P2H4 = PH3 + P4H2

H_4P_2 diphosphine ⟶ PH_3 phosphine + P4H2

Balance the chemical equation algebraically: H_4P_2 ⟶ PH_3 + P4H2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_4P_2 ⟶ c_2 PH_3 + c_3 P4H2 Set the number of atoms in the reactants equal to the number of atoms in the products for H and P: H: | 4 c_1 = 3 c_2 + 2 c_3 P: | 2 c_1 = c_2 + 4 c_3 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 = 5 c_2 = 6 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_4P_2 ⟶ 6 PH_3 + P4H2

⟶ + P4H2

diphosphine ⟶ phosphine + P4H2

Construct the equilibrium constant, K, expression for: H_4P_2 ⟶ PH_3 + P4H2 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: 5 H_4P_2 ⟶ 6 PH_3 + P4H2 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_4P_2 | 5 | -5 PH_3 | 6 | 6 P4H2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_4P_2 | 5 | -5 | ([H4P2])^(-5) PH_3 | 6 | 6 | ([PH3])^6 P4H2 | 1 | 1 | [P4H2] 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 = ([H4P2])^(-5) ([PH3])^6 [P4H2] = (([PH3])^6 [P4H2])/([H4P2])^5

Construct the rate of reaction expression for: H_4P_2 ⟶ PH_3 + P4H2 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: 5 H_4P_2 ⟶ 6 PH_3 + P4H2 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_4P_2 | 5 | -5 PH_3 | 6 | 6 P4H2 | 1 | 1 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_4P_2 | 5 | -5 | -1/5 (Δ[H4P2])/(Δt) PH_3 | 6 | 6 | 1/6 (Δ[PH3])/(Δt) P4H2 | 1 | 1 | (Δ[P4H2])/(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 = -1/5 (Δ[H4P2])/(Δt) = 1/6 (Δ[PH3])/(Δt) = (Δ[P4H2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| diphosphine | phosphine | P4H2 formula | H_4P_2 | PH_3 | P4H2 Hill formula | H_4P_2 | H_3P | H2P4 name | diphosphine | phosphine | IUPAC name | phosphinophosphine | phosphine |

| diphosphine | phosphine | P4H2 molar mass | 65.98 g/mol | 33.998 g/mol | 125.911 g/mol phase | | gas (at STP) | melting point | | -132.8 °C | boiling point | | -87.5 °C | density | | 0.00139 g/cm^3 (at 25 °C) | solubility in water | | slightly soluble | dynamic viscosity | | 1.1×10^-5 Pa s (at 0 °C) |