Br2 + PBr3 = PBr5

Br_2 bromine + PBr_3 phosphorus tribromide ⟶ PBr_5 phosphorus pentabromide

Balance the chemical equation algebraically: Br_2 + PBr_3 ⟶ PBr_5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Br_2 + c_2 PBr_3 ⟶ c_3 PBr_5 Set the number of atoms in the reactants equal to the number of atoms in the products for Br and P: Br: | 2 c_1 + 3 c_2 = 5 c_3 P: | 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Br_2 + PBr_3 ⟶ PBr_5

+ ⟶

bromine + phosphorus tribromide ⟶ phosphorus pentabromide

Construct the equilibrium constant, K, expression for: Br_2 + PBr_3 ⟶ PBr_5 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: Br_2 + PBr_3 ⟶ PBr_5 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 Br_2 | 1 | -1 PBr_3 | 1 | -1 PBr_5 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Br_2 | 1 | -1 | ([Br2])^(-1) PBr_3 | 1 | -1 | ([PBr3])^(-1) PBr_5 | 1 | 1 | [PBr5] 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 = ([Br2])^(-1) ([PBr3])^(-1) [PBr5] = ([PBr5])/([Br2] [PBr3])

Construct the rate of reaction expression for: Br_2 + PBr_3 ⟶ PBr_5 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: Br_2 + PBr_3 ⟶ PBr_5 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 Br_2 | 1 | -1 PBr_3 | 1 | -1 PBr_5 | 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 Br_2 | 1 | -1 | -(Δ[Br2])/(Δt) PBr_3 | 1 | -1 | -(Δ[PBr3])/(Δt) PBr_5 | 1 | 1 | (Δ[PBr5])/(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[Br2])/(Δt) = -(Δ[PBr3])/(Δt) = (Δ[PBr5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| bromine | phosphorus tribromide | phosphorus pentabromide formula | Br_2 | PBr_3 | PBr_5 Hill formula | Br_2 | Br_3P | Br_5P name | bromine | phosphorus tribromide | phosphorus pentabromide IUPAC name | molecular bromine | tribromophosphane | pentabromophosphorane

| bromine | phosphorus tribromide | phosphorus pentabromide molar mass | 159.81 g/mol | 270.69 g/mol | 430.49 g/mol phase | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | -7.2 °C | -41.5 °C | 100 °C boiling point | 58.8 °C | 175 °C | density | 3.119 g/cm^3 | 2.88 g/cm^3 | 3.61 g/cm^3 solubility in water | insoluble | reacts | decomposes surface tension | 0.0409 N/m | 0.0458 N/m | dynamic viscosity | 9.44×10^-4 Pa s (at 25 °C) | 0.001302 Pa s (at 60 °C) |