HCl + Cu + As4O6 = H2O + As + CuCl

HCl hydrogen chloride + Cu copper + As4O6 ⟶ H_2O water + As gray arsenic + CuCl cuprous chloride

Balance the chemical equation algebraically: HCl + Cu + As4O6 ⟶ H_2O + As + CuCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Cu + c_3 As4O6 ⟶ c_4 H_2O + c_5 As + c_6 CuCl Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cu, As and O: Cl: | c_1 = c_6 H: | c_1 = 2 c_4 Cu: | c_2 = c_6 As: | 4 c_3 = c_5 O: | 6 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 = 12 c_2 = 12 c_3 = 1 c_4 = 6 c_5 = 4 c_6 = 12 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 HCl + 12 Cu + As4O6 ⟶ 6 H_2O + 4 As + 12 CuCl

+ + As4O6 ⟶ + +

hydrogen chloride + copper + As4O6 ⟶ water + gray arsenic + cuprous chloride

Construct the equilibrium constant, K, expression for: HCl + Cu + As4O6 ⟶ H_2O + As + CuCl 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: 12 HCl + 12 Cu + As4O6 ⟶ 6 H_2O + 4 As + 12 CuCl 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 HCl | 12 | -12 Cu | 12 | -12 As4O6 | 1 | -1 H_2O | 6 | 6 As | 4 | 4 CuCl | 12 | 12 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 12 | -12 | ([HCl])^(-12) Cu | 12 | -12 | ([Cu])^(-12) As4O6 | 1 | -1 | ([As4O6])^(-1) H_2O | 6 | 6 | ([H2O])^6 As | 4 | 4 | ([As])^4 CuCl | 12 | 12 | ([CuCl])^12 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 = ([HCl])^(-12) ([Cu])^(-12) ([As4O6])^(-1) ([H2O])^6 ([As])^4 ([CuCl])^12 = (([H2O])^6 ([As])^4 ([CuCl])^12)/(([HCl])^12 ([Cu])^12 [As4O6])

Construct the rate of reaction expression for: HCl + Cu + As4O6 ⟶ H_2O + As + CuCl 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: 12 HCl + 12 Cu + As4O6 ⟶ 6 H_2O + 4 As + 12 CuCl 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 HCl | 12 | -12 Cu | 12 | -12 As4O6 | 1 | -1 H_2O | 6 | 6 As | 4 | 4 CuCl | 12 | 12 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 HCl | 12 | -12 | -1/12 (Δ[HCl])/(Δt) Cu | 12 | -12 | -1/12 (Δ[Cu])/(Δt) As4O6 | 1 | -1 | -(Δ[As4O6])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) As | 4 | 4 | 1/4 (Δ[As])/(Δt) CuCl | 12 | 12 | 1/12 (Δ[CuCl])/(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 = -1/12 (Δ[HCl])/(Δt) = -1/12 (Δ[Cu])/(Δt) = -(Δ[As4O6])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/4 (Δ[As])/(Δt) = 1/12 (Δ[CuCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | copper | As4O6 | water | gray arsenic | cuprous chloride formula | HCl | Cu | As4O6 | H_2O | As | CuCl Hill formula | ClH | Cu | As4O6 | H_2O | As | ClCu name | hydrogen chloride | copper | | water | gray arsenic | cuprous chloride IUPAC name | hydrogen chloride | copper | | water | arsenic |

| hydrogen chloride | copper | As4O6 | water | gray arsenic | cuprous chloride molar mass | 36.46 g/mol | 63.546 g/mol | 395.68 g/mol | 18.015 g/mol | 74.921595 g/mol | 99 g/mol phase | gas (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -114.17 °C | 1083 °C | | 0 °C | 817 °C | 430 °C boiling point | -85 °C | 2567 °C | | 99.9839 °C | 616 °C | 1490 °C density | 0.00149 g/cm^3 (at 25 °C) | 8.96 g/cm^3 | | 1 g/cm^3 | 5.727 g/cm^3 | 4.145 g/cm^3 solubility in water | miscible | insoluble | | | insoluble | surface tension | | | | 0.0728 N/m | | dynamic viscosity | | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | | odorless | odorless |