H2O + HNO3 + As2O3 = H3AsO4 + N2O2

H_2O water + HNO_3 nitric acid + As_2O_3 arsenic trioxide ⟶ H_3AsO_4 arsenic acid, solid + N2O2

Balance the chemical equation algebraically: H_2O + HNO_3 + As_2O_3 ⟶ H_3AsO_4 + N2O2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HNO_3 + c_3 As_2O_3 ⟶ c_4 H_3AsO_4 + c_5 N2O2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N and As: H: | 2 c_1 + c_2 = 3 c_4 O: | c_1 + 3 c_2 + 3 c_3 = 4 c_4 + 2 c_5 N: | c_2 = 2 c_5 As: | 2 c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7/2 c_2 = 2 c_3 = 3/2 c_4 = 3 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 7 c_2 = 4 c_3 = 3 c_4 = 6 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 H_2O + 4 HNO_3 + 3 As_2O_3 ⟶ 6 H_3AsO_4 + 2 N2O2

+ + ⟶ + N2O2

water + nitric acid + arsenic trioxide ⟶ arsenic acid, solid + N2O2

Construct the equilibrium constant, K, expression for: H_2O + HNO_3 + As_2O_3 ⟶ H_3AsO_4 + N2O2 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 HNO_3 + 3 As_2O_3 ⟶ 6 H_3AsO_4 + 2 N2O2 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 HNO_3 | 4 | -4 As_2O_3 | 3 | -3 H_3AsO_4 | 6 | 6 N2O2 | 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 | 7 | -7 | ([H2O])^(-7) HNO_3 | 4 | -4 | ([HNO3])^(-4) As_2O_3 | 3 | -3 | ([As2O3])^(-3) H_3AsO_4 | 6 | 6 | ([H3AsO4])^6 N2O2 | 2 | 2 | ([N2O2])^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])^(-7) ([HNO3])^(-4) ([As2O3])^(-3) ([H3AsO4])^6 ([N2O2])^2 = (([H3AsO4])^6 ([N2O2])^2)/(([H2O])^7 ([HNO3])^4 ([As2O3])^3)

Construct the rate of reaction expression for: H_2O + HNO_3 + As_2O_3 ⟶ H_3AsO_4 + N2O2 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 HNO_3 + 3 As_2O_3 ⟶ 6 H_3AsO_4 + 2 N2O2 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 HNO_3 | 4 | -4 As_2O_3 | 3 | -3 H_3AsO_4 | 6 | 6 N2O2 | 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 | 7 | -7 | -1/7 (Δ[H2O])/(Δt) HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) As_2O_3 | 3 | -3 | -1/3 (Δ[As2O3])/(Δt) H_3AsO_4 | 6 | 6 | 1/6 (Δ[H3AsO4])/(Δt) N2O2 | 2 | 2 | 1/2 (Δ[N2O2])/(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[HNO3])/(Δt) = -1/3 (Δ[As2O3])/(Δt) = 1/6 (Δ[H3AsO4])/(Δt) = 1/2 (Δ[N2O2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | nitric acid | arsenic trioxide | arsenic acid, solid | N2O2 formula | H_2O | HNO_3 | As_2O_3 | H_3AsO_4 | N2O2 Hill formula | H_2O | HNO_3 | As_2O_3 | AsH_3O_4 | N2O2 name | water | nitric acid | arsenic trioxide | arsenic acid, solid | IUPAC name | water | nitric acid | 2, 4, 5-trioxa-1, 3-diarsabicyclo[1.1.1]pentane | arsoric acid |