H2O + HCl + NaNO3 + As2O3 = NaCl + NO + H3AsO4

H_2O water + HCl hydrogen chloride + NaNO_3 sodium nitrate + As_2O_3 arsenic trioxide ⟶ NaCl sodium chloride + NO nitric oxide + H_3AsO_4 arsenic acid, solid

Balance the chemical equation algebraically: H_2O + HCl + NaNO_3 + As_2O_3 ⟶ NaCl + NO + H_3AsO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HCl + c_3 NaNO_3 + c_4 As_2O_3 ⟶ c_5 NaCl + c_6 NO + c_7 H_3AsO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, N, Na and As: H: | 2 c_1 + c_2 = 3 c_7 O: | c_1 + 3 c_3 + 3 c_4 = c_6 + 4 c_7 Cl: | c_2 = c_5 N: | c_3 = c_6 Na: | c_3 = c_5 As: | 2 c_4 = c_7 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7/3 c_2 = 4/3 c_3 = 4/3 c_4 = 1 c_5 = 4/3 c_6 = 4/3 c_7 = 2 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 7 c_2 = 4 c_3 = 4 c_4 = 3 c_5 = 4 c_6 = 4 c_7 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 H_2O + 4 HCl + 4 NaNO_3 + 3 As_2O_3 ⟶ 4 NaCl + 4 NO + 6 H_3AsO_4

+ + + ⟶ + +

water + hydrogen chloride + sodium nitrate + arsenic trioxide ⟶ sodium chloride + nitric oxide + arsenic acid, solid

Construct the equilibrium constant, K, expression for: H_2O + HCl + NaNO_3 + As_2O_3 ⟶ NaCl + NO + 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: 7 H_2O + 4 HCl + 4 NaNO_3 + 3 As_2O_3 ⟶ 4 NaCl + 4 NO + 6 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 | 7 | -7 HCl | 4 | -4 NaNO_3 | 4 | -4 As_2O_3 | 3 | -3 NaCl | 4 | 4 NO | 4 | 4 H_3AsO_4 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 7 | -7 | ([H2O])^(-7) HCl | 4 | -4 | ([HCl])^(-4) NaNO_3 | 4 | -4 | ([NaNO3])^(-4) As_2O_3 | 3 | -3 | ([As2O3])^(-3) NaCl | 4 | 4 | ([NaCl])^4 NO | 4 | 4 | ([NO])^4 H_3AsO_4 | 6 | 6 | ([H3AsO4])^6 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])^(-7) ([HCl])^(-4) ([NaNO3])^(-4) ([As2O3])^(-3) ([NaCl])^4 ([NO])^4 ([H3AsO4])^6 = (([NaCl])^4 ([NO])^4 ([H3AsO4])^6)/(([H2O])^7 ([HCl])^4 ([NaNO3])^4 ([As2O3])^3)

Construct the rate of reaction expression for: H_2O + HCl + NaNO_3 + As_2O_3 ⟶ NaCl + NO + 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: 7 H_2O + 4 HCl + 4 NaNO_3 + 3 As_2O_3 ⟶ 4 NaCl + 4 NO + 6 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 | 7 | -7 HCl | 4 | -4 NaNO_3 | 4 | -4 As_2O_3 | 3 | -3 NaCl | 4 | 4 NO | 4 | 4 H_3AsO_4 | 6 | 6 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 | 7 | -7 | -1/7 (Δ[H2O])/(Δt) HCl | 4 | -4 | -1/4 (Δ[HCl])/(Δt) NaNO_3 | 4 | -4 | -1/4 (Δ[NaNO3])/(Δt) As_2O_3 | 3 | -3 | -1/3 (Δ[As2O3])/(Δt) NaCl | 4 | 4 | 1/4 (Δ[NaCl])/(Δt) NO | 4 | 4 | 1/4 (Δ[NO])/(Δt) H_3AsO_4 | 6 | 6 | 1/6 (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 = -1/7 (Δ[H2O])/(Δt) = -1/4 (Δ[HCl])/(Δt) = -1/4 (Δ[NaNO3])/(Δt) = -1/3 (Δ[As2O3])/(Δt) = 1/4 (Δ[NaCl])/(Δt) = 1/4 (Δ[NO])/(Δt) = 1/6 (Δ[H3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | hydrogen chloride | sodium nitrate | arsenic trioxide | sodium chloride | nitric oxide | arsenic acid, solid formula | H_2O | HCl | NaNO_3 | As_2O_3 | NaCl | NO | H_3AsO_4 Hill formula | H_2O | ClH | NNaO_3 | As_2O_3 | ClNa | NO | AsH_3O_4 name | water | hydrogen chloride | sodium nitrate | arsenic trioxide | sodium chloride | nitric oxide | arsenic acid, solid IUPAC name | water | hydrogen chloride | sodium nitrate | 2, 4, 5-trioxa-1, 3-diarsabicyclo[1.1.1]pentane | sodium chloride | nitric oxide | arsoric acid