H2SO4 + Mg3(PO4)2 = H3PO4 + Mg(HSO4)2

Input interpretation

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H_2SO_4 sulfuric acid + Mg_3(PO_4)_2·5H_2O Trimagnesium diphosphate pentahydrate ⟶ H_3PO_4 phosphoric acid + Mg(HSO4)2

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + Mg_3(PO_4)_2·5H_2O ⟶ H_3PO_4 + Mg(HSO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Mg_3(PO_4)_2·5H_2O ⟶ c_3 H_3PO_4 + c_4 Mg(HSO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Mg and P: H: | 2 c_1 = 3 c_3 + 2 c_4 O: | 4 c_1 + 8 c_2 = 4 c_3 + 8 c_4 S: | c_1 = 2 c_4 Mg: | 3 c_2 = c_4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2SO_4 + Mg_3(PO_4)_2·5H_2O ⟶ 2 H_3PO_4 + 3 Mg(HSO4)2

+ ⟶ + Mg(HSO4)2

Names

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sulfuric acid + Trimagnesium diphosphate pentahydrate ⟶ phosphoric acid + Mg(HSO4)2

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + Mg_3(PO_4)_2·5H_2O ⟶ H_3PO_4 + Mg(HSO4)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: 6 H_2SO_4 + Mg_3(PO_4)_2·5H_2O ⟶ 2 H_3PO_4 + 3 Mg(HSO4)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 H_2SO_4 | 6 | -6 Mg_3(PO_4)_2·5H_2O | 1 | -1 H_3PO_4 | 2 | 2 Mg(HSO4)2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 6 | -6 | ([H2SO4])^(-6) Mg_3(PO_4)_2·5H_2O | 1 | -1 | ([Mg3(PO4)2·5H2O])^(-1) H_3PO_4 | 2 | 2 | ([H3PO4])^2 Mg(HSO4)2 | 3 | 3 | ([Mg(HSO4)2])^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 = ([H2SO4])^(-6) ([Mg3(PO4)2·5H2O])^(-1) ([H3PO4])^2 ([Mg(HSO4)2])^3 = (([H3PO4])^2 ([Mg(HSO4)2])^3)/(([H2SO4])^6 [Mg3(PO4)2·5H2O])

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + Mg_3(PO_4)_2·5H_2O ⟶ H_3PO_4 + Mg(HSO4)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: 6 H_2SO_4 + Mg_3(PO_4)_2·5H_2O ⟶ 2 H_3PO_4 + 3 Mg(HSO4)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 H_2SO_4 | 6 | -6 Mg_3(PO_4)_2·5H_2O | 1 | -1 H_3PO_4 | 2 | 2 Mg(HSO4)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 H_2SO_4 | 6 | -6 | -1/6 (Δ[H2SO4])/(Δt) Mg_3(PO_4)_2·5H_2O | 1 | -1 | -(Δ[Mg3(PO4)2·5H2O])/(Δt) H_3PO_4 | 2 | 2 | 1/2 (Δ[H3PO4])/(Δt) Mg(HSO4)2 | 3 | 3 | 1/3 (Δ[Mg(HSO4)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 = -1/6 (Δ[H2SO4])/(Δt) = -(Δ[Mg3(PO4)2·5H2O])/(Δt) = 1/2 (Δ[H3PO4])/(Δt) = 1/3 (Δ[Mg(HSO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)