#### Input interpretation

NaOH sodium hydroxide + As gray arsenic ⟶ H_2 hydrogen + Na3AsO3

#### Balanced equation

Balance the chemical equation algebraically: NaOH + As ⟶ H_2 + Na3AsO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 As ⟶ c_3 H_2 + c_4 Na3AsO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O and As: H: | c_1 = 2 c_3 Na: | c_1 = 3 c_4 O: | c_1 = 3 c_4 As: | 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 = 3 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NaOH + 2 As ⟶ 3 H_2 + 2 Na3AsO3

#### Structures

+ ⟶ + Na3AsO3

#### Names

sodium hydroxide + gray arsenic ⟶ hydrogen + Na3AsO3

#### Equilibrium constant

Construct the equilibrium constant, K, expression for: NaOH + As ⟶ H_2 + Na3AsO3 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: 6 NaOH + 2 As ⟶ 3 H_2 + 2 Na3AsO3 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 NaOH | 6 | -6 As | 2 | -2 H_2 | 3 | 3 Na3AsO3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 6 | -6 | ([NaOH])^(-6) As | 2 | -2 | ([As])^(-2) H_2 | 3 | 3 | ([H2])^3 Na3AsO3 | 2 | 2 | ([Na3AsO3])^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 = ([NaOH])^(-6) ([As])^(-2) ([H2])^3 ([Na3AsO3])^2 = (([H2])^3 ([Na3AsO3])^2)/(([NaOH])^6 ([As])^2)

#### Rate of reaction

Construct the rate of reaction expression for: NaOH + As ⟶ H_2 + Na3AsO3 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: 6 NaOH + 2 As ⟶ 3 H_2 + 2 Na3AsO3 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 NaOH | 6 | -6 As | 2 | -2 H_2 | 3 | 3 Na3AsO3 | 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 NaOH | 6 | -6 | -1/6 (Δ[NaOH])/(Δt) As | 2 | -2 | -1/2 (Δ[As])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Na3AsO3 | 2 | 2 | 1/2 (Δ[Na3AsO3])/(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 = -1/6 (Δ[NaOH])/(Δt) = -1/2 (Δ[As])/(Δt) = 1/3 (Δ[H2])/(Δt) = 1/2 (Δ[Na3AsO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

#### Chemical names and formulas

| sodium hydroxide | gray arsenic | hydrogen | Na3AsO3 formula | NaOH | As | H_2 | Na3AsO3 Hill formula | HNaO | As | H_2 | AsNa3O3 name | sodium hydroxide | gray arsenic | hydrogen | IUPAC name | sodium hydroxide | arsenic | molecular hydrogen |

#### Substance properties

| sodium hydroxide | gray arsenic | hydrogen | Na3AsO3 molar mass | 39.997 g/mol | 74.921595 g/mol | 2.016 g/mol | 191.888 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 323 °C | 817 °C | -259.2 °C | boiling point | 1390 °C | 616 °C | -252.8 °C | density | 2.13 g/cm^3 | 5.727 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | soluble | insoluble | | surface tension | 0.07435 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | | odorless | odorless |

Units