H2O + KOH + P4 = PH3 + KH2PO2

H_2O (water) + KOH (potassium hydroxide) + P_4 (white phosphorus) ⟶ PH_3 (phosphine) + KH_2PO_2 (potassium phosphinate)

Balance the chemical equation algebraically: H_2O + KOH + P_4 ⟶ PH_3 + KH_2PO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KOH + c_3 P_4 ⟶ c_4 PH_3 + c_5 KH_2PO_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 = 3 c_4 + 2 c_5 O: | c_1 + c_2 = 2 c_5 K: | c_2 = c_5 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 = 3 c_2 = 3 c_3 = 1 c_4 = 1 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 3 KOH + P_4 ⟶ PH_3 + 3 KH_2PO_2

+ + ⟶ +

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

Construct the equilibrium constant, K, expression for: H_2O + KOH + P_4 ⟶ PH_3 + KH_2PO_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: 3 H_2O + 3 KOH + P_4 ⟶ PH_3 + 3 KH_2PO_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 | 3 | -3 KOH | 3 | -3 P_4 | 1 | -1 PH_3 | 1 | 1 KH_2PO_2 | 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) KOH | 3 | -3 | ([KOH])^(-3) P_4 | 1 | -1 | ([P4])^(-1) PH_3 | 1 | 1 | [PH3] KH_2PO_2 | 3 | 3 | ([KH2PO2])^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) ([KOH])^(-3) ([P4])^(-1) [PH3] ([KH2PO2])^3 = ([PH3] ([KH2PO2])^3)/(([H2O])^3 ([KOH])^3 [P4])

Construct the rate of reaction expression for: H_2O + KOH + P_4 ⟶ PH_3 + KH_2PO_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: 3 H_2O + 3 KOH + P_4 ⟶ PH_3 + 3 KH_2PO_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 | 3 | -3 KOH | 3 | -3 P_4 | 1 | -1 PH_3 | 1 | 1 KH_2PO_2 | 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) KOH | 3 | -3 | -1/3 (Δ[KOH])/(Δt) P_4 | 1 | -1 | -(Δ[P4])/(Δt) PH_3 | 1 | 1 | (Δ[PH3])/(Δt) KH_2PO_2 | 3 | 3 | 1/3 (Δ[KH2PO2])/(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) = -1/3 (Δ[KOH])/(Δt) = -(Δ[P4])/(Δt) = (Δ[PH3])/(Δt) = 1/3 (Δ[KH2PO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium hydroxide | white phosphorus | phosphine | potassium phosphinate formula | H_2O | KOH | P_4 | PH_3 | KH_2PO_2 Hill formula | H_2O | HKO | P_4 | H_3P | H_2KO_2P name | water | potassium hydroxide | white phosphorus | phosphine | potassium phosphinate IUPAC name | water | potassium hydroxide | tetraphosphorus | phosphine |

| water | potassium hydroxide | white phosphorus | phosphine | potassium phosphinate molar mass | 18.015 g/mol | 56.105 g/mol | 123.89504799 g/mol | 33.998 g/mol | 104.09 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | 406 °C | 44.15 °C | -132.8 °C | boiling point | 99.9839 °C | 1327 °C | 280.5 °C | -87.5 °C | density | 1 g/cm^3 | 2.044 g/cm^3 | 1.823 g/cm^3 | 0.00139 g/cm^3 (at 25 °C) | solubility in water | | soluble | insoluble | slightly soluble | 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) | 1.1×10^-5 Pa s (at 0 °C) | odor | odorless | | odorless | |