H2 + As = AsH3

H_2 hydrogen + As gray arsenic ⟶ AsH_3 arsine

Balance the chemical equation algebraically: H_2 + As ⟶ AsH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 As ⟶ c_3 AsH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H and As: H: | 2 c_1 = 3 c_3 As: | c_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 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2 + 2 As ⟶ 2 AsH_3

+ ⟶

hydrogen + gray arsenic ⟶ arsine

| hydrogen | gray arsenic | arsine molecular enthalpy | 0 kJ/mol | 0 kJ/mol | 66.4 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | 132.8 kJ/mol | H_initial = 0 kJ/mol | | H_final = 132.8 kJ/mol ΔH_rxn^0 | 132.8 kJ/mol - 0 kJ/mol = 132.8 kJ/mol (endothermic) | |

Construct the equilibrium constant, K, expression for: H_2 + As ⟶ AsH_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: 3 H_2 + 2 As ⟶ 2 AsH_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_2 | 3 | -3 As | 2 | -2 AsH_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_2 | 3 | -3 | ([H2])^(-3) As | 2 | -2 | ([As])^(-2) AsH_3 | 2 | 2 | ([AsH3])^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 = ([H2])^(-3) ([As])^(-2) ([AsH3])^2 = ([AsH3])^2/(([H2])^3 ([As])^2)

Construct the rate of reaction expression for: H_2 + As ⟶ AsH_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: 3 H_2 + 2 As ⟶ 2 AsH_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_2 | 3 | -3 As | 2 | -2 AsH_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_2 | 3 | -3 | -1/3 (Δ[H2])/(Δt) As | 2 | -2 | -1/2 (Δ[As])/(Δt) AsH_3 | 2 | 2 | 1/2 (Δ[AsH3])/(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[H2])/(Δt) = -1/2 (Δ[As])/(Δt) = 1/2 (Δ[AsH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | gray arsenic | arsine formula | H_2 | As | AsH_3 name | hydrogen | gray arsenic | arsine IUPAC name | molecular hydrogen | arsenic | arsane

| hydrogen | gray arsenic | arsine molar mass | 2.016 g/mol | 74.921595 g/mol | 77.946 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) melting point | -259.2 °C | 817 °C | -111.2 °C boiling point | -252.8 °C | 616 °C | -62.5 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 5.727 g/cm^3 | 0.003186 g/cm^3 (at 25 °C) solubility in water | | insoluble | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 1.47×10^-5 Pa s (at 0 °C) odor | odorless | odorless |