HCl + K2Cr2O7 + CrCl2 = H2O + KCl + CrCl3

HCl hydrogen chloride + K_2Cr_2O_7 potassium dichromate + CrCl_2 chromous chloride ⟶ H_2O water + KCl potassium chloride + CrCl_3 chromic chloride

Balance the chemical equation algebraically: HCl + K_2Cr_2O_7 + CrCl_2 ⟶ H_2O + KCl + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2Cr_2O_7 + c_3 CrCl_2 ⟶ c_4 H_2O + c_5 KCl + c_6 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr, K and O: Cl: | c_1 + 2 c_3 = c_5 + 3 c_6 H: | c_1 = 2 c_4 Cr: | 2 c_2 + c_3 = c_6 K: | 2 c_2 = c_5 O: | 7 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 = 14 c_2 = 1 c_3 = 6 c_4 = 7 c_5 = 2 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HCl + K_2Cr_2O_7 + 6 CrCl_2 ⟶ 7 H_2O + 2 KCl + 8 CrCl_3

+ + ⟶ + +

hydrogen chloride + potassium dichromate + chromous chloride ⟶ water + potassium chloride + chromic chloride

Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + CrCl_2 ⟶ H_2O + KCl + CrCl_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: 14 HCl + K_2Cr_2O_7 + 6 CrCl_2 ⟶ 7 H_2O + 2 KCl + 8 CrCl_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 HCl | 14 | -14 K_2Cr_2O_7 | 1 | -1 CrCl_2 | 6 | -6 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 14 | -14 | ([HCl])^(-14) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) CrCl_2 | 6 | -6 | ([CrCl2])^(-6) H_2O | 7 | 7 | ([H2O])^7 KCl | 2 | 2 | ([KCl])^2 CrCl_3 | 8 | 8 | ([CrCl3])^8 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])^(-14) ([K2Cr2O7])^(-1) ([CrCl2])^(-6) ([H2O])^7 ([KCl])^2 ([CrCl3])^8 = (([H2O])^7 ([KCl])^2 ([CrCl3])^8)/(([HCl])^14 [K2Cr2O7] ([CrCl2])^6)

Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + CrCl_2 ⟶ H_2O + KCl + CrCl_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: 14 HCl + K_2Cr_2O_7 + 6 CrCl_2 ⟶ 7 H_2O + 2 KCl + 8 CrCl_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 HCl | 14 | -14 K_2Cr_2O_7 | 1 | -1 CrCl_2 | 6 | -6 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 8 | 8 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 | 14 | -14 | -1/14 (Δ[HCl])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) CrCl_2 | 6 | -6 | -1/6 (Δ[CrCl2])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) CrCl_3 | 8 | 8 | 1/8 (Δ[CrCl3])/(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 = -1/14 (Δ[HCl])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/6 (Δ[CrCl2])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/8 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium dichromate | chromous chloride | water | potassium chloride | chromic chloride formula | HCl | K_2Cr_2O_7 | CrCl_2 | H_2O | KCl | CrCl_3 Hill formula | ClH | Cr_2K_2O_7 | Cl_2Cr | H_2O | ClK | Cl_3Cr name | hydrogen chloride | potassium dichromate | chromous chloride | water | potassium chloride | chromic chloride IUPAC name | hydrogen chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | dichlorochromium | water | potassium chloride | trichlorochromium

| hydrogen chloride | potassium dichromate | chromous chloride | water | potassium chloride | chromic chloride molar mass | 36.46 g/mol | 294.18 g/mol | 122.9 g/mol | 18.015 g/mol | 74.55 g/mol | 158.3 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -114.17 °C | 398 °C | 824 °C | 0 °C | 770 °C | 1152 °C boiling point | -85 °C | | 1302 °C | 99.9839 °C | 1420 °C | density | 0.00149 g/cm^3 (at 25 °C) | 2.67 g/cm^3 | 2.9 g/cm^3 | 1 g/cm^3 | 1.98 g/cm^3 | 2.87 g/cm^3 solubility in water | miscible | | soluble | | soluble | slightly soluble surface tension | | | | 0.0728 N/m | | dynamic viscosity | | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | | odorless | odorless |