NaOH + NaClO3 + NaAsO2 = H2O + NaCl + Na3AsO4

Input interpretation

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NaOH sodium hydroxide + NaClO_3 sodium chlorate + 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: NaOH + NaClO_3 + NaAsO_2 ⟶ H_2O + NaCl + AsNa_3O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 NaClO_3 + 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 H, Na, O, Cl and As: H: | c_1 = 2 c_4 Na: | c_1 + c_2 + c_3 = c_5 + 3 c_6 O: | c_1 + 3 c_2 + 2 c_3 = c_4 + 4 c_6 Cl: | c_2 = c_5 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 3 c_4 = 3 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NaOH + NaClO_3 + 3 NaAsO_2 ⟶ 3 H_2O + NaCl + 3 AsNa_3O_4

+ + ⟶ + +

Names

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

Equilibrium constant

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Construct the equilibrium constant, K, expression for: NaOH + NaClO_3 + 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: 6 NaOH + NaClO_3 + 3 NaAsO_2 ⟶ 3 H_2O + NaCl + 3 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 NaOH | 6 | -6 NaClO_3 | 1 | -1 NaAsO_2 | 3 | -3 H_2O | 3 | 3 NaCl | 1 | 1 AsNa_3O_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 6 | -6 | ([NaOH])^(-6) NaClO_3 | 1 | -1 | ([NaClO3])^(-1) NaAsO_2 | 3 | -3 | ([NaAsO2])^(-3) H_2O | 3 | 3 | ([H2O])^3 NaCl | 1 | 1 | [NaCl] AsNa_3O_4 | 3 | 3 | ([AsNa3O4])^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 = ([NaOH])^(-6) ([NaClO3])^(-1) ([NaAsO2])^(-3) ([H2O])^3 [NaCl] ([AsNa3O4])^3 = (([H2O])^3 [NaCl] ([AsNa3O4])^3)/(([NaOH])^6 [NaClO3] ([NaAsO2])^3)

Rate of reaction

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Construct the rate of reaction expression for: NaOH + NaClO_3 + 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: 6 NaOH + NaClO_3 + 3 NaAsO_2 ⟶ 3 H_2O + NaCl + 3 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 NaOH | 6 | -6 NaClO_3 | 1 | -1 NaAsO_2 | 3 | -3 H_2O | 3 | 3 NaCl | 1 | 1 AsNa_3O_4 | 3 | 3 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 NaOH | 6 | -6 | -1/6 (Δ[NaOH])/(Δt) NaClO_3 | 1 | -1 | -(Δ[NaClO3])/(Δt) NaAsO_2 | 3 | -3 | -1/3 (Δ[NaAsO2])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) NaCl | 1 | 1 | (Δ[NaCl])/(Δt) AsNa_3O_4 | 3 | 3 | 1/3 (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 = -1/6 (Δ[NaOH])/(Δt) = -(Δ[NaClO3])/(Δt) = -1/3 (Δ[NaAsO2])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[NaCl])/(Δt) = 1/3 (Δ[AsNa3O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)