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H2O + HNO3 + As2S3 = H2SO4 + NO + H3AsO3

Input interpretation

H_2O water + HNO_3 nitric acid + As_2S_3 arsenic(III) sulfide ⟶ H_2SO_4 sulfuric acid + NO nitric oxide + As(OH)_3 arsenious acid
H_2O water + HNO_3 nitric acid + As_2S_3 arsenic(III) sulfide ⟶ H_2SO_4 sulfuric acid + NO nitric oxide + As(OH)_3 arsenious acid

Balanced equation

Balance the chemical equation algebraically: H_2O + HNO_3 + As_2S_3 ⟶ H_2SO_4 + NO + As(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HNO_3 + c_3 As_2S_3 ⟶ c_4 H_2SO_4 + c_5 NO + c_6 As(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N, As and S: H: | 2 c_1 + c_2 = 2 c_4 + 3 c_6 O: | c_1 + 3 c_2 = 4 c_4 + c_5 + 3 c_6 N: | c_2 = c_5 As: | 2 c_3 = c_6 S: | 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 8 c_3 = 1 c_4 = 3 c_5 = 8 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 8 HNO_3 + As_2S_3 ⟶ 3 H_2SO_4 + 8 NO + 2 As(OH)_3
Balance the chemical equation algebraically: H_2O + HNO_3 + As_2S_3 ⟶ H_2SO_4 + NO + As(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HNO_3 + c_3 As_2S_3 ⟶ c_4 H_2SO_4 + c_5 NO + c_6 As(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N, As and S: H: | 2 c_1 + c_2 = 2 c_4 + 3 c_6 O: | c_1 + 3 c_2 = 4 c_4 + c_5 + 3 c_6 N: | c_2 = c_5 As: | 2 c_3 = c_6 S: | 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 8 c_3 = 1 c_4 = 3 c_5 = 8 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 8 HNO_3 + As_2S_3 ⟶ 3 H_2SO_4 + 8 NO + 2 As(OH)_3

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

water + nitric acid + arsenic(III) sulfide ⟶ sulfuric acid + nitric oxide + arsenious acid
water + nitric acid + arsenic(III) sulfide ⟶ sulfuric acid + nitric oxide + arsenious acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + HNO_3 + As_2S_3 ⟶ H_2SO_4 + NO + As(OH)_3 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: 2 H_2O + 8 HNO_3 + As_2S_3 ⟶ 3 H_2SO_4 + 8 NO + 2 As(OH)_3 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 | 2 | -2 HNO_3 | 8 | -8 As_2S_3 | 1 | -1 H_2SO_4 | 3 | 3 NO | 8 | 8 As(OH)_3 | 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 | 2 | -2 | ([H2O])^(-2) HNO_3 | 8 | -8 | ([HNO3])^(-8) As_2S_3 | 1 | -1 | ([As2S3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 NO | 8 | 8 | ([NO])^8 As(OH)_3 | 2 | 2 | ([As(OH)3])^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])^(-2) ([HNO3])^(-8) ([As2S3])^(-1) ([H2SO4])^3 ([NO])^8 ([As(OH)3])^2 = (([H2SO4])^3 ([NO])^8 ([As(OH)3])^2)/(([H2O])^2 ([HNO3])^8 [As2S3])
Construct the equilibrium constant, K, expression for: H_2O + HNO_3 + As_2S_3 ⟶ H_2SO_4 + NO + As(OH)_3 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: 2 H_2O + 8 HNO_3 + As_2S_3 ⟶ 3 H_2SO_4 + 8 NO + 2 As(OH)_3 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 | 2 | -2 HNO_3 | 8 | -8 As_2S_3 | 1 | -1 H_2SO_4 | 3 | 3 NO | 8 | 8 As(OH)_3 | 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 | 2 | -2 | ([H2O])^(-2) HNO_3 | 8 | -8 | ([HNO3])^(-8) As_2S_3 | 1 | -1 | ([As2S3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 NO | 8 | 8 | ([NO])^8 As(OH)_3 | 2 | 2 | ([As(OH)3])^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])^(-2) ([HNO3])^(-8) ([As2S3])^(-1) ([H2SO4])^3 ([NO])^8 ([As(OH)3])^2 = (([H2SO4])^3 ([NO])^8 ([As(OH)3])^2)/(([H2O])^2 ([HNO3])^8 [As2S3])

Rate of reaction

Construct the rate of reaction expression for: H_2O + HNO_3 + As_2S_3 ⟶ H_2SO_4 + NO + As(OH)_3 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: 2 H_2O + 8 HNO_3 + As_2S_3 ⟶ 3 H_2SO_4 + 8 NO + 2 As(OH)_3 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 | 2 | -2 HNO_3 | 8 | -8 As_2S_3 | 1 | -1 H_2SO_4 | 3 | 3 NO | 8 | 8 As(OH)_3 | 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) HNO_3 | 8 | -8 | -1/8 (Δ[HNO3])/(Δt) As_2S_3 | 1 | -1 | -(Δ[As2S3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) NO | 8 | 8 | 1/8 (Δ[NO])/(Δt) As(OH)_3 | 2 | 2 | 1/2 (Δ[As(OH)3])/(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 = -1/2 (Δ[H2O])/(Δt) = -1/8 (Δ[HNO3])/(Δt) = -(Δ[As2S3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/8 (Δ[NO])/(Δt) = 1/2 (Δ[As(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + HNO_3 + As_2S_3 ⟶ H_2SO_4 + NO + As(OH)_3 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: 2 H_2O + 8 HNO_3 + As_2S_3 ⟶ 3 H_2SO_4 + 8 NO + 2 As(OH)_3 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 | 2 | -2 HNO_3 | 8 | -8 As_2S_3 | 1 | -1 H_2SO_4 | 3 | 3 NO | 8 | 8 As(OH)_3 | 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) HNO_3 | 8 | -8 | -1/8 (Δ[HNO3])/(Δt) As_2S_3 | 1 | -1 | -(Δ[As2S3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) NO | 8 | 8 | 1/8 (Δ[NO])/(Δt) As(OH)_3 | 2 | 2 | 1/2 (Δ[As(OH)3])/(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 = -1/2 (Δ[H2O])/(Δt) = -1/8 (Δ[HNO3])/(Δt) = -(Δ[As2S3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/8 (Δ[NO])/(Δt) = 1/2 (Δ[As(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | nitric acid | arsenic(III) sulfide | sulfuric acid | nitric oxide | arsenious acid formula | H_2O | HNO_3 | As_2S_3 | H_2SO_4 | NO | As(OH)_3 Hill formula | H_2O | HNO_3 | As_2S_3 | H_2O_4S | NO | AsH_3O_3 name | water | nitric acid | arsenic(III) sulfide | sulfuric acid | nitric oxide | arsenious acid IUPAC name | water | nitric acid | | sulfuric acid | nitric oxide | arsorous acid
| water | nitric acid | arsenic(III) sulfide | sulfuric acid | nitric oxide | arsenious acid formula | H_2O | HNO_3 | As_2S_3 | H_2SO_4 | NO | As(OH)_3 Hill formula | H_2O | HNO_3 | As_2S_3 | H_2O_4S | NO | AsH_3O_3 name | water | nitric acid | arsenic(III) sulfide | sulfuric acid | nitric oxide | arsenious acid IUPAC name | water | nitric acid | | sulfuric acid | nitric oxide | arsorous acid

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