SO2 + HI = H2O + S + I2

SO_2 sulfur dioxide + HI hydrogen iodide ⟶ H_2O water + S mixed sulfur + I_2 iodine

Balance the chemical equation algebraically: SO_2 + HI ⟶ H_2O + S + I_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 HI ⟶ c_3 H_2O + c_4 S + c_5 I_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, S, H and I: O: | 2 c_1 = c_3 S: | c_1 = c_4 H: | c_2 = 2 c_3 I: | c_2 = 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 2 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | SO_2 + 4 HI ⟶ 2 H_2O + S + 2 I_2

+ ⟶ + +

sulfur dioxide + hydrogen iodide ⟶ water + mixed sulfur + iodine

Construct the equilibrium constant, K, expression for: SO_2 + HI ⟶ H_2O + S + I_2 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: SO_2 + 4 HI ⟶ 2 H_2O + S + 2 I_2 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 SO_2 | 1 | -1 HI | 4 | -4 H_2O | 2 | 2 S | 1 | 1 I_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 1 | -1 | ([SO2])^(-1) HI | 4 | -4 | ([HI])^(-4) H_2O | 2 | 2 | ([H2O])^2 S | 1 | 1 | [S] I_2 | 2 | 2 | ([I2])^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 = ([SO2])^(-1) ([HI])^(-4) ([H2O])^2 [S] ([I2])^2 = (([H2O])^2 [S] ([I2])^2)/([SO2] ([HI])^4)

Construct the rate of reaction expression for: SO_2 + HI ⟶ H_2O + S + I_2 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: SO_2 + 4 HI ⟶ 2 H_2O + S + 2 I_2 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 SO_2 | 1 | -1 HI | 4 | -4 H_2O | 2 | 2 S | 1 | 1 I_2 | 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 SO_2 | 1 | -1 | -(Δ[SO2])/(Δt) HI | 4 | -4 | -1/4 (Δ[HI])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) I_2 | 2 | 2 | 1/2 (Δ[I2])/(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 = -(Δ[SO2])/(Δt) = -1/4 (Δ[HI])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[S])/(Δt) = 1/2 (Δ[I2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | hydrogen iodide | water | mixed sulfur | iodine formula | SO_2 | HI | H_2O | S | I_2 Hill formula | O_2S | HI | H_2O | S | I_2 name | sulfur dioxide | hydrogen iodide | water | mixed sulfur | iodine IUPAC name | sulfur dioxide | hydrogen iodide | water | sulfur | molecular iodine