H2O + KOH + P4 = KH2PO2 + P2H4

H_2O water + KOH potassium hydroxide + P_4 white phosphorus ⟶ KH_2PO_2 potassium phosphinate + H_4P_2 diphosphine

Balance the chemical equation algebraically: H_2O + KOH + P_4 ⟶ KH_2PO_2 + H_4P_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KOH + c_3 P_4 ⟶ c_4 KH_2PO_2 + c_5 H_4P_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K and P: H: | 2 c_1 + c_2 = 2 c_4 + 4 c_5 O: | c_1 + c_2 = 2 c_4 K: | c_2 = c_4 P: | 4 c_3 = c_4 + 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 4 c_3 = 3/2 c_4 = 4 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 8 c_3 = 3 c_4 = 8 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2O + 8 KOH + 3 P_4 ⟶ 8 KH_2PO_2 + 2 H_4P_2

+ + ⟶ +

water + potassium hydroxide + white phosphorus ⟶ potassium phosphinate + diphosphine

Construct the equilibrium constant, K, expression for: H_2O + KOH + P_4 ⟶ KH_2PO_2 + H_4P_2 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 + 8 KOH + 3 P_4 ⟶ 8 KH_2PO_2 + 2 H_4P_2 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 KOH | 8 | -8 P_4 | 3 | -3 KH_2PO_2 | 8 | 8 H_4P_2 | 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) KOH | 8 | -8 | ([KOH])^(-8) P_4 | 3 | -3 | ([P4])^(-3) KH_2PO_2 | 8 | 8 | ([KH2PO2])^8 H_4P_2 | 2 | 2 | ([H4P2])^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) ([KOH])^(-8) ([P4])^(-3) ([KH2PO2])^8 ([H4P2])^2 = (([KH2PO2])^8 ([H4P2])^2)/(([H2O])^8 ([KOH])^8 ([P4])^3)

Construct the rate of reaction expression for: H_2O + KOH + P_4 ⟶ KH_2PO_2 + H_4P_2 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 + 8 KOH + 3 P_4 ⟶ 8 KH_2PO_2 + 2 H_4P_2 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 KOH | 8 | -8 P_4 | 3 | -3 KH_2PO_2 | 8 | 8 H_4P_2 | 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) KOH | 8 | -8 | -1/8 (Δ[KOH])/(Δt) P_4 | 3 | -3 | -1/3 (Δ[P4])/(Δt) KH_2PO_2 | 8 | 8 | 1/8 (Δ[KH2PO2])/(Δt) H_4P_2 | 2 | 2 | 1/2 (Δ[H4P2])/(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) = -1/8 (Δ[KOH])/(Δt) = -1/3 (Δ[P4])/(Δt) = 1/8 (Δ[KH2PO2])/(Δt) = 1/2 (Δ[H4P2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium hydroxide | white phosphorus | potassium phosphinate | diphosphine formula | H_2O | KOH | P_4 | KH_2PO_2 | H_4P_2 Hill formula | H_2O | HKO | P_4 | H_2KO_2P | H_4P_2 name | water | potassium hydroxide | white phosphorus | potassium phosphinate | diphosphine IUPAC name | water | potassium hydroxide | tetraphosphorus | | phosphinophosphine

| water | potassium hydroxide | white phosphorus | potassium phosphinate | diphosphine molar mass | 18.015 g/mol | 56.105 g/mol | 123.89504799 g/mol | 104.09 g/mol | 65.98 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | | melting point | 0 °C | 406 °C | 44.15 °C | | boiling point | 99.9839 °C | 1327 °C | 280.5 °C | | density | 1 g/cm^3 | 2.044 g/cm^3 | 1.823 g/cm^3 | | solubility in water | | soluble | insoluble | soluble | surface tension | 0.0728 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | 0.00169 Pa s (at 50 °C) | | odor | odorless | | odorless | |