Cl2 + NaOH + NaAsO2 = H2O + NaCl + Na3AsO4

Input interpretation

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Cl_2 chlorine + NaOH sodium hydroxide + NaAsO_2 sodium arsenite ⟶ H_2O water + NaCl sodium chloride + AsNa_3O_4 arsenic acid, trisodium salt

Balanced equation

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Balance the chemical equation algebraically: Cl_2 + NaOH + NaAsO_2 ⟶ H_2O + NaCl + AsNa_3O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 NaOH + c_3 NaAsO_2 ⟶ c_4 H_2O + c_5 NaCl + c_6 AsNa_3O_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Na, O and As: Cl: | 2 c_1 = c_5 H: | c_2 = 2 c_4 Na: | c_2 + c_3 = c_5 + 3 c_6 O: | c_2 + 2 c_3 = c_4 + 4 c_6 As: | c_3 = c_6 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 = 4 c_3 = 1 c_4 = 2 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cl_2 + 4 NaOH + NaAsO_2 ⟶ 2 H_2O + 2 NaCl + AsNa_3O_4

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Names

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chlorine + sodium hydroxide + sodium arsenite ⟶ water + sodium chloride + arsenic acid, trisodium salt

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Cl_2 + NaOH + NaAsO_2 ⟶ H_2O + NaCl + AsNa_3O_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: Cl_2 + 4 NaOH + NaAsO_2 ⟶ 2 H_2O + 2 NaCl + AsNa_3O_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 Cl_2 | 1 | -1 NaOH | 4 | -4 NaAsO_2 | 1 | -1 H_2O | 2 | 2 NaCl | 2 | 2 AsNa_3O_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 1 | -1 | ([Cl2])^(-1) NaOH | 4 | -4 | ([NaOH])^(-4) NaAsO_2 | 1 | -1 | ([NaAsO2])^(-1) H_2O | 2 | 2 | ([H2O])^2 NaCl | 2 | 2 | ([NaCl])^2 AsNa_3O_4 | 1 | 1 | [AsNa3O4] 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 = ([Cl2])^(-1) ([NaOH])^(-4) ([NaAsO2])^(-1) ([H2O])^2 ([NaCl])^2 [AsNa3O4] = (([H2O])^2 ([NaCl])^2 [AsNa3O4])/([Cl2] ([NaOH])^4 [NaAsO2])

Rate of reaction

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Construct the rate of reaction expression for: Cl_2 + NaOH + NaAsO_2 ⟶ H_2O + NaCl + AsNa_3O_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: Cl_2 + 4 NaOH + NaAsO_2 ⟶ 2 H_2O + 2 NaCl + AsNa_3O_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 Cl_2 | 1 | -1 NaOH | 4 | -4 NaAsO_2 | 1 | -1 H_2O | 2 | 2 NaCl | 2 | 2 AsNa_3O_4 | 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 Cl_2 | 1 | -1 | -(Δ[Cl2])/(Δt) NaOH | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) NaAsO_2 | 1 | -1 | -(Δ[NaAsO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) AsNa_3O_4 | 1 | 1 | (Δ[AsNa3O4])/(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[Cl2])/(Δt) = -1/4 (Δ[NaOH])/(Δt) = -(Δ[NaAsO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = (Δ[AsNa3O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)