H2O + NaClO + As = NaCl + H3AsO4

H_2O water + NaOCl sodium hypochlorite + As gray arsenic ⟶ NaCl sodium chloride + H_3AsO_4 arsenic acid, solid

Balance the chemical equation algebraically: H_2O + NaOCl + As ⟶ NaCl + H_3AsO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NaOCl + c_3 As ⟶ c_4 NaCl + c_5 H_3AsO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, Na and As: H: | 2 c_1 = 3 c_5 O: | c_1 + c_2 = 4 c_5 Cl: | c_2 = c_4 Na: | c_2 = c_4 As: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 5/2 c_3 = 1 c_4 = 5/2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 5 c_3 = 2 c_4 = 5 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 5 NaOCl + 2 As ⟶ 5 NaCl + 2 H_3AsO_4

+ + ⟶ +

water + sodium hypochlorite + gray arsenic ⟶ sodium chloride + arsenic acid, solid

Construct the equilibrium constant, K, expression for: H_2O + NaOCl + As ⟶ NaCl + H_3AsO_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: 3 H_2O + 5 NaOCl + 2 As ⟶ 5 NaCl + 2 H_3AsO_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 H_2O | 3 | -3 NaOCl | 5 | -5 As | 2 | -2 NaCl | 5 | 5 H_3AsO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) NaOCl | 5 | -5 | ([NaOCl])^(-5) As | 2 | -2 | ([As])^(-2) NaCl | 5 | 5 | ([NaCl])^5 H_3AsO_4 | 2 | 2 | ([H3AsO4])^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 = ([H2O])^(-3) ([NaOCl])^(-5) ([As])^(-2) ([NaCl])^5 ([H3AsO4])^2 = (([NaCl])^5 ([H3AsO4])^2)/(([H2O])^3 ([NaOCl])^5 ([As])^2)

Construct the rate of reaction expression for: H_2O + NaOCl + As ⟶ NaCl + H_3AsO_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: 3 H_2O + 5 NaOCl + 2 As ⟶ 5 NaCl + 2 H_3AsO_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 H_2O | 3 | -3 NaOCl | 5 | -5 As | 2 | -2 NaCl | 5 | 5 H_3AsO_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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) NaOCl | 5 | -5 | -1/5 (Δ[NaOCl])/(Δt) As | 2 | -2 | -1/2 (Δ[As])/(Δt) NaCl | 5 | 5 | 1/5 (Δ[NaCl])/(Δt) H_3AsO_4 | 2 | 2 | 1/2 (Δ[H3AsO4])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/5 (Δ[NaOCl])/(Δt) = -1/2 (Δ[As])/(Δt) = 1/5 (Δ[NaCl])/(Δt) = 1/2 (Δ[H3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium hypochlorite | gray arsenic | sodium chloride | arsenic acid, solid formula | H_2O | NaOCl | As | NaCl | H_3AsO_4 Hill formula | H_2O | ClNaO | As | ClNa | AsH_3O_4 name | water | sodium hypochlorite | gray arsenic | sodium chloride | arsenic acid, solid IUPAC name | water | sodium hypochlorite | arsenic | sodium chloride | arsoric acid

| water | sodium hypochlorite | gray arsenic | sodium chloride | arsenic acid, solid molar mass | 18.015 g/mol | 74.44 g/mol | 74.921595 g/mol | 58.44 g/mol | 141.94 g/mol phase | liquid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | -6 °C | 817 °C | 801 °C | 35.5 °C boiling point | 99.9839 °C | | 616 °C | 1413 °C | 160 °C density | 1 g/cm^3 | 1.11 g/cm^3 | 5.727 g/cm^3 | 2.16 g/cm^3 | 2.2 g/cm^3 solubility in water | | miscible | insoluble | soluble | surface tension | 0.0728 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | odor | odorless | | odorless | odorless |