H2O + NaOH + P = PH3 + Na3PO4

H_2O water + NaOH sodium hydroxide + P red phosphorus ⟶ PH_3 phosphine + Na_3PO_4 trisodium phosphate

Balance the chemical equation algebraically: H_2O + NaOH + P ⟶ PH_3 + Na_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NaOH + c_3 P ⟶ c_4 PH_3 + c_5 Na_3PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na and P: H: | 2 c_1 + c_2 = 3 c_4 O: | c_1 + c_2 = 4 c_5 Na: | c_2 = 3 c_5 P: | c_3 = c_4 + 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 = 3 c_3 = 8/3 c_4 = 5/3 c_5 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 3 c_2 = 9 c_3 = 8 c_4 = 5 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 9 NaOH + 8 P ⟶ 5 PH_3 + 3 Na_3PO_4

+ + ⟶ +

water + sodium hydroxide + red phosphorus ⟶ phosphine + trisodium phosphate

Construct the equilibrium constant, K, expression for: H_2O + NaOH + P ⟶ PH_3 + Na_3PO_4 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: 3 H_2O + 9 NaOH + 8 P ⟶ 5 PH_3 + 3 Na_3PO_4 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 | 3 | -3 NaOH | 9 | -9 P | 8 | -8 PH_3 | 5 | 5 Na_3PO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) NaOH | 9 | -9 | ([NaOH])^(-9) P | 8 | -8 | ([P])^(-8) PH_3 | 5 | 5 | ([PH3])^5 Na_3PO_4 | 3 | 3 | ([Na3PO4])^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 = ([H2O])^(-3) ([NaOH])^(-9) ([P])^(-8) ([PH3])^5 ([Na3PO4])^3 = (([PH3])^5 ([Na3PO4])^3)/(([H2O])^3 ([NaOH])^9 ([P])^8)

Construct the rate of reaction expression for: H_2O + NaOH + P ⟶ PH_3 + Na_3PO_4 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: 3 H_2O + 9 NaOH + 8 P ⟶ 5 PH_3 + 3 Na_3PO_4 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 | 3 | -3 NaOH | 9 | -9 P | 8 | -8 PH_3 | 5 | 5 Na_3PO_4 | 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_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) NaOH | 9 | -9 | -1/9 (Δ[NaOH])/(Δt) P | 8 | -8 | -1/8 (Δ[P])/(Δt) PH_3 | 5 | 5 | 1/5 (Δ[PH3])/(Δt) Na_3PO_4 | 3 | 3 | 1/3 (Δ[Na3PO4])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/9 (Δ[NaOH])/(Δt) = -1/8 (Δ[P])/(Δt) = 1/5 (Δ[PH3])/(Δt) = 1/3 (Δ[Na3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium hydroxide | red phosphorus | phosphine | trisodium phosphate formula | H_2O | NaOH | P | PH_3 | Na_3PO_4 Hill formula | H_2O | HNaO | P | H_3P | Na_3O_4P name | water | sodium hydroxide | red phosphorus | phosphine | trisodium phosphate IUPAC name | water | sodium hydroxide | phosphorus | phosphine | trisodium phosphate

| water | sodium hydroxide | red phosphorus | phosphine | trisodium phosphate molar mass | 18.015 g/mol | 39.997 g/mol | 30.973761998 g/mol | 33.998 g/mol | 163.94 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 0 °C | 323 °C | 579.2 °C | -132.8 °C | 75 °C boiling point | 99.9839 °C | 1390 °C | | -87.5 °C | density | 1 g/cm^3 | 2.13 g/cm^3 | 2.16 g/cm^3 | 0.00139 g/cm^3 (at 25 °C) | 2.536 g/cm^3 solubility in water | | soluble | insoluble | slightly soluble | soluble surface tension | 0.0728 N/m | 0.07435 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.004 Pa s (at 350 °C) | 7.6×10^-4 Pa s (at 20.2 °C) | 1.1×10^-5 Pa s (at 0 °C) | odor | odorless | | | | odorless