H2SO4 + HI = H2O + S + I2 + H2S

H_2SO_4 sulfuric acid + HI hydrogen iodide ⟶ H_2O water + S mixed sulfur + I_2 iodine + H_2S hydrogen sulfide

Balance the chemical equation algebraically: H_2SO_4 + HI ⟶ H_2O + S + I_2 + H_2S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 HI ⟶ c_3 H_2O + c_4 S + c_5 I_2 + c_6 H_2S Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and I: H: | 2 c_1 + c_2 = 2 c_3 + 2 c_6 O: | 4 c_1 = c_3 S: | c_1 = c_4 + c_6 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_4 = 1 and solve the system of equations for the remaining coefficients: c_2 = 8 c_1 - 2 c_3 = 4 c_1 c_4 = 1 c_5 = 4 c_1 - 1 c_6 = c_1 - 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 30 c_3 = 16 c_4 = 1 c_5 = 15 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 30 HI ⟶ 16 H_2O + S + 15 I_2 + 3 H_2S

+ ⟶ + + +

sulfuric acid + hydrogen iodide ⟶ water + mixed sulfur + iodine + hydrogen sulfide

Construct the equilibrium constant, K, expression for: H_2SO_4 + HI ⟶ H_2O + S + I_2 + H_2S 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: 4 H_2SO_4 + 30 HI ⟶ 16 H_2O + S + 15 I_2 + 3 H_2S 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 H_2SO_4 | 4 | -4 HI | 30 | -30 H_2O | 16 | 16 S | 1 | 1 I_2 | 15 | 15 H_2S | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) HI | 30 | -30 | ([HI])^(-30) H_2O | 16 | 16 | ([H2O])^16 S | 1 | 1 | [S] I_2 | 15 | 15 | ([I2])^15 H_2S | 3 | 3 | ([H2S])^3 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 = ([H2SO4])^(-4) ([HI])^(-30) ([H2O])^16 [S] ([I2])^15 ([H2S])^3 = (([H2O])^16 [S] ([I2])^15 ([H2S])^3)/(([H2SO4])^4 ([HI])^30)

Construct the rate of reaction expression for: H_2SO_4 + HI ⟶ H_2O + S + I_2 + H_2S 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: 4 H_2SO_4 + 30 HI ⟶ 16 H_2O + S + 15 I_2 + 3 H_2S 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 H_2SO_4 | 4 | -4 HI | 30 | -30 H_2O | 16 | 16 S | 1 | 1 I_2 | 15 | 15 H_2S | 3 | 3 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 H_2SO_4 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) HI | 30 | -30 | -1/30 (Δ[HI])/(Δt) H_2O | 16 | 16 | 1/16 (Δ[H2O])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) I_2 | 15 | 15 | 1/15 (Δ[I2])/(Δt) H_2S | 3 | 3 | 1/3 (Δ[H2S])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/30 (Δ[HI])/(Δt) = 1/16 (Δ[H2O])/(Δt) = (Δ[S])/(Δt) = 1/15 (Δ[I2])/(Δt) = 1/3 (Δ[H2S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | hydrogen iodide | water | mixed sulfur | iodine | hydrogen sulfide formula | H_2SO_4 | HI | H_2O | S | I_2 | H_2S Hill formula | H_2O_4S | HI | H_2O | S | I_2 | H_2S name | sulfuric acid | hydrogen iodide | water | mixed sulfur | iodine | hydrogen sulfide IUPAC name | sulfuric acid | hydrogen iodide | water | sulfur | molecular iodine | hydrogen sulfide

| sulfuric acid | hydrogen iodide | water | mixed sulfur | iodine | hydrogen sulfide molar mass | 98.07 g/mol | 127.912 g/mol | 18.015 g/mol | 32.06 g/mol | 253.80894 g/mol | 34.08 g/mol phase | liquid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) melting point | 10.371 °C | -50.76 °C | 0 °C | 112.8 °C | 113 °C | -85 °C boiling point | 279.6 °C | -35.55 °C | 99.9839 °C | 444.7 °C | 184 °C | -60 °C density | 1.8305 g/cm^3 | 0.005228 g/cm^3 (at 25 °C) | 1 g/cm^3 | 2.07 g/cm^3 | 4.94 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) solubility in water | very soluble | very soluble | | | | surface tension | 0.0735 N/m | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 0.001321 Pa s (at -39 °C) | 8.9×10^-4 Pa s (at 25 °C) | | 0.00227 Pa s (at 116 °C) | 1.239×10^-5 Pa s (at 25 °C) odor | odorless | | odorless | | |