 2 c_2 + 2 c_3 = 2 c_6 C: | 2 c_3 = c_5 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_7 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 3 c_4 = 8 c_5 = 6 c_6 = 5 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2SO_4 + 2 Na_2CrO_4 + 3 Na_2C_2O_4 ⟶ 8 H_2O + 6 CO_2 + 5 Na_2SO_4 + Cr_2(SO_4)_3

+ + ⟶ + + +

sulfuric acid + sodium chromate + sodium oxalate ⟶ water + carbon dioxide + sodium sulfate + chromium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + Na_2CrO_4 + Na_2C_2O_4 ⟶ H_2O + CO_2 + Na_2SO_4 + Cr_2(SO_4)_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: 8 H_2SO_4 + 2 Na_2CrO_4 + 3 Na_2C_2O_4 ⟶ 8 H_2O + 6 CO_2 + 5 Na_2SO_4 + Cr_2(SO_4)_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 H_2SO_4 | 8 | -8 Na_2CrO_4 | 2 | -2 Na_2C_2O_4 | 3 | -3 H_2O | 8 | 8 CO_2 | 6 | 6 Na_2SO_4 | 5 | 5 Cr_2(SO_4)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 8 | -8 | ([H2SO4])^(-8) Na_2CrO_4 | 2 | -2 | ([Na2CrO4])^(-2) Na_2C_2O_4 | 3 | -3 | ([Na2C2O4])^(-3) H_2O | 8 | 8 | ([H2O])^8 CO_2 | 6 | 6 | ([CO2])^6 Na_2SO_4 | 5 | 5 | ([Na2SO4])^5 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] 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 = ([H2SO4])^(-8) ([Na2CrO4])^(-2) ([Na2C2O4])^(-3) ([H2O])^8 ([CO2])^6 ([Na2SO4])^5 [Cr2(SO4)3] = (([H2O])^8 ([CO2])^6 ([Na2SO4])^5 [Cr2(SO4)3])/(([H2SO4])^8 ([Na2CrO4])^2 ([Na2C2O4])^3)

Construct the rate of reaction expression for: H_2SO_4 + Na_2CrO_4 + Na_2C_2O_4 ⟶ H_2O + CO_2 + Na_2SO_4 + Cr_2(SO_4)_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: 8 H_2SO_4 + 2 Na_2CrO_4 + 3 Na_2C_2O_4 ⟶ 8 H_2O + 6 CO_2 + 5 Na_2SO_4 + Cr_2(SO_4)_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 H_2SO_4 | 8 | -8 Na_2CrO_4 | 2 | -2 Na_2C_2O_4 | 3 | -3 H_2O | 8 | 8 CO_2 | 6 | 6 Na_2SO_4 | 5 | 5 Cr_2(SO_4)_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 H_2SO_4 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) Na_2CrO_4 | 2 | -2 | -1/2 (Δ[Na2CrO4])/(Δt) Na_2C_2O_4 | 3 | -3 | -1/3 (Δ[Na2C2O4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(Δt) Na_2SO_4 | 5 | 5 | 1/5 (Δ[Na2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(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 = -1/8 (Δ[H2SO4])/(Δt) = -1/2 (Δ[Na2CrO4])/(Δt) = -1/3 (Δ[Na2C2O4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/6 (Δ[CO2])/(Δt) = 1/5 (Δ[Na2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | sodium chromate | sodium oxalate | water | carbon dioxide | sodium sulfate | chromium sulfate formula | H_2SO_4 | Na_2CrO_4 | Na_2C_2O_4 | H_2O | CO_2 | Na_2SO_4 | Cr_2(SO_4)_3 Hill formula | H_2O_4S | CrNa_2O_4 | Na_2C_2O_4 | H_2O | CO_2 | Na_2O_4S | Cr_2O_12S_3 name | sulfuric acid | sodium chromate | sodium oxalate | water | carbon dioxide | sodium sulfate | chromium sulfate IUPAC name | sulfuric acid | disodium dioxido(dioxo)chromium | disodium oxalate | water | carbon dioxide | disodium sulfate | chromium(+3) cation trisulfate