HNO3 + K3AsS3 = H2O + H2SO4 + NO + K3AsO4

HNO_3 nitric acid + K3AsS3 ⟶ H_2O water + H_2SO_4 sulfuric acid + NO nitric oxide + K3AsO4

Balance the chemical equation algebraically: HNO_3 + K3AsS3 ⟶ H_2O + H_2SO_4 + NO + K3AsO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 K3AsS3 ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 NO + c_6 K3AsO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, K, As and S: H: | c_1 = 2 c_3 + 2 c_4 N: | c_1 = c_5 O: | 3 c_1 = c_3 + 4 c_4 + c_5 + 4 c_6 K: | 3 c_2 = 3 c_6 As: | c_2 = c_6 S: | 3 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 26/3 c_2 = 1 c_3 = 4/3 c_4 = 3 c_5 = 26/3 c_6 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 26 c_2 = 3 c_3 = 4 c_4 = 9 c_5 = 26 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 26 HNO_3 + 3 K3AsS3 ⟶ 4 H_2O + 9 H_2SO_4 + 26 NO + 3 K3AsO4

+ K3AsS3 ⟶ + + + K3AsO4

nitric acid + K3AsS3 ⟶ water + sulfuric acid + nitric oxide + K3AsO4

Construct the equilibrium constant, K, expression for: HNO_3 + K3AsS3 ⟶ H_2O + H_2SO_4 + NO + K3AsO4 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: 26 HNO_3 + 3 K3AsS3 ⟶ 4 H_2O + 9 H_2SO_4 + 26 NO + 3 K3AsO4 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 HNO_3 | 26 | -26 K3AsS3 | 3 | -3 H_2O | 4 | 4 H_2SO_4 | 9 | 9 NO | 26 | 26 K3AsO4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 26 | -26 | ([HNO3])^(-26) K3AsS3 | 3 | -3 | ([K3AsS3])^(-3) H_2O | 4 | 4 | ([H2O])^4 H_2SO_4 | 9 | 9 | ([H2SO4])^9 NO | 26 | 26 | ([NO])^26 K3AsO4 | 3 | 3 | ([K3AsO4])^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 = ([HNO3])^(-26) ([K3AsS3])^(-3) ([H2O])^4 ([H2SO4])^9 ([NO])^26 ([K3AsO4])^3 = (([H2O])^4 ([H2SO4])^9 ([NO])^26 ([K3AsO4])^3)/(([HNO3])^26 ([K3AsS3])^3)

Construct the rate of reaction expression for: HNO_3 + K3AsS3 ⟶ H_2O + H_2SO_4 + NO + K3AsO4 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: 26 HNO_3 + 3 K3AsS3 ⟶ 4 H_2O + 9 H_2SO_4 + 26 NO + 3 K3AsO4 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 HNO_3 | 26 | -26 K3AsS3 | 3 | -3 H_2O | 4 | 4 H_2SO_4 | 9 | 9 NO | 26 | 26 K3AsO4 | 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 HNO_3 | 26 | -26 | -1/26 (Δ[HNO3])/(Δt) K3AsS3 | 3 | -3 | -1/3 (Δ[K3AsS3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) H_2SO_4 | 9 | 9 | 1/9 (Δ[H2SO4])/(Δt) NO | 26 | 26 | 1/26 (Δ[NO])/(Δt) K3AsO4 | 3 | 3 | 1/3 (Δ[K3AsO4])/(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 = -1/26 (Δ[HNO3])/(Δt) = -1/3 (Δ[K3AsS3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/9 (Δ[H2SO4])/(Δt) = 1/26 (Δ[NO])/(Δt) = 1/3 (Δ[K3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | K3AsS3 | water | sulfuric acid | nitric oxide | K3AsO4 formula | HNO_3 | K3AsS3 | H_2O | H_2SO_4 | NO | K3AsO4 Hill formula | HNO_3 | AsK3S3 | H_2O | H_2O_4S | NO | AsK3O4 name | nitric acid | | water | sulfuric acid | nitric oxide |

| nitric acid | K3AsS3 | water | sulfuric acid | nitric oxide | K3AsO4 molar mass | 63.012 g/mol | 288.4 g/mol | 18.015 g/mol | 98.07 g/mol | 30.006 g/mol | 256.212 g/mol phase | liquid (at STP) | | liquid (at STP) | liquid (at STP) | gas (at STP) | melting point | -41.6 °C | | 0 °C | 10.371 °C | -163.6 °C | boiling point | 83 °C | | 99.9839 °C | 279.6 °C | -151.7 °C | density | 1.5129 g/cm^3 | | 1 g/cm^3 | 1.8305 g/cm^3 | 0.001226 g/cm^3 (at 25 °C) | solubility in water | miscible | | | very soluble | | surface tension | | | 0.0728 N/m | 0.0735 N/m | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 0.021 Pa s (at 25 °C) | 1.911×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless | |