H2O + HIO3 + P2S3 = S + H3PO4 + HI

H_2O water + HIO_3 iodic acid + P_2S_3 phosphorus trisulfide ⟶ S mixed sulfur + H_3PO_4 phosphoric acid + HI hydrogen iodide

Balance the chemical equation algebraically: H_2O + HIO_3 + P_2S_3 ⟶ S + H_3PO_4 + HI Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HIO_3 + c_3 P_2S_3 ⟶ c_4 S + c_5 H_3PO_4 + c_6 HI Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, I, P and S: H: | 2 c_1 + c_2 = 3 c_5 + c_6 O: | c_1 + 3 c_2 = 4 c_5 I: | c_2 = c_6 P: | 2 c_3 = c_5 S: | 3 c_3 = c_4 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 5/3 c_3 = 1 c_4 = 3 c_5 = 2 c_6 = 5/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 9 c_2 = 5 c_3 = 3 c_4 = 9 c_5 = 6 c_6 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 H_2O + 5 HIO_3 + 3 P_2S_3 ⟶ 9 S + 6 H_3PO_4 + 5 HI

+ + ⟶ + +

water + iodic acid + phosphorus trisulfide ⟶ mixed sulfur + phosphoric acid + hydrogen iodide

Construct the equilibrium constant, K, expression for: H_2O + HIO_3 + P_2S_3 ⟶ S + H_3PO_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: 9 H_2O + 5 HIO_3 + 3 P_2S_3 ⟶ 9 S + 6 H_3PO_4 + 5 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_2O | 9 | -9 HIO_3 | 5 | -5 P_2S_3 | 3 | -3 S | 9 | 9 H_3PO_4 | 6 | 6 HI | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 9 | -9 | ([H2O])^(-9) HIO_3 | 5 | -5 | ([HIO3])^(-5) P_2S_3 | 3 | -3 | ([P2S3])^(-3) S | 9 | 9 | ([S])^9 H_3PO_4 | 6 | 6 | ([H3PO4])^6 HI | 5 | 5 | ([HI])^5 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 = ([H2O])^(-9) ([HIO3])^(-5) ([P2S3])^(-3) ([S])^9 ([H3PO4])^6 ([HI])^5 = (([S])^9 ([H3PO4])^6 ([HI])^5)/(([H2O])^9 ([HIO3])^5 ([P2S3])^3)

Construct the rate of reaction expression for: H_2O + HIO_3 + P_2S_3 ⟶ S + H_3PO_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: 9 H_2O + 5 HIO_3 + 3 P_2S_3 ⟶ 9 S + 6 H_3PO_4 + 5 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_2O | 9 | -9 HIO_3 | 5 | -5 P_2S_3 | 3 | -3 S | 9 | 9 H_3PO_4 | 6 | 6 HI | 5 | 5 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_2O | 9 | -9 | -1/9 (Δ[H2O])/(Δt) HIO_3 | 5 | -5 | -1/5 (Δ[HIO3])/(Δt) P_2S_3 | 3 | -3 | -1/3 (Δ[P2S3])/(Δt) S | 9 | 9 | 1/9 (Δ[S])/(Δt) H_3PO_4 | 6 | 6 | 1/6 (Δ[H3PO4])/(Δt) HI | 5 | 5 | 1/5 (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 = -1/9 (Δ[H2O])/(Δt) = -1/5 (Δ[HIO3])/(Δt) = -1/3 (Δ[P2S3])/(Δt) = 1/9 (Δ[S])/(Δt) = 1/6 (Δ[H3PO4])/(Δt) = 1/5 (Δ[HI])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | iodic acid | phosphorus trisulfide | mixed sulfur | phosphoric acid | hydrogen iodide formula | H_2O | HIO_3 | P_2S_3 | S | H_3PO_4 | HI Hill formula | H_2O | HIO_3 | P_2S_3 | S | H_3O_4P | HI name | water | iodic acid | phosphorus trisulfide | mixed sulfur | phosphoric acid | hydrogen iodide IUPAC name | water | iodic acid | | sulfur | phosphoric acid | hydrogen iodide

| water | iodic acid | phosphorus trisulfide | mixed sulfur | phosphoric acid | hydrogen iodide molar mass | 18.015 g/mol | 175.91 g/mol | 158.1 g/mol | 32.06 g/mol | 97.994 g/mol | 127.912 g/mol phase | liquid (at STP) | solid (at STP) | | solid (at STP) | liquid (at STP) | gas (at STP) melting point | 0 °C | 110 °C | | 112.8 °C | 42.4 °C | -50.76 °C boiling point | 99.9839 °C | | | 444.7 °C | 158 °C | -35.55 °C density | 1 g/cm^3 | 4.629 g/cm^3 | | 2.07 g/cm^3 | 1.685 g/cm^3 | 0.005228 g/cm^3 (at 25 °C) solubility in water | | very soluble | | | very soluble | very soluble surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | | 0.001321 Pa s (at -39 °C) odor | odorless | | | | odorless |