PH3 = H2 + P

PH_3 phosphine ⟶ H_2 hydrogen + P red phosphorus

Balance the chemical equation algebraically: PH_3 ⟶ H_2 + P Add stoichiometric coefficients, c_i, to the reactants and products: c_1 PH_3 ⟶ c_2 H_2 + c_3 P Set the number of atoms in the reactants equal to the number of atoms in the products for H and P: H: | 3 c_1 = 2 c_2 P: | c_1 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3/2 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 PH_3 ⟶ 3 H_2 + 2 P

⟶ +

phosphine ⟶ hydrogen + red phosphorus

| phosphine | hydrogen | red phosphorus molecular enthalpy | 5.4 kJ/mol | 0 kJ/mol | -17.6 kJ/mol total enthalpy | 10.8 kJ/mol | 0 kJ/mol | -35.2 kJ/mol | H_initial = 10.8 kJ/mol | H_final = -35.2 kJ/mol | ΔH_rxn^0 | -35.2 kJ/mol - 10.8 kJ/mol = -46 kJ/mol (exothermic) | |

| phosphine | hydrogen | red phosphorus molecular entropy | 210 J/(mol K) | 115 J/(mol K) | 22.8 J/(mol K) total entropy | 420 J/(mol K) | 345 J/(mol K) | 45.6 J/(mol K) | S_initial = 420 J/(mol K) | S_final = 390.6 J/(mol K) | ΔS_rxn^0 | 390.6 J/(mol K) - 420 J/(mol K) = -29.4 J/(mol K) (exoentropic) | |

Construct the equilibrium constant, K, expression for: PH_3 ⟶ H_2 + P 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: 2 PH_3 ⟶ 3 H_2 + 2 P 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 PH_3 | 2 | -2 H_2 | 3 | 3 P | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression PH_3 | 2 | -2 | ([PH3])^(-2) H_2 | 3 | 3 | ([H2])^3 P | 2 | 2 | ([P])^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 = ([PH3])^(-2) ([H2])^3 ([P])^2 = (([H2])^3 ([P])^2)/([PH3])^2

Construct the rate of reaction expression for: PH_3 ⟶ H_2 + P 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: 2 PH_3 ⟶ 3 H_2 + 2 P 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 PH_3 | 2 | -2 H_2 | 3 | 3 P | 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 PH_3 | 2 | -2 | -1/2 (Δ[PH3])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) P | 2 | 2 | 1/2 (Δ[P])/(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 = -1/2 (Δ[PH3])/(Δt) = 1/3 (Δ[H2])/(Δt) = 1/2 (Δ[P])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| phosphine | hydrogen | red phosphorus formula | PH_3 | H_2 | P Hill formula | H_3P | H_2 | P name | phosphine | hydrogen | red phosphorus IUPAC name | phosphine | molecular hydrogen | phosphorus

| phosphine | hydrogen | red phosphorus molar mass | 33.998 g/mol | 2.016 g/mol | 30.973761998 g/mol phase | gas (at STP) | gas (at STP) | solid (at STP) melting point | -132.8 °C | -259.2 °C | 579.2 °C boiling point | -87.5 °C | -252.8 °C | density | 0.00139 g/cm^3 (at 25 °C) | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.16 g/cm^3 solubility in water | slightly soluble | | insoluble dynamic viscosity | 1.1×10^-5 Pa s (at 0 °C) | 8.9×10^-6 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 20.2 °C) odor | | odorless |