CuO + P2O5 = Cu3(PO4)2

CuO cupric oxide + P2O5 ⟶ Cu_3(PO_4)_2 copper(II) phosphate

Balance the chemical equation algebraically: CuO + P2O5 ⟶ Cu_3(PO_4)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuO + c_2 P2O5 ⟶ c_3 Cu_3(PO_4)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, O and P: Cu: | c_1 = 3 c_3 O: | c_1 + 5 c_2 = 8 c_3 P: | 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CuO + P2O5 ⟶ Cu_3(PO_4)_2

+ P2O5 ⟶

cupric oxide + P2O5 ⟶ copper(II) phosphate

Construct the equilibrium constant, K, expression for: CuO + P2O5 ⟶ Cu_3(PO_4)_2 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 CuO + P2O5 ⟶ Cu_3(PO_4)_2 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 CuO | 3 | -3 P2O5 | 1 | -1 Cu_3(PO_4)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CuO | 3 | -3 | ([CuO])^(-3) P2O5 | 1 | -1 | ([P2O5])^(-1) Cu_3(PO_4)_2 | 1 | 1 | [Cu3(PO4)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 = ([CuO])^(-3) ([P2O5])^(-1) [Cu3(PO4)2] = ([Cu3(PO4)2])/(([CuO])^3 [P2O5])

Construct the rate of reaction expression for: CuO + P2O5 ⟶ Cu_3(PO_4)_2 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 CuO + P2O5 ⟶ Cu_3(PO_4)_2 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 CuO | 3 | -3 P2O5 | 1 | -1 Cu_3(PO_4)_2 | 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 CuO | 3 | -3 | -1/3 (Δ[CuO])/(Δt) P2O5 | 1 | -1 | -(Δ[P2O5])/(Δt) Cu_3(PO_4)_2 | 1 | 1 | (Δ[Cu3(PO4)2])/(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[CuO])/(Δt) = -(Δ[P2O5])/(Δt) = (Δ[Cu3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| cupric oxide | P2O5 | copper(II) phosphate formula | CuO | P2O5 | Cu_3(PO_4)_2 Hill formula | CuO | O5P2 | Cu_3O_8P_2 name | cupric oxide | | copper(II) phosphate IUPAC name | | | tricopper diphosphate

| cupric oxide | P2O5 | copper(II) phosphate molar mass | 79.545 g/mol | 141.94 g/mol | 380.58 g/mol phase | solid (at STP) | | melting point | 1326 °C | | boiling point | 2000 °C | | density | 6.315 g/cm^3 | | solubility in water | insoluble | | insoluble