Cl2 + P = P2Cl3

Cl_2 chlorine + P red phosphorus ⟶ P2Cl3

Balance the chemical equation algebraically: Cl_2 + P ⟶ P2Cl3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 P ⟶ c_3 P2Cl3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl and P: Cl: | 2 c_1 = 3 c_3 P: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 2 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 4 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cl_2 + 4 P ⟶ 2 P2Cl3

+ ⟶ P2Cl3

chlorine + red phosphorus ⟶ P2Cl3

Construct the equilibrium constant, K, expression for: Cl_2 + P ⟶ P2Cl3 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: 3 Cl_2 + 4 P ⟶ 2 P2Cl3 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 Cl_2 | 3 | -3 P | 4 | -4 P2Cl3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 3 | -3 | ([Cl2])^(-3) P | 4 | -4 | ([P])^(-4) P2Cl3 | 2 | 2 | ([P2Cl3])^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 = ([Cl2])^(-3) ([P])^(-4) ([P2Cl3])^2 = ([P2Cl3])^2/(([Cl2])^3 ([P])^4)

Construct the rate of reaction expression for: Cl_2 + P ⟶ P2Cl3 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: 3 Cl_2 + 4 P ⟶ 2 P2Cl3 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 Cl_2 | 3 | -3 P | 4 | -4 P2Cl3 | 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 Cl_2 | 3 | -3 | -1/3 (Δ[Cl2])/(Δt) P | 4 | -4 | -1/4 (Δ[P])/(Δt) P2Cl3 | 2 | 2 | 1/2 (Δ[P2Cl3])/(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 = -1/3 (Δ[Cl2])/(Δt) = -1/4 (Δ[P])/(Δt) = 1/2 (Δ[P2Cl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | red phosphorus | P2Cl3 formula | Cl_2 | P | P2Cl3 Hill formula | Cl_2 | P | Cl3P2 name | chlorine | red phosphorus | IUPAC name | molecular chlorine | phosphorus |

| chlorine | red phosphorus | P2Cl3 molar mass | 70.9 g/mol | 30.973761998 g/mol | 168.3 g/mol phase | gas (at STP) | solid (at STP) | melting point | -101 °C | 579.2 °C | boiling point | -34 °C | | density | 0.003214 g/cm^3 (at 0 °C) | 2.16 g/cm^3 | solubility in water | | insoluble | dynamic viscosity | | 7.6×10^-4 Pa s (at 20.2 °C) |