H2O + NaOH + P4 = NaH2PO4 + PH4

H_2O water + NaOH sodium hydroxide + P_4 white phosphorus ⟶ NaH_2PO_4 sodium dihydrogen phosphate + PH4

Balance the chemical equation algebraically: H_2O + NaOH + P_4 ⟶ NaH_2PO_4 + PH4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NaOH + c_3 P_4 ⟶ c_4 NaH_2PO_4 + c_5 PH4 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 = 2 c_4 + 4 c_5 O: | c_1 + c_2 = 4 c_4 Na: | c_2 = c_4 P: | 4 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 16/3 c_2 = 16/9 c_3 = 1 c_4 = 16/9 c_5 = 20/9 Multiply by the least common denominator, 9, to eliminate fractional coefficients: c_1 = 48 c_2 = 16 c_3 = 9 c_4 = 16 c_5 = 20 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 48 H_2O + 16 NaOH + 9 P_4 ⟶ 16 NaH_2PO_4 + 20 PH4

+ + ⟶ + PH4

water + sodium hydroxide + white phosphorus ⟶ sodium dihydrogen phosphate + PH4

Construct the equilibrium constant, K, expression for: H_2O + NaOH + P_4 ⟶ NaH_2PO_4 + PH4 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: 48 H_2O + 16 NaOH + 9 P_4 ⟶ 16 NaH_2PO_4 + 20 PH4 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 | 48 | -48 NaOH | 16 | -16 P_4 | 9 | -9 NaH_2PO_4 | 16 | 16 PH4 | 20 | 20 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 48 | -48 | ([H2O])^(-48) NaOH | 16 | -16 | ([NaOH])^(-16) P_4 | 9 | -9 | ([P4])^(-9) NaH_2PO_4 | 16 | 16 | ([NaH2PO4])^16 PH4 | 20 | 20 | ([PH4])^20 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])^(-48) ([NaOH])^(-16) ([P4])^(-9) ([NaH2PO4])^16 ([PH4])^20 = (([NaH2PO4])^16 ([PH4])^20)/(([H2O])^48 ([NaOH])^16 ([P4])^9)

Construct the rate of reaction expression for: H_2O + NaOH + P_4 ⟶ NaH_2PO_4 + PH4 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: 48 H_2O + 16 NaOH + 9 P_4 ⟶ 16 NaH_2PO_4 + 20 PH4 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 | 48 | -48 NaOH | 16 | -16 P_4 | 9 | -9 NaH_2PO_4 | 16 | 16 PH4 | 20 | 20 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 | 48 | -48 | -1/48 (Δ[H2O])/(Δt) NaOH | 16 | -16 | -1/16 (Δ[NaOH])/(Δt) P_4 | 9 | -9 | -1/9 (Δ[P4])/(Δt) NaH_2PO_4 | 16 | 16 | 1/16 (Δ[NaH2PO4])/(Δt) PH4 | 20 | 20 | 1/20 (Δ[PH4])/(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 = -1/48 (Δ[H2O])/(Δt) = -1/16 (Δ[NaOH])/(Δt) = -1/9 (Δ[P4])/(Δt) = 1/16 (Δ[NaH2PO4])/(Δt) = 1/20 (Δ[PH4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium hydroxide | white phosphorus | sodium dihydrogen phosphate | PH4 formula | H_2O | NaOH | P_4 | NaH_2PO_4 | PH4 Hill formula | H_2O | HNaO | P_4 | H_2NaO_4P | H4P name | water | sodium hydroxide | white phosphorus | sodium dihydrogen phosphate | IUPAC name | water | sodium hydroxide | tetraphosphorus | sodium dihydrogen phosphate |

| water | sodium hydroxide | white phosphorus | sodium dihydrogen phosphate | PH4 molar mass | 18.015 g/mol | 39.997 g/mol | 123.89504799 g/mol | 119.98 g/mol | 35.006 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | | melting point | 0 °C | 323 °C | 44.15 °C | | boiling point | 99.9839 °C | 1390 °C | 280.5 °C | | density | 1 g/cm^3 | 2.13 g/cm^3 | 1.823 g/cm^3 | 0.9996 g/cm^3 | solubility in water | | soluble | insoluble | | 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) | 0.00169 Pa s (at 50 °C) | | odor | odorless | | odorless | odorless |