H2O + HCl + As2O3 + CrO3 = CrCl3 + H3AsO4

H_2O (water) + HCl (hydrogen chloride) + As_2O_3 (arsenic trioxide) + CrO_3 (chromium trioxide) ⟶ CrCl_3 (chromic chloride) + H_3AsO_4 (arsenic acid, solid)

Balance the chemical equation algebraically: H_2O + HCl + As_2O_3 + CrO_3 ⟶ CrCl_3 + H_3AsO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HCl + c_3 As_2O_3 + c_4 CrO_3 ⟶ c_5 CrCl_3 + c_6 H_3AsO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, As and Cr: H: | 2 c_1 + c_2 = 3 c_6 O: | c_1 + 3 c_3 + 3 c_4 = 4 c_6 Cl: | c_2 = 3 c_5 As: | 2 c_3 = c_6 Cr: | c_4 = c_5 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 1 c_4 = 4/3 c_5 = 4/3 c_6 = 2 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 3 c_2 = 12 c_3 = 3 c_4 = 4 c_5 = 4 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 12 HCl + 3 As_2O_3 + 4 CrO_3 ⟶ 4 CrCl_3 + 6 H_3AsO_4

+ + + ⟶ +

water + hydrogen chloride + arsenic trioxide + chromium trioxide ⟶ chromic chloride + arsenic acid, solid

Construct the equilibrium constant, K, expression for: H_2O + HCl + As_2O_3 + CrO_3 ⟶ CrCl_3 + H_3AsO_4 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_2O + 12 HCl + 3 As_2O_3 + 4 CrO_3 ⟶ 4 CrCl_3 + 6 H_3AsO_4 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_2O | 3 | -3 HCl | 12 | -12 As_2O_3 | 3 | -3 CrO_3 | 4 | -4 CrCl_3 | 4 | 4 H_3AsO_4 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) HCl | 12 | -12 | ([HCl])^(-12) As_2O_3 | 3 | -3 | ([As2O3])^(-3) CrO_3 | 4 | -4 | ([CrO3])^(-4) CrCl_3 | 4 | 4 | ([CrCl3])^4 H_3AsO_4 | 6 | 6 | ([H3AsO4])^6 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 = ([H2O])^(-3) ([HCl])^(-12) ([As2O3])^(-3) ([CrO3])^(-4) ([CrCl3])^4 ([H3AsO4])^6 = (([CrCl3])^4 ([H3AsO4])^6)/(([H2O])^3 ([HCl])^12 ([As2O3])^3 ([CrO3])^4)

Construct the rate of reaction expression for: H_2O + HCl + As_2O_3 + CrO_3 ⟶ CrCl_3 + H_3AsO_4 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_2O + 12 HCl + 3 As_2O_3 + 4 CrO_3 ⟶ 4 CrCl_3 + 6 H_3AsO_4 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_2O | 3 | -3 HCl | 12 | -12 As_2O_3 | 3 | -3 CrO_3 | 4 | -4 CrCl_3 | 4 | 4 H_3AsO_4 | 6 | 6 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_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) HCl | 12 | -12 | -1/12 (Δ[HCl])/(Δt) As_2O_3 | 3 | -3 | -1/3 (Δ[As2O3])/(Δt) CrO_3 | 4 | -4 | -1/4 (Δ[CrO3])/(Δt) CrCl_3 | 4 | 4 | 1/4 (Δ[CrCl3])/(Δt) H_3AsO_4 | 6 | 6 | 1/6 (Δ[H3AsO4])/(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[H2O])/(Δt) = -1/12 (Δ[HCl])/(Δt) = -1/3 (Δ[As2O3])/(Δt) = -1/4 (Δ[CrO3])/(Δt) = 1/4 (Δ[CrCl3])/(Δt) = 1/6 (Δ[H3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | hydrogen chloride | arsenic trioxide | chromium trioxide | chromic chloride | arsenic acid, solid formula | H_2O | HCl | As_2O_3 | CrO_3 | CrCl_3 | H_3AsO_4 Hill formula | H_2O | ClH | As_2O_3 | CrO_3 | Cl_3Cr | AsH_3O_4 name | water | hydrogen chloride | arsenic trioxide | chromium trioxide | chromic chloride | arsenic acid, solid IUPAC name | water | hydrogen chloride | 2, 4, 5-trioxa-1, 3-diarsabicyclo[1.1.1]pentane | trioxochromium | trichlorochromium | arsoric acid

| water | hydrogen chloride | arsenic trioxide | chromium trioxide | chromic chloride | arsenic acid, solid molar mass | 18.015 g/mol | 36.46 g/mol | 197.84 g/mol | 99.993 g/mol | 158.3 g/mol | 141.94 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | -114.17 °C | 312 °C | 196 °C | 1152 °C | 35.5 °C boiling point | 99.9839 °C | -85 °C | 465 °C | | | 160 °C density | 1 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) | 4.15 g/cm^3 | | 2.87 g/cm^3 | 2.2 g/cm^3 solubility in water | | miscible | | very soluble | slightly soluble | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | | odor | odorless | | | odorless | |