Al2O3 + P2O5 = AlPO4

Al_2O_3 aluminum oxide + P2O5 ⟶ AlPO_4 aluminum phosphate

Balance the chemical equation algebraically: Al_2O_3 + P2O5 ⟶ AlPO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al_2O_3 + c_2 P2O5 ⟶ c_3 AlPO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, O and P: Al: | 2 c_1 = c_3 O: | 3 c_1 + 5 c_2 = 4 c_3 P: | 2 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 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al_2O_3 + P2O5 ⟶ 2 AlPO_4

+ P2O5 ⟶

aluminum oxide + P2O5 ⟶ aluminum phosphate

Construct the equilibrium constant, K, expression for: Al_2O_3 + P2O5 ⟶ AlPO_4 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: Al_2O_3 + P2O5 ⟶ 2 AlPO_4 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 Al_2O_3 | 1 | -1 P2O5 | 1 | -1 AlPO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) P2O5 | 1 | -1 | ([P2O5])^(-1) AlPO_4 | 2 | 2 | ([AlO4P])^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 = ([Al2O3])^(-1) ([P2O5])^(-1) ([AlO4P])^2 = ([AlO4P])^2/([Al2O3] [P2O5])

Construct the rate of reaction expression for: Al_2O_3 + P2O5 ⟶ AlPO_4 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: Al_2O_3 + P2O5 ⟶ 2 AlPO_4 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 Al_2O_3 | 1 | -1 P2O5 | 1 | -1 AlPO_4 | 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 Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) P2O5 | 1 | -1 | -(Δ[P2O5])/(Δt) AlPO_4 | 2 | 2 | 1/2 (Δ[AlO4P])/(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[Al2O3])/(Δt) = -(Δ[P2O5])/(Δt) = 1/2 (Δ[AlO4P])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum oxide | P2O5 | aluminum phosphate formula | Al_2O_3 | P2O5 | AlPO_4 Hill formula | Al_2O_3 | O5P2 | AlPO_4 name | aluminum oxide | | aluminum phosphate IUPAC name | dialuminum;oxygen(2-) | | aluminum phosphate

| aluminum oxide | P2O5 | aluminum phosphate molar mass | 101.96 g/mol | 141.94 g/mol | 121.95 g/mol phase | solid (at STP) | | solid (at STP) melting point | 2040 °C | | 1800 °C density | | | 2.56 g/cm^3 solubility in water | | | insoluble odor | odorless | |