Cu + P = Cu3P2

Cu copper + P red phosphorus ⟶ Cu3P2

Balance the chemical equation algebraically: Cu + P ⟶ Cu3P2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 P ⟶ c_3 Cu3P2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu and P: Cu: | 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 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cu + 2 P ⟶ Cu3P2

+ ⟶ Cu3P2

copper + red phosphorus ⟶ Cu3P2

Construct the equilibrium constant, K, expression for: Cu + P ⟶ Cu3P2 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 Cu + 2 P ⟶ Cu3P2 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 Cu | 3 | -3 P | 2 | -2 Cu3P2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 3 | -3 | ([Cu])^(-3) P | 2 | -2 | ([P])^(-2) Cu3P2 | 1 | 1 | [Cu3P2] 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 = ([Cu])^(-3) ([P])^(-2) [Cu3P2] = ([Cu3P2])/(([Cu])^3 ([P])^2)

Construct the rate of reaction expression for: Cu + P ⟶ Cu3P2 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 Cu + 2 P ⟶ Cu3P2 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 Cu | 3 | -3 P | 2 | -2 Cu3P2 | 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 Cu | 3 | -3 | -1/3 (Δ[Cu])/(Δt) P | 2 | -2 | -1/2 (Δ[P])/(Δt) Cu3P2 | 1 | 1 | (Δ[Cu3P2])/(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[Cu])/(Δt) = -1/2 (Δ[P])/(Δt) = (Δ[Cu3P2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper | red phosphorus | Cu3P2 formula | Cu | P | Cu3P2 name | copper | red phosphorus | IUPAC name | copper | phosphorus |

| copper | red phosphorus | Cu3P2 molar mass | 63.546 g/mol | 30.973761998 g/mol | 252.59 g/mol phase | solid (at STP) | solid (at STP) | melting point | 1083 °C | 579.2 °C | boiling point | 2567 °C | | density | 8.96 g/cm^3 | 2.16 g/cm^3 | solubility in water | insoluble | insoluble | dynamic viscosity | | 7.6×10^-4 Pa s (at 20.2 °C) | odor | odorless | |