Na2CO3 + NaClO + Cr(OH)3 = H2O + CO2 + NaCl + Na2CrO4

Na_2CO_3 soda ash + NaOCl sodium hypochlorite + Cr(OH)3 ⟶ H_2O water + CO_2 carbon dioxide + NaCl sodium chloride + Na_2CrO_4 sodium chromate

Balance the chemical equation algebraically: Na_2CO_3 + NaOCl + Cr(OH)3 ⟶ H_2O + CO_2 + NaCl + Na_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2CO_3 + c_2 NaOCl + c_3 Cr(OH)3 ⟶ c_4 H_2O + c_5 CO_2 + c_6 NaCl + c_7 Na_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Na, O, Cl, Cr and H: C: | c_1 = c_5 Na: | 2 c_1 + c_2 = c_6 + 2 c_7 O: | 3 c_1 + c_2 + 3 c_3 = c_4 + 2 c_5 + 4 c_7 Cl: | c_2 = c_6 Cr: | c_3 = c_7 H: | 3 c_3 = 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 = 3/2 c_3 = 1 c_4 = 3/2 c_5 = 1 c_6 = 3/2 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 2 c_4 = 3 c_5 = 2 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Na_2CO_3 + 3 NaOCl + 2 Cr(OH)3 ⟶ 3 H_2O + 2 CO_2 + 3 NaCl + 2 Na_2CrO_4

+ + Cr(OH)3 ⟶ + + +

soda ash + sodium hypochlorite + Cr(OH)3 ⟶ water + carbon dioxide + sodium chloride + sodium chromate

Construct the equilibrium constant, K, expression for: Na_2CO_3 + NaOCl + Cr(OH)3 ⟶ H_2O + CO_2 + NaCl + Na_2CrO_4 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 Na_2CO_3 + 3 NaOCl + 2 Cr(OH)3 ⟶ 3 H_2O + 2 CO_2 + 3 NaCl + 2 Na_2CrO_4 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 | 2 | -2 NaOCl | 3 | -3 Cr(OH)3 | 2 | -2 H_2O | 3 | 3 CO_2 | 2 | 2 NaCl | 3 | 3 Na_2CrO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2CO_3 | 2 | -2 | ([Na2CO3])^(-2) NaOCl | 3 | -3 | ([NaOCl])^(-3) Cr(OH)3 | 2 | -2 | ([Cr(OH)3])^(-2) H_2O | 3 | 3 | ([H2O])^3 CO_2 | 2 | 2 | ([CO2])^2 NaCl | 3 | 3 | ([NaCl])^3 Na_2CrO_4 | 2 | 2 | ([Na2CrO4])^2 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])^(-2) ([NaOCl])^(-3) ([Cr(OH)3])^(-2) ([H2O])^3 ([CO2])^2 ([NaCl])^3 ([Na2CrO4])^2 = (([H2O])^3 ([CO2])^2 ([NaCl])^3 ([Na2CrO4])^2)/(([Na2CO3])^2 ([NaOCl])^3 ([Cr(OH)3])^2)

Construct the rate of reaction expression for: Na_2CO_3 + NaOCl + Cr(OH)3 ⟶ H_2O + CO_2 + NaCl + Na_2CrO_4 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 Na_2CO_3 + 3 NaOCl + 2 Cr(OH)3 ⟶ 3 H_2O + 2 CO_2 + 3 NaCl + 2 Na_2CrO_4 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 | 2 | -2 NaOCl | 3 | -3 Cr(OH)3 | 2 | -2 H_2O | 3 | 3 CO_2 | 2 | 2 NaCl | 3 | 3 Na_2CrO_4 | 2 | 2 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 | 2 | -2 | -1/2 (Δ[Na2CO3])/(Δt) NaOCl | 3 | -3 | -1/3 (Δ[NaOCl])/(Δt) Cr(OH)3 | 2 | -2 | -1/2 (Δ[Cr(OH)3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) NaCl | 3 | 3 | 1/3 (Δ[NaCl])/(Δt) Na_2CrO_4 | 2 | 2 | 1/2 (Δ[Na2CrO4])/(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[Na2CO3])/(Δt) = -1/3 (Δ[NaOCl])/(Δt) = -1/2 (Δ[Cr(OH)3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/3 (Δ[NaCl])/(Δt) = 1/2 (Δ[Na2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| soda ash | sodium hypochlorite | Cr(OH)3 | water | carbon dioxide | sodium chloride | sodium chromate formula | Na_2CO_3 | NaOCl | Cr(OH)3 | H_2O | CO_2 | NaCl | Na_2CrO_4 Hill formula | CNa_2O_3 | ClNaO | H3CrO3 | H_2O | CO_2 | ClNa | CrNa_2O_4 name | soda ash | sodium hypochlorite | | water | carbon dioxide | sodium chloride | sodium chromate IUPAC name | disodium carbonate | sodium hypochlorite | | water | carbon dioxide | sodium chloride | disodium dioxido(dioxo)chromium