P + PCl5 = PCl3

P red phosphorus + PCl_5 phosphorus pentachloride ⟶ PCl_3 phosphorus trichloride

Balance the chemical equation algebraically: P + PCl_5 ⟶ PCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 P + c_2 PCl_5 ⟶ c_3 PCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for P and Cl: P: | c_1 + c_2 = c_3 Cl: | 5 c_2 = 3 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 = 5/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 P + 3 PCl_5 ⟶ 5 PCl_3

+ ⟶

red phosphorus + phosphorus pentachloride ⟶ phosphorus trichloride

Construct the equilibrium constant, K, expression for: P + PCl_5 ⟶ PCl_3 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 P + 3 PCl_5 ⟶ 5 PCl_3 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 P | 2 | -2 PCl_5 | 3 | -3 PCl_3 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression P | 2 | -2 | ([P])^(-2) PCl_5 | 3 | -3 | ([PCl5])^(-3) PCl_3 | 5 | 5 | ([PCl3])^5 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 = ([P])^(-2) ([PCl5])^(-3) ([PCl3])^5 = ([PCl3])^5/(([P])^2 ([PCl5])^3)

Construct the rate of reaction expression for: P + PCl_5 ⟶ PCl_3 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 P + 3 PCl_5 ⟶ 5 PCl_3 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 P | 2 | -2 PCl_5 | 3 | -3 PCl_3 | 5 | 5 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 P | 2 | -2 | -1/2 (Δ[P])/(Δt) PCl_5 | 3 | -3 | -1/3 (Δ[PCl5])/(Δt) PCl_3 | 5 | 5 | 1/5 (Δ[PCl3])/(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[P])/(Δt) = -1/3 (Δ[PCl5])/(Δt) = 1/5 (Δ[PCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| red phosphorus | phosphorus pentachloride | phosphorus trichloride formula | P | PCl_5 | PCl_3 Hill formula | P | Cl_5P | Cl_3P name | red phosphorus | phosphorus pentachloride | phosphorus trichloride IUPAC name | phosphorus | pentachlorophosphorane | trichlorophosphane

| red phosphorus | phosphorus pentachloride | phosphorus trichloride molar mass | 30.973761998 g/mol | 208.2 g/mol | 137.3 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) melting point | 579.2 °C | 148 °C | -112 °C boiling point | | | 76 °C density | 2.16 g/cm^3 | 3.6 g/cm^3 | 1.574 g/cm^3 solubility in water | insoluble | reacts | decomposes surface tension | | | 0.0291 N/m dynamic viscosity | 7.6×10^-4 Pa s (at 20.2 °C) | | 5.29×10^-4 Pa s (at 25 °C)