Fe2(SO4)3 + AsH3 = H2SO4 + FeSO4 + As

Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate + AsH_3 arsine ⟶ H_2SO_4 sulfuric acid + FeSO_4 duretter + As gray arsenic

Balance the chemical equation algebraically: Fe_2(SO_4)_3·xH_2O + AsH_3 ⟶ H_2SO_4 + FeSO_4 + As Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe_2(SO_4)_3·xH_2O + c_2 AsH_3 ⟶ c_3 H_2SO_4 + c_4 FeSO_4 + c_5 As Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, O, S, As and H: Fe: | 2 c_1 = c_4 O: | 12 c_1 = 4 c_3 + 4 c_4 S: | 3 c_1 = c_3 + c_4 As: | c_2 = c_5 H: | 3 c_2 = 2 c_3 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 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 3 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 6 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Fe_2(SO_4)_3·xH_2O + 2 AsH_3 ⟶ 3 H_2SO_4 + 6 FeSO_4 + 2 As

+ ⟶ + +

iron(III) sulfate hydrate + arsine ⟶ sulfuric acid + duretter + gray arsenic

Construct the equilibrium constant, K, expression for: Fe_2(SO_4)_3·xH_2O + AsH_3 ⟶ H_2SO_4 + FeSO_4 + As 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 Fe_2(SO_4)_3·xH_2O + 2 AsH_3 ⟶ 3 H_2SO_4 + 6 FeSO_4 + 2 As 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 Fe_2(SO_4)_3·xH_2O | 3 | -3 AsH_3 | 2 | -2 H_2SO_4 | 3 | 3 FeSO_4 | 6 | 6 As | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe_2(SO_4)_3·xH_2O | 3 | -3 | ([Fe2(SO4)3·xH2O])^(-3) AsH_3 | 2 | -2 | ([AsH3])^(-2) H_2SO_4 | 3 | 3 | ([H2SO4])^3 FeSO_4 | 6 | 6 | ([FeSO4])^6 As | 2 | 2 | ([As])^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 = ([Fe2(SO4)3·xH2O])^(-3) ([AsH3])^(-2) ([H2SO4])^3 ([FeSO4])^6 ([As])^2 = (([H2SO4])^3 ([FeSO4])^6 ([As])^2)/(([Fe2(SO4)3·xH2O])^3 ([AsH3])^2)

Construct the rate of reaction expression for: Fe_2(SO_4)_3·xH_2O + AsH_3 ⟶ H_2SO_4 + FeSO_4 + As 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 Fe_2(SO_4)_3·xH_2O + 2 AsH_3 ⟶ 3 H_2SO_4 + 6 FeSO_4 + 2 As 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 Fe_2(SO_4)_3·xH_2O | 3 | -3 AsH_3 | 2 | -2 H_2SO_4 | 3 | 3 FeSO_4 | 6 | 6 As | 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 Fe_2(SO_4)_3·xH_2O | 3 | -3 | -1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) AsH_3 | 2 | -2 | -1/2 (Δ[AsH3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) FeSO_4 | 6 | 6 | 1/6 (Δ[FeSO4])/(Δt) As | 2 | 2 | 1/2 (Δ[As])/(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[Fe2(SO4)3·xH2O])/(Δt) = -1/2 (Δ[AsH3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/6 (Δ[FeSO4])/(Δt) = 1/2 (Δ[As])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron(III) sulfate hydrate | arsine | sulfuric acid | duretter | gray arsenic formula | Fe_2(SO_4)_3·xH_2O | AsH_3 | H_2SO_4 | FeSO_4 | As Hill formula | Fe_2O_12S_3 | AsH_3 | H_2O_4S | FeO_4S | As name | iron(III) sulfate hydrate | arsine | sulfuric acid | duretter | gray arsenic IUPAC name | diferric trisulfate | arsane | sulfuric acid | iron(+2) cation sulfate | arsenic

| iron(III) sulfate hydrate | arsine | sulfuric acid | duretter | gray arsenic molar mass | 399.9 g/mol | 77.946 g/mol | 98.07 g/mol | 151.9 g/mol | 74.921595 g/mol phase | | gas (at STP) | liquid (at STP) | | solid (at STP) melting point | | -111.2 °C | 10.371 °C | | 817 °C boiling point | | -62.5 °C | 279.6 °C | | 616 °C density | | 0.003186 g/cm^3 (at 25 °C) | 1.8305 g/cm^3 | 2.841 g/cm^3 | 5.727 g/cm^3 solubility in water | slightly soluble | | very soluble | | insoluble surface tension | | | 0.0735 N/m | | dynamic viscosity | | 1.47×10^-5 Pa s (at 0 °C) | 0.021 Pa s (at 25 °C) | | odor | | | odorless | | odorless