Mg + H3PO4 = H2 + Mg(PO4)2

Mg magnesium + H_3PO_4 phosphoric acid ⟶ H_2 hydrogen + Mg(PO4)2

Balance the chemical equation algebraically: Mg + H_3PO_4 ⟶ H_2 + Mg(PO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 H_3PO_4 ⟶ c_3 H_2 + c_4 Mg(PO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, H, O and P: Mg: | c_1 = c_4 H: | 3 c_2 = 2 c_3 O: | 4 c_2 = 8 c_4 P: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Mg + 2 H_3PO_4 ⟶ 3 H_2 + Mg(PO4)2

+ ⟶ + Mg(PO4)2

magnesium + phosphoric acid ⟶ hydrogen + Mg(PO4)2

Construct the equilibrium constant, K, expression for: Mg + H_3PO_4 ⟶ H_2 + Mg(PO4)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: Mg + 2 H_3PO_4 ⟶ 3 H_2 + Mg(PO4)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 Mg | 1 | -1 H_3PO_4 | 2 | -2 H_2 | 3 | 3 Mg(PO4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 1 | -1 | ([Mg])^(-1) H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) H_2 | 3 | 3 | ([H2])^3 Mg(PO4)2 | 1 | 1 | [Mg(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 = ([Mg])^(-1) ([H3PO4])^(-2) ([H2])^3 [Mg(PO4)2] = (([H2])^3 [Mg(PO4)2])/([Mg] ([H3PO4])^2)

Construct the rate of reaction expression for: Mg + H_3PO_4 ⟶ H_2 + Mg(PO4)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: Mg + 2 H_3PO_4 ⟶ 3 H_2 + Mg(PO4)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 Mg | 1 | -1 H_3PO_4 | 2 | -2 H_2 | 3 | 3 Mg(PO4)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 Mg | 1 | -1 | -(Δ[Mg])/(Δt) H_3PO_4 | 2 | -2 | -1/2 (Δ[H3PO4])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Mg(PO4)2 | 1 | 1 | (Δ[Mg(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 = -(Δ[Mg])/(Δt) = -1/2 (Δ[H3PO4])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[Mg(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | phosphoric acid | hydrogen | Mg(PO4)2 formula | Mg | H_3PO_4 | H_2 | Mg(PO4)2 Hill formula | Mg | H_3O_4P | H_2 | MgO8P2 name | magnesium | phosphoric acid | hydrogen | IUPAC name | magnesium | phosphoric acid | molecular hydrogen |

| magnesium | phosphoric acid | hydrogen | Mg(PO4)2 molar mass | 24.305 g/mol | 97.994 g/mol | 2.016 g/mol | 214.24 g/mol phase | solid (at STP) | liquid (at STP) | gas (at STP) | melting point | 648 °C | 42.4 °C | -259.2 °C | boiling point | 1090 °C | 158 °C | -252.8 °C | density | 1.738 g/cm^3 | 1.685 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | reacts | very soluble | | dynamic viscosity | | | 8.9×10^-6 Pa s (at 25 °C) | odor | | odorless | odorless |