HCl + KCr2O7 = H2O + Cl2 + KCl + CrCl3

HCl hydrogen chloride + KCr2O7 ⟶ H_2O water + Cl_2 chlorine + KCl potassium chloride + CrCl_3 chromic chloride

Balance the chemical equation algebraically: HCl + KCr2O7 ⟶ H_2O + Cl_2 + KCl + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 KCr2O7 ⟶ c_3 H_2O + c_4 Cl_2 + 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, K, Cr and O: Cl: | c_1 = 2 c_4 + c_5 + 3 c_6 H: | c_1 = 2 c_3 K: | c_2 = c_5 Cr: | 2 c_2 = c_6 O: | 7 c_2 = c_3 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 = 7 c_4 = 7/2 c_5 = 1 c_6 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 28 c_2 = 2 c_3 = 14 c_4 = 7 c_5 = 2 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 28 HCl + 2 KCr2O7 ⟶ 14 H_2O + 7 Cl_2 + 2 KCl + 4 CrCl_3

+ KCr2O7 ⟶ + + +

hydrogen chloride + KCr2O7 ⟶ water + chlorine + potassium chloride + chromic chloride

Construct the equilibrium constant, K, expression for: HCl + KCr2O7 ⟶ H_2O + Cl_2 + 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: 28 HCl + 2 KCr2O7 ⟶ 14 H_2O + 7 Cl_2 + 2 KCl + 4 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 | 28 | -28 KCr2O7 | 2 | -2 H_2O | 14 | 14 Cl_2 | 7 | 7 KCl | 2 | 2 CrCl_3 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 28 | -28 | ([HCl])^(-28) KCr2O7 | 2 | -2 | ([KCr2O7])^(-2) H_2O | 14 | 14 | ([H2O])^14 Cl_2 | 7 | 7 | ([Cl2])^7 KCl | 2 | 2 | ([KCl])^2 CrCl_3 | 4 | 4 | ([CrCl3])^4 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])^(-28) ([KCr2O7])^(-2) ([H2O])^14 ([Cl2])^7 ([KCl])^2 ([CrCl3])^4 = (([H2O])^14 ([Cl2])^7 ([KCl])^2 ([CrCl3])^4)/(([HCl])^28 ([KCr2O7])^2)

Construct the rate of reaction expression for: HCl + KCr2O7 ⟶ H_2O + Cl_2 + 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: 28 HCl + 2 KCr2O7 ⟶ 14 H_2O + 7 Cl_2 + 2 KCl + 4 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 | 28 | -28 KCr2O7 | 2 | -2 H_2O | 14 | 14 Cl_2 | 7 | 7 KCl | 2 | 2 CrCl_3 | 4 | 4 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 | 28 | -28 | -1/28 (Δ[HCl])/(Δt) KCr2O7 | 2 | -2 | -1/2 (Δ[KCr2O7])/(Δt) H_2O | 14 | 14 | 1/14 (Δ[H2O])/(Δt) Cl_2 | 7 | 7 | 1/7 (Δ[Cl2])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) CrCl_3 | 4 | 4 | 1/4 (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 = -1/28 (Δ[HCl])/(Δt) = -1/2 (Δ[KCr2O7])/(Δt) = 1/14 (Δ[H2O])/(Δt) = 1/7 (Δ[Cl2])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/4 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | KCr2O7 | water | chlorine | potassium chloride | chromic chloride formula | HCl | KCr2O7 | H_2O | Cl_2 | KCl | CrCl_3 Hill formula | ClH | Cr2KO7 | H_2O | Cl_2 | ClK | Cl_3Cr name | hydrogen chloride | | water | chlorine | potassium chloride | chromic chloride IUPAC name | hydrogen chloride | | water | molecular chlorine | potassium chloride | trichlorochromium

| hydrogen chloride | KCr2O7 | water | chlorine | potassium chloride | chromic chloride molar mass | 36.46 g/mol | 255.08 g/mol | 18.015 g/mol | 70.9 g/mol | 74.55 g/mol | 158.3 g/mol phase | gas (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | -114.17 °C | | 0 °C | -101 °C | 770 °C | 1152 °C boiling point | -85 °C | | 99.9839 °C | -34 °C | 1420 °C | density | 0.00149 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 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 |