MgO + P2O5 = Mg3(PO4)2

MgO magnesium oxide + P2O5 ⟶ Mg_3(PO_4)_2·5H_2O Trimagnesium diphosphate pentahydrate

Balance the chemical equation algebraically: MgO + P2O5 ⟶ Mg_3(PO_4)_2·5H_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MgO + c_2 P2O5 ⟶ c_3 Mg_3(PO_4)_2·5H_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, O and P: Mg: | 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 MgO + P2O5 ⟶ Mg_3(PO_4)_2·5H_2O

+ P2O5 ⟶

magnesium oxide + P2O5 ⟶ Trimagnesium diphosphate pentahydrate

Construct the equilibrium constant, K, expression for: MgO + P2O5 ⟶ Mg_3(PO_4)_2·5H_2O 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 MgO + P2O5 ⟶ Mg_3(PO_4)_2·5H_2O 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 MgO | 3 | -3 P2O5 | 1 | -1 Mg_3(PO_4)_2·5H_2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MgO | 3 | -3 | ([MgO])^(-3) P2O5 | 1 | -1 | ([P2O5])^(-1) Mg_3(PO_4)_2·5H_2O | 1 | 1 | [Mg3(PO4)2·5H2O] 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 = ([MgO])^(-3) ([P2O5])^(-1) [Mg3(PO4)2·5H2O] = ([Mg3(PO4)2·5H2O])/(([MgO])^3 [P2O5])

Construct the rate of reaction expression for: MgO + P2O5 ⟶ Mg_3(PO_4)_2·5H_2O 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 MgO + P2O5 ⟶ Mg_3(PO_4)_2·5H_2O 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 MgO | 3 | -3 P2O5 | 1 | -1 Mg_3(PO_4)_2·5H_2O | 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 MgO | 3 | -3 | -1/3 (Δ[MgO])/(Δt) P2O5 | 1 | -1 | -(Δ[P2O5])/(Δt) Mg_3(PO_4)_2·5H_2O | 1 | 1 | (Δ[Mg3(PO4)2·5H2O])/(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[MgO])/(Δt) = -(Δ[P2O5])/(Δt) = (Δ[Mg3(PO4)2·5H2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium oxide | P2O5 | Trimagnesium diphosphate pentahydrate formula | MgO | P2O5 | Mg_3(PO_4)_2·5H_2O Hill formula | MgO | O5P2 | Mg_3O_8P_2 name | magnesium oxide | | Trimagnesium diphosphate pentahydrate IUPAC name | oxomagnesium | | trimagnesium diphosphate

| magnesium oxide | P2O5 | Trimagnesium diphosphate pentahydrate molar mass | 40.304 g/mol | 141.94 g/mol | 262.85 g/mol phase | solid (at STP) | | solid (at STP) melting point | 2852 °C | | 1357 °C boiling point | 3600 °C | | density | 3.58 g/cm^3 | | solubility in water | | | insoluble odor | odorless | |