HCl + K2Cr2O7 + K3AsO3 = H2O + KCl + CrCl3 + K3AsO4

HCl hydrogen chloride + K_2Cr_2O_7 potassium dichromate + K3AsO3 ⟶ H_2O water + KCl potassium chloride + CrCl_3 chromic chloride + K3AsO4

Balance the chemical equation algebraically: HCl + K_2Cr_2O_7 + K3AsO3 ⟶ H_2O + KCl + CrCl_3 + K3AsO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2Cr_2O_7 + c_3 K3AsO3 ⟶ c_4 H_2O + c_5 KCl + c_6 CrCl_3 + c_7 K3AsO4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr, K, O and As: Cl: | c_1 = c_5 + 3 c_6 H: | c_1 = 2 c_4 Cr: | 2 c_2 = c_6 K: | 2 c_2 + 3 c_3 = c_5 + 3 c_7 O: | 7 c_2 + 3 c_3 = c_4 + 4 c_7 As: | c_3 = c_7 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 = 8 c_2 = 1 c_3 = 3 c_4 = 4 c_5 = 2 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + K_2Cr_2O_7 + 3 K3AsO3 ⟶ 4 H_2O + 2 KCl + 2 CrCl_3 + 3 K3AsO4

+ + K3AsO3 ⟶ + + + K3AsO4

hydrogen chloride + potassium dichromate + K3AsO3 ⟶ water + potassium chloride + chromic chloride + K3AsO4

Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + K3AsO3 ⟶ H_2O + KCl + CrCl_3 + K3AsO4 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: 8 HCl + K_2Cr_2O_7 + 3 K3AsO3 ⟶ 4 H_2O + 2 KCl + 2 CrCl_3 + 3 K3AsO4 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 | 8 | -8 K_2Cr_2O_7 | 1 | -1 K3AsO3 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 CrCl_3 | 2 | 2 K3AsO4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) K3AsO3 | 3 | -3 | ([K3AsO3])^(-3) H_2O | 4 | 4 | ([H2O])^4 KCl | 2 | 2 | ([KCl])^2 CrCl_3 | 2 | 2 | ([CrCl3])^2 K3AsO4 | 3 | 3 | ([K3AsO4])^3 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])^(-8) ([K2Cr2O7])^(-1) ([K3AsO3])^(-3) ([H2O])^4 ([KCl])^2 ([CrCl3])^2 ([K3AsO4])^3 = (([H2O])^4 ([KCl])^2 ([CrCl3])^2 ([K3AsO4])^3)/(([HCl])^8 [K2Cr2O7] ([K3AsO3])^3)

Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + K3AsO3 ⟶ H_2O + KCl + CrCl_3 + K3AsO4 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: 8 HCl + K_2Cr_2O_7 + 3 K3AsO3 ⟶ 4 H_2O + 2 KCl + 2 CrCl_3 + 3 K3AsO4 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 | 8 | -8 K_2Cr_2O_7 | 1 | -1 K3AsO3 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 CrCl_3 | 2 | 2 K3AsO4 | 3 | 3 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 | 8 | -8 | -1/8 (Δ[HCl])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) K3AsO3 | 3 | -3 | -1/3 (Δ[K3AsO3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) CrCl_3 | 2 | 2 | 1/2 (Δ[CrCl3])/(Δt) K3AsO4 | 3 | 3 | 1/3 (Δ[K3AsO4])/(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 = -1/8 (Δ[HCl])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/3 (Δ[K3AsO3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) = 1/3 (Δ[K3AsO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium dichromate | K3AsO3 | water | potassium chloride | chromic chloride | K3AsO4 formula | HCl | K_2Cr_2O_7 | K3AsO3 | H_2O | KCl | CrCl_3 | K3AsO4 Hill formula | ClH | Cr_2K_2O_7 | AsK3O3 | H_2O | ClK | Cl_3Cr | AsK3O4 name | hydrogen chloride | potassium dichromate | | water | potassium chloride | chromic chloride | IUPAC name | hydrogen chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | | water | potassium chloride | trichlorochromium |

| hydrogen chloride | potassium dichromate | K3AsO3 | water | potassium chloride | chromic chloride | K3AsO4 molar mass | 36.46 g/mol | 294.18 g/mol | 240.213 g/mol | 18.015 g/mol | 74.55 g/mol | 158.3 g/mol | 256.212 g/mol phase | gas (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | -114.17 °C | 398 °C | | 0 °C | 770 °C | 1152 °C | boiling point | -85 °C | | | 99.9839 °C | 1420 °C | | density | 0.00149 g/cm^3 (at 25 °C) | 2.67 g/cm^3 | | 1 g/cm^3 | 1.98 g/cm^3 | 2.87 g/cm^3 | solubility in water | miscible | | | | soluble | slightly soluble | surface tension | | | | 0.0728 N/m | | | dynamic viscosity | | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | odorless | | odorless | odorless | |