P2O5 + PCl5 = POCl3

P2O5 + PCl_5 phosphorus pentachloride ⟶ POCl_3 phosphoryl chloride

Balance the chemical equation algebraically: P2O5 + PCl_5 ⟶ POCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 P2O5 + c_2 PCl_5 ⟶ c_3 POCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for P, O and Cl: P: | 2 c_1 + c_2 = c_3 O: | 5 c_1 = 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 c_3 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | P2O5 + 3 PCl_5 ⟶ 5 POCl_3

P2O5 + ⟶

P2O5 + phosphorus pentachloride ⟶ phosphoryl chloride

Construct the equilibrium constant, K, expression for: P2O5 + PCl_5 ⟶ POCl_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: P2O5 + 3 PCl_5 ⟶ 5 POCl_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 P2O5 | 1 | -1 PCl_5 | 3 | -3 POCl_3 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression P2O5 | 1 | -1 | ([P2O5])^(-1) PCl_5 | 3 | -3 | ([PCl5])^(-3) POCl_3 | 5 | 5 | ([POCl3])^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 = ([P2O5])^(-1) ([PCl5])^(-3) ([POCl3])^5 = ([POCl3])^5/([P2O5] ([PCl5])^3)

Construct the rate of reaction expression for: P2O5 + PCl_5 ⟶ POCl_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: P2O5 + 3 PCl_5 ⟶ 5 POCl_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 P2O5 | 1 | -1 PCl_5 | 3 | -3 POCl_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 P2O5 | 1 | -1 | -(Δ[P2O5])/(Δt) PCl_5 | 3 | -3 | -1/3 (Δ[PCl5])/(Δt) POCl_3 | 5 | 5 | 1/5 (Δ[POCl3])/(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[P2O5])/(Δt) = -1/3 (Δ[PCl5])/(Δt) = 1/5 (Δ[POCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| P2O5 | phosphorus pentachloride | phosphoryl chloride formula | P2O5 | PCl_5 | POCl_3 Hill formula | O5P2 | Cl_5P | Cl_3OP name | | phosphorus pentachloride | phosphoryl chloride IUPAC name | | pentachlorophosphorane |

| P2O5 | phosphorus pentachloride | phosphoryl chloride molar mass | 141.94 g/mol | 208.2 g/mol | 153.3 g/mol phase | | solid (at STP) | liquid (at STP) melting point | | 148 °C | 1.25 °C boiling point | | | 105.8 °C density | | 3.6 g/cm^3 | 1.645 g/cm^3 solubility in water | | reacts | reacts