Al + Ca3(PO4)2 = Al2O3 + Ca3P2

Al aluminum + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ Al_2O_3 aluminum oxide + Ca_3P_2 calcium phosphide

Balance the chemical equation algebraically: Al + Ca_3(PO_4)_2 ⟶ Al_2O_3 + Ca_3P_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 Ca_3(PO_4)_2 ⟶ c_3 Al_2O_3 + c_4 Ca_3P_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Ca, O and P: Al: | c_1 = 2 c_3 Ca: | 3 c_2 = 3 c_4 O: | 8 c_2 = 3 c_3 P: | 2 c_2 = 2 c_4 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 = 16/3 c_2 = 1 c_3 = 8/3 c_4 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 16 c_2 = 3 c_3 = 8 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 Al + 3 Ca_3(PO_4)_2 ⟶ 8 Al_2O_3 + 3 Ca_3P_2

+ ⟶ +

aluminum + tricalcium diphosphate ⟶ aluminum oxide + calcium phosphide

Construct the equilibrium constant, K, expression for: Al + Ca_3(PO_4)_2 ⟶ Al_2O_3 + Ca_3P_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: 16 Al + 3 Ca_3(PO_4)_2 ⟶ 8 Al_2O_3 + 3 Ca_3P_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 Al | 16 | -16 Ca_3(PO_4)_2 | 3 | -3 Al_2O_3 | 8 | 8 Ca_3P_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 16 | -16 | ([Al])^(-16) Ca_3(PO_4)_2 | 3 | -3 | ([Ca3(PO4)2])^(-3) Al_2O_3 | 8 | 8 | ([Al2O3])^8 Ca_3P_2 | 3 | 3 | ([Ca3P2])^3 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 = ([Al])^(-16) ([Ca3(PO4)2])^(-3) ([Al2O3])^8 ([Ca3P2])^3 = (([Al2O3])^8 ([Ca3P2])^3)/(([Al])^16 ([Ca3(PO4)2])^3)

Construct the rate of reaction expression for: Al + Ca_3(PO_4)_2 ⟶ Al_2O_3 + Ca_3P_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: 16 Al + 3 Ca_3(PO_4)_2 ⟶ 8 Al_2O_3 + 3 Ca_3P_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 Al | 16 | -16 Ca_3(PO_4)_2 | 3 | -3 Al_2O_3 | 8 | 8 Ca_3P_2 | 3 | 3 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 | 16 | -16 | -1/16 (Δ[Al])/(Δt) Ca_3(PO_4)_2 | 3 | -3 | -1/3 (Δ[Ca3(PO4)2])/(Δt) Al_2O_3 | 8 | 8 | 1/8 (Δ[Al2O3])/(Δt) Ca_3P_2 | 3 | 3 | 1/3 (Δ[Ca3P2])/(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 = -1/16 (Δ[Al])/(Δt) = -1/3 (Δ[Ca3(PO4)2])/(Δt) = 1/8 (Δ[Al2O3])/(Δt) = 1/3 (Δ[Ca3P2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | tricalcium diphosphate | aluminum oxide | calcium phosphide formula | Al | Ca_3(PO_4)_2 | Al_2O_3 | Ca_3P_2 Hill formula | Al | Ca_3O_8P_2 | Al_2O_3 | Ca_3P_2 name | aluminum | tricalcium diphosphate | aluminum oxide | calcium phosphide IUPAC name | aluminum | tricalcium diphosphate | dialuminum;oxygen(2-) | calcium phosphanidylidenecalcium

| aluminum | tricalcium diphosphate | aluminum oxide | calcium phosphide molar mass | 26.9815385 g/mol | 310.17 g/mol | 101.96 g/mol | 182.18 g/mol phase | solid (at STP) | | solid (at STP) | liquid (at STP) melting point | 660.4 °C | | 2040 °C | 0.16 °C boiling point | 2460 °C | | | density | 2.7 g/cm^3 | 3.14 g/cm^3 | | 2.51 g/cm^3 solubility in water | insoluble | | | decomposes surface tension | 0.817 N/m | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | | odor | odorless | | odorless |