HCl + K2CrO4 = H2O + Cl2 + KCl + K2Cr2O7 + CrCl3

HCl hydrogen chloride + K_2CrO_4 potassium chromate ⟶ H_2O water + Cl_2 chlorine + KCl potassium chloride + K_2Cr_2O_7 potassium dichromate + CrCl_3 chromic chloride

Balance the chemical equation algebraically: HCl + K_2CrO_4 ⟶ H_2O + Cl_2 + KCl + K_2Cr_2O_7 + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2CrO_4 ⟶ c_3 H_2O + c_4 Cl_2 + c_5 KCl + c_6 K_2Cr_2O_7 + c_7 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_4 + c_5 + 3 c_7 H: | c_1 = 2 c_3 Cr: | c_2 = 2 c_6 + c_7 K: | 2 c_2 = c_5 + 2 c_6 O: | 4 c_2 = c_3 + 7 c_6 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_6 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/8 + 7/4 c_3 = c_1/2 c_4 = (3 c_1)/16 - 3/8 c_5 = c_1/4 + 3/2 c_6 = 1 c_7 = c_1/8 - 1/4 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 18 and solve for the remaining coefficients: c_1 = 18 c_2 = 4 c_3 = 9 c_4 = 3 c_5 = 6 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 18 HCl + 4 K_2CrO_4 ⟶ 9 H_2O + 3 Cl_2 + 6 KCl + K_2Cr_2O_7 + 2 CrCl_3

+ ⟶ + + + +

hydrogen chloride + potassium chromate ⟶ water + chlorine + potassium chloride + potassium dichromate + chromic chloride

Construct the equilibrium constant, K, expression for: HCl + K_2CrO_4 ⟶ H_2O + Cl_2 + KCl + K_2Cr_2O_7 + 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: 18 HCl + 4 K_2CrO_4 ⟶ 9 H_2O + 3 Cl_2 + 6 KCl + K_2Cr_2O_7 + 2 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 | 18 | -18 K_2CrO_4 | 4 | -4 H_2O | 9 | 9 Cl_2 | 3 | 3 KCl | 6 | 6 K_2Cr_2O_7 | 1 | 1 CrCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 18 | -18 | ([HCl])^(-18) K_2CrO_4 | 4 | -4 | ([K2CrO4])^(-4) H_2O | 9 | 9 | ([H2O])^9 Cl_2 | 3 | 3 | ([Cl2])^3 KCl | 6 | 6 | ([KCl])^6 K_2Cr_2O_7 | 1 | 1 | [K2Cr2O7] CrCl_3 | 2 | 2 | ([CrCl3])^2 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])^(-18) ([K2CrO4])^(-4) ([H2O])^9 ([Cl2])^3 ([KCl])^6 [K2Cr2O7] ([CrCl3])^2 = (([H2O])^9 ([Cl2])^3 ([KCl])^6 [K2Cr2O7] ([CrCl3])^2)/(([HCl])^18 ([K2CrO4])^4)

Construct the rate of reaction expression for: HCl + K_2CrO_4 ⟶ H_2O + Cl_2 + KCl + K_2Cr_2O_7 + 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: 18 HCl + 4 K_2CrO_4 ⟶ 9 H_2O + 3 Cl_2 + 6 KCl + K_2Cr_2O_7 + 2 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 | 18 | -18 K_2CrO_4 | 4 | -4 H_2O | 9 | 9 Cl_2 | 3 | 3 KCl | 6 | 6 K_2Cr_2O_7 | 1 | 1 CrCl_3 | 2 | 2 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 | 18 | -18 | -1/18 (Δ[HCl])/(Δt) K_2CrO_4 | 4 | -4 | -1/4 (Δ[K2CrO4])/(Δt) H_2O | 9 | 9 | 1/9 (Δ[H2O])/(Δt) Cl_2 | 3 | 3 | 1/3 (Δ[Cl2])/(Δt) KCl | 6 | 6 | 1/6 (Δ[KCl])/(Δt) K_2Cr_2O_7 | 1 | 1 | (Δ[K2Cr2O7])/(Δt) CrCl_3 | 2 | 2 | 1/2 (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 = -1/18 (Δ[HCl])/(Δt) = -1/4 (Δ[K2CrO4])/(Δt) = 1/9 (Δ[H2O])/(Δt) = 1/3 (Δ[Cl2])/(Δt) = 1/6 (Δ[KCl])/(Δt) = (Δ[K2Cr2O7])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | potassium chromate | water | chlorine | potassium chloride | potassium dichromate | chromic chloride formula | HCl | K_2CrO_4 | H_2O | Cl_2 | KCl | K_2Cr_2O_7 | CrCl_3 Hill formula | ClH | CrK_2O_4 | H_2O | Cl_2 | ClK | Cr_2K_2O_7 | Cl_3Cr name | hydrogen chloride | potassium chromate | water | chlorine | potassium chloride | potassium dichromate | chromic chloride IUPAC name | hydrogen chloride | dipotassium dioxido-dioxochromium | water | molecular chlorine | potassium chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | trichlorochromium

| hydrogen chloride | potassium chromate | water | chlorine | potassium chloride | potassium dichromate | chromic chloride molar mass | 36.46 g/mol | 194.19 g/mol | 18.015 g/mol | 70.9 g/mol | 74.55 g/mol | 294.18 g/mol | 158.3 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | -114.17 °C | 971 °C | 0 °C | -101 °C | 770 °C | 398 °C | 1152 °C boiling point | -85 °C | | 99.9839 °C | -34 °C | 1420 °C | | density | 0.00149 g/cm^3 (at 25 °C) | 2.73 g/cm^3 | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 1.98 g/cm^3 | 2.67 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 | odorless |