PH3 + PCl3 = HCl + P

PH_3 phosphine + PCl_3 phosphorus trichloride ⟶ HCl hydrogen chloride + P red phosphorus

Balance the chemical equation algebraically: PH_3 + PCl_3 ⟶ HCl + P Add stoichiometric coefficients, c_i, to the reactants and products: c_1 PH_3 + c_2 PCl_3 ⟶ c_3 HCl + c_4 P Set the number of atoms in the reactants equal to the number of atoms in the products for H, P and Cl: H: | 3 c_1 = c_3 P: | c_1 + c_2 = c_4 Cl: | 3 c_2 = 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 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | PH_3 + PCl_3 ⟶ 3 HCl + 2 P

+ ⟶ +

phosphine + phosphorus trichloride ⟶ hydrogen chloride + red phosphorus

Construct the equilibrium constant, K, expression for: PH_3 + PCl_3 ⟶ HCl + 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: PH_3 + PCl_3 ⟶ 3 HCl + 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 | 1 | -1 PCl_3 | 1 | -1 HCl | 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 | 1 | -1 | ([PH3])^(-1) PCl_3 | 1 | -1 | ([PCl3])^(-1) HCl | 3 | 3 | ([HCl])^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])^(-1) ([PCl3])^(-1) ([HCl])^3 ([P])^2 = (([HCl])^3 ([P])^2)/([PH3] [PCl3])

Construct the rate of reaction expression for: PH_3 + PCl_3 ⟶ HCl + 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: PH_3 + PCl_3 ⟶ 3 HCl + 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 | 1 | -1 PCl_3 | 1 | -1 HCl | 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 | 1 | -1 | -(Δ[PH3])/(Δt) PCl_3 | 1 | -1 | -(Δ[PCl3])/(Δt) HCl | 3 | 3 | 1/3 (Δ[HCl])/(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 = -(Δ[PH3])/(Δt) = -(Δ[PCl3])/(Δt) = 1/3 (Δ[HCl])/(Δt) = 1/2 (Δ[P])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| phosphine | phosphorus trichloride | hydrogen chloride | red phosphorus formula | PH_3 | PCl_3 | HCl | P Hill formula | H_3P | Cl_3P | ClH | P name | phosphine | phosphorus trichloride | hydrogen chloride | red phosphorus IUPAC name | phosphine | trichlorophosphane | hydrogen chloride | phosphorus

| phosphine | phosphorus trichloride | hydrogen chloride | red phosphorus molar mass | 33.998 g/mol | 137.3 g/mol | 36.46 g/mol | 30.973761998 g/mol phase | gas (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -132.8 °C | -112 °C | -114.17 °C | 579.2 °C boiling point | -87.5 °C | 76 °C | -85 °C | density | 0.00139 g/cm^3 (at 25 °C) | 1.574 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) | 2.16 g/cm^3 solubility in water | slightly soluble | decomposes | miscible | insoluble surface tension | | 0.0291 N/m | | dynamic viscosity | 1.1×10^-5 Pa s (at 0 °C) | 5.29×10^-4 Pa s (at 25 °C) | | 7.6×10^-4 Pa s (at 20.2 °C)