H2O + I2 + P4 = H3PO4 + HI + PH4I

H_2O water + I_2 iodine + P_4 white phosphorus ⟶ H_3PO_4 phosphoric acid + HI hydrogen iodide + PH_4I phosphonium iodide

Balance the chemical equation algebraically: H_2O + I_2 + P_4 ⟶ H_3PO_4 + HI + PH_4I Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 I_2 + c_3 P_4 ⟶ c_4 H_3PO_4 + c_5 HI + c_6 PH_4I Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, I and P: H: | 2 c_1 = 3 c_4 + c_5 + 4 c_6 O: | c_1 = 4 c_4 I: | 2 c_2 = c_5 + c_6 P: | 4 c_3 = c_4 + c_6 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_2 = c_1 - 6 c_3 = 1 c_4 = c_1/4 c_5 = (9 c_1)/4 - 16 c_6 = 4 - c_1/4 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 8 and solve for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2O + 2 I_2 + P_4 ⟶ 2 H_3PO_4 + 2 HI + 2 PH_4I

+ + ⟶ + +

water + iodine + white phosphorus ⟶ phosphoric acid + hydrogen iodide + phosphonium iodide

Construct the equilibrium constant, K, expression for: H_2O + I_2 + P_4 ⟶ H_3PO_4 + HI + PH_4I 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: 8 H_2O + 2 I_2 + P_4 ⟶ 2 H_3PO_4 + 2 HI + 2 PH_4I 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 | 8 | -8 I_2 | 2 | -2 P_4 | 1 | -1 H_3PO_4 | 2 | 2 HI | 2 | 2 PH_4I | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 8 | -8 | ([H2O])^(-8) I_2 | 2 | -2 | ([I2])^(-2) P_4 | 1 | -1 | ([P4])^(-1) H_3PO_4 | 2 | 2 | ([H3PO4])^2 HI | 2 | 2 | ([HI])^2 PH_4I | 2 | 2 | ([PH4I])^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 = ([H2O])^(-8) ([I2])^(-2) ([P4])^(-1) ([H3PO4])^2 ([HI])^2 ([PH4I])^2 = (([H3PO4])^2 ([HI])^2 ([PH4I])^2)/(([H2O])^8 ([I2])^2 [P4])

Construct the rate of reaction expression for: H_2O + I_2 + P_4 ⟶ H_3PO_4 + HI + PH_4I 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: 8 H_2O + 2 I_2 + P_4 ⟶ 2 H_3PO_4 + 2 HI + 2 PH_4I 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 | 8 | -8 I_2 | 2 | -2 P_4 | 1 | -1 H_3PO_4 | 2 | 2 HI | 2 | 2 PH_4I | 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_2O | 8 | -8 | -1/8 (Δ[H2O])/(Δt) I_2 | 2 | -2 | -1/2 (Δ[I2])/(Δt) P_4 | 1 | -1 | -(Δ[P4])/(Δt) H_3PO_4 | 2 | 2 | 1/2 (Δ[H3PO4])/(Δt) HI | 2 | 2 | 1/2 (Δ[HI])/(Δt) PH_4I | 2 | 2 | 1/2 (Δ[PH4I])/(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 = -1/8 (Δ[H2O])/(Δt) = -1/2 (Δ[I2])/(Δt) = -(Δ[P4])/(Δt) = 1/2 (Δ[H3PO4])/(Δt) = 1/2 (Δ[HI])/(Δt) = 1/2 (Δ[PH4I])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | iodine | white phosphorus | phosphoric acid | hydrogen iodide | phosphonium iodide formula | H_2O | I_2 | P_4 | H_3PO_4 | HI | PH_4I Hill formula | H_2O | I_2 | P_4 | H_3O_4P | HI | H_4IP name | water | iodine | white phosphorus | phosphoric acid | hydrogen iodide | phosphonium iodide IUPAC name | water | molecular iodine | tetraphosphorus | phosphoric acid | hydrogen iodide |

| water | iodine | white phosphorus | phosphoric acid | hydrogen iodide | phosphonium iodide molar mass | 18.015 g/mol | 253.80894 g/mol | 123.89504799 g/mol | 97.994 g/mol | 127.912 g/mol | 161.91 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | melting point | 0 °C | 113 °C | 44.15 °C | 42.4 °C | -50.76 °C | 18.5 °C boiling point | 99.9839 °C | 184 °C | 280.5 °C | 158 °C | -35.55 °C | 62.5 °C density | 1 g/cm^3 | 4.94 g/cm^3 | 1.823 g/cm^3 | 1.685 g/cm^3 | 0.005228 g/cm^3 (at 25 °C) | 2.86 g/cm^3 solubility in water | | | insoluble | very soluble | very soluble | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.00227 Pa s (at 116 °C) | 0.00169 Pa s (at 50 °C) | | 0.001321 Pa s (at -39 °C) | odor | odorless | | odorless | odorless | |