H2SO4 + I2 + Na2S = S + Na2SO4 + HI

H_2SO_4 sulfuric acid + I_2 iodine + Na_2S sodium sulfide ⟶ S mixed sulfur + Na_2SO_4 sodium sulfate + HI hydrogen iodide

Balance the chemical equation algebraically: H_2SO_4 + I_2 + Na_2S ⟶ S + Na_2SO_4 + HI Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 I_2 + c_3 Na_2S ⟶ c_4 S + c_5 Na_2SO_4 + c_6 HI Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, I and Na: H: | 2 c_1 = c_6 O: | 4 c_1 = 4 c_5 S: | c_1 + c_3 = c_4 + c_5 I: | 2 c_2 = c_6 Na: | 2 c_3 = 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 = 1 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + I_2 + Na_2S ⟶ S + Na_2SO_4 + 2 HI

+ + ⟶ + +

sulfuric acid + iodine + sodium sulfide ⟶ mixed sulfur + sodium sulfate + hydrogen iodide

Construct the equilibrium constant, K, expression for: H_2SO_4 + I_2 + Na_2S ⟶ S + Na_2SO_4 + HI 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: H_2SO_4 + I_2 + Na_2S ⟶ S + Na_2SO_4 + 2 HI 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 | 1 | -1 I_2 | 1 | -1 Na_2S | 1 | -1 S | 1 | 1 Na_2SO_4 | 1 | 1 HI | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) I_2 | 1 | -1 | ([I2])^(-1) Na_2S | 1 | -1 | ([Na2S])^(-1) S | 1 | 1 | [S] Na_2SO_4 | 1 | 1 | [Na2SO4] HI | 2 | 2 | ([HI])^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 = ([H2SO4])^(-1) ([I2])^(-1) ([Na2S])^(-1) [S] [Na2SO4] ([HI])^2 = ([S] [Na2SO4] ([HI])^2)/([H2SO4] [I2] [Na2S])

Construct the rate of reaction expression for: H_2SO_4 + I_2 + Na_2S ⟶ S + Na_2SO_4 + HI 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: H_2SO_4 + I_2 + Na_2S ⟶ S + Na_2SO_4 + 2 HI 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 | 1 | -1 I_2 | 1 | -1 Na_2S | 1 | -1 S | 1 | 1 Na_2SO_4 | 1 | 1 HI | 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 H_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) I_2 | 1 | -1 | -(Δ[I2])/(Δt) Na_2S | 1 | -1 | -(Δ[Na2S])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) HI | 2 | 2 | 1/2 (Δ[HI])/(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[H2SO4])/(Δt) = -(Δ[I2])/(Δt) = -(Δ[Na2S])/(Δt) = (Δ[S])/(Δt) = (Δ[Na2SO4])/(Δt) = 1/2 (Δ[HI])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | iodine | sodium sulfide | mixed sulfur | sodium sulfate | hydrogen iodide formula | H_2SO_4 | I_2 | Na_2S | S | Na_2SO_4 | HI Hill formula | H_2O_4S | I_2 | Na_2S_1 | S | Na_2O_4S | HI name | sulfuric acid | iodine | sodium sulfide | mixed sulfur | sodium sulfate | hydrogen iodide IUPAC name | sulfuric acid | molecular iodine | | sulfur | disodium sulfate | hydrogen iodide

| sulfuric acid | iodine | sodium sulfide | mixed sulfur | sodium sulfate | hydrogen iodide molar mass | 98.07 g/mol | 253.80894 g/mol | 78.04 g/mol | 32.06 g/mol | 142.04 g/mol | 127.912 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) melting point | 10.371 °C | 113 °C | 1172 °C | 112.8 °C | 884 °C | -50.76 °C boiling point | 279.6 °C | 184 °C | | 444.7 °C | 1429 °C | -35.55 °C density | 1.8305 g/cm^3 | 4.94 g/cm^3 | 1.856 g/cm^3 | 2.07 g/cm^3 | 2.68 g/cm^3 | 0.005228 g/cm^3 (at 25 °C) solubility in water | very soluble | | | | soluble | very soluble surface tension | 0.0735 N/m | | | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 0.00227 Pa s (at 116 °C) | | | | 0.001321 Pa s (at -39 °C) odor | odorless | | | | |