Al + H3PO4 = H2 + AlH2PO4

Al aluminum + H_3PO_4 phosphoric acid ⟶ H_2 hydrogen + AlH2PO4

Balance the chemical equation algebraically: Al + H_3PO_4 ⟶ H_2 + AlH2PO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 H_3PO_4 ⟶ c_3 H_2 + c_4 AlH2PO4 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, H, O and P: Al: | c_1 = c_4 H: | 3 c_2 = 2 c_3 + 2 c_4 O: | 4 c_2 = 4 c_4 P: | c_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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + 2 H_3PO_4 ⟶ H_2 + 2 AlH2PO4

+ ⟶ + AlH2PO4

aluminum + phosphoric acid ⟶ hydrogen + AlH2PO4

Construct the equilibrium constant, K, expression for: Al + H_3PO_4 ⟶ H_2 + AlH2PO4 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: 2 Al + 2 H_3PO_4 ⟶ H_2 + 2 AlH2PO4 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 | 2 | -2 H_3PO_4 | 2 | -2 H_2 | 1 | 1 AlH2PO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 2 | -2 | ([Al])^(-2) H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) H_2 | 1 | 1 | [H2] AlH2PO4 | 2 | 2 | ([AlH2PO4])^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 = ([Al])^(-2) ([H3PO4])^(-2) [H2] ([AlH2PO4])^2 = ([H2] ([AlH2PO4])^2)/(([Al])^2 ([H3PO4])^2)

Construct the rate of reaction expression for: Al + H_3PO_4 ⟶ H_2 + AlH2PO4 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: 2 Al + 2 H_3PO_4 ⟶ H_2 + 2 AlH2PO4 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 | 2 | -2 H_3PO_4 | 2 | -2 H_2 | 1 | 1 AlH2PO4 | 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 | 2 | -2 | -1/2 (Δ[Al])/(Δt) H_3PO_4 | 2 | -2 | -1/2 (Δ[H3PO4])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) AlH2PO4 | 2 | 2 | 1/2 (Δ[AlH2PO4])/(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 = -1/2 (Δ[Al])/(Δt) = -1/2 (Δ[H3PO4])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[AlH2PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | phosphoric acid | hydrogen | AlH2PO4 formula | Al | H_3PO_4 | H_2 | AlH2PO4 Hill formula | Al | H_3O_4P | H_2 | H2AlO4P name | aluminum | phosphoric acid | hydrogen | IUPAC name | aluminum | phosphoric acid | molecular hydrogen |

| aluminum | phosphoric acid | hydrogen | AlH2PO4 molar mass | 26.9815385 g/mol | 97.994 g/mol | 2.016 g/mol | 123.97 g/mol phase | solid (at STP) | liquid (at STP) | gas (at STP) | melting point | 660.4 °C | 42.4 °C | -259.2 °C | boiling point | 2460 °C | 158 °C | -252.8 °C | density | 2.7 g/cm^3 | 1.685 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | insoluble | very soluble | | surface tension | 0.817 N/m | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | odorless | odorless |