HI + CrO3 = H2O + I2 + Cr2O3

HI hydrogen iodide + CrO_3 chromium trioxide ⟶ H_2O water + I_2 iodine + Cr_2O_3 chromium(III) oxide

Balance the chemical equation algebraically: HI + CrO_3 ⟶ H_2O + I_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HI + c_2 CrO_3 ⟶ c_3 H_2O + c_4 I_2 + c_5 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, I, Cr and O: H: | c_1 = 2 c_3 I: | c_1 = 2 c_4 Cr: | c_2 = 2 c_5 O: | 3 c_2 = c_3 + 3 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HI + 2 CrO_3 ⟶ 3 H_2O + 3 I_2 + Cr_2O_3

+ ⟶ + +

hydrogen iodide + chromium trioxide ⟶ water + iodine + chromium(III) oxide

| hydrogen iodide | chromium trioxide | water | iodine | chromium(III) oxide molecular free energy | 1.7 kJ/mol | -502 kJ/mol | -237.1 kJ/mol | 0 kJ/mol | -1058 kJ/mol total free energy | 10.2 kJ/mol | -1004 kJ/mol | -711.3 kJ/mol | 0 kJ/mol | -1058 kJ/mol | G_initial = -993.8 kJ/mol | | G_final = -1769 kJ/mol | | ΔG_rxn^0 | -1769 kJ/mol - -993.8 kJ/mol = -775.6 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: HI + CrO_3 ⟶ H_2O + I_2 + Cr_2O_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: 6 HI + 2 CrO_3 ⟶ 3 H_2O + 3 I_2 + Cr_2O_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 HI | 6 | -6 CrO_3 | 2 | -2 H_2O | 3 | 3 I_2 | 3 | 3 Cr_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HI | 6 | -6 | ([HI])^(-6) CrO_3 | 2 | -2 | ([CrO3])^(-2) H_2O | 3 | 3 | ([H2O])^3 I_2 | 3 | 3 | ([I2])^3 Cr_2O_3 | 1 | 1 | [Cr2O3] 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 = ([HI])^(-6) ([CrO3])^(-2) ([H2O])^3 ([I2])^3 [Cr2O3] = (([H2O])^3 ([I2])^3 [Cr2O3])/(([HI])^6 ([CrO3])^2)

Construct the rate of reaction expression for: HI + CrO_3 ⟶ H_2O + I_2 + Cr_2O_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: 6 HI + 2 CrO_3 ⟶ 3 H_2O + 3 I_2 + Cr_2O_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 HI | 6 | -6 CrO_3 | 2 | -2 H_2O | 3 | 3 I_2 | 3 | 3 Cr_2O_3 | 1 | 1 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 HI | 6 | -6 | -1/6 (Δ[HI])/(Δt) CrO_3 | 2 | -2 | -1/2 (Δ[CrO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) I_2 | 3 | 3 | 1/3 (Δ[I2])/(Δt) Cr_2O_3 | 1 | 1 | (Δ[Cr2O3])/(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 = -1/6 (Δ[HI])/(Δt) = -1/2 (Δ[CrO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[I2])/(Δt) = (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen iodide | chromium trioxide | water | iodine | chromium(III) oxide formula | HI | CrO_3 | H_2O | I_2 | Cr_2O_3 name | hydrogen iodide | chromium trioxide | water | iodine | chromium(III) oxide IUPAC name | hydrogen iodide | trioxochromium | water | molecular iodine |

| hydrogen iodide | chromium trioxide | water | iodine | chromium(III) oxide molar mass | 127.912 g/mol | 99.993 g/mol | 18.015 g/mol | 253.80894 g/mol | 151.99 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -50.76 °C | 196 °C | 0 °C | 113 °C | 2435 °C boiling point | -35.55 °C | | 99.9839 °C | 184 °C | 4000 °C density | 0.005228 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 4.94 g/cm^3 | 4.8 g/cm^3 solubility in water | very soluble | very soluble | | | insoluble surface tension | | | 0.0728 N/m | | dynamic viscosity | 0.001321 Pa s (at -39 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 0.00227 Pa s (at 116 °C) | odor | | odorless | odorless | |