Ca3(PO4)2 + Na2(SO4) = Na3PO4 + Ca(SO4)

Input interpretation

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Ca_3(PO_4)_2 tricalcium diphosphate + Na_2SO_4 sodium sulfate ⟶ Na_3PO_4 trisodium phosphate + CaSO_4 calcium sulfate

Balanced equation

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Balance the chemical equation algebraically: Ca_3(PO_4)_2 + Na_2SO_4 ⟶ Na_3PO_4 + CaSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca_3(PO_4)_2 + c_2 Na_2SO_4 ⟶ c_3 Na_3PO_4 + c_4 CaSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, O, P, Na and S: Ca: | 3 c_1 = c_4 O: | 8 c_1 + 4 c_2 = 4 c_3 + 4 c_4 P: | 2 c_1 = c_3 Na: | 2 c_2 = 3 c_3 S: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Ca_3(PO_4)_2 + 3 Na_2SO_4 ⟶ 2 Na_3PO_4 + 3 CaSO_4

+ ⟶ +

Names

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tricalcium diphosphate + sodium sulfate ⟶ trisodium phosphate + calcium sulfate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Ca_3(PO_4)_2 + Na_2SO_4 ⟶ Na_3PO_4 + CaSO_4 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: Ca_3(PO_4)_2 + 3 Na_2SO_4 ⟶ 2 Na_3PO_4 + 3 CaSO_4 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 Ca_3(PO_4)_2 | 1 | -1 Na_2SO_4 | 3 | -3 Na_3PO_4 | 2 | 2 CaSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) Na_2SO_4 | 3 | -3 | ([Na2SO4])^(-3) Na_3PO_4 | 2 | 2 | ([Na3PO4])^2 CaSO_4 | 3 | 3 | ([CaSO4])^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 = ([Ca3(PO4)2])^(-1) ([Na2SO4])^(-3) ([Na3PO4])^2 ([CaSO4])^3 = (([Na3PO4])^2 ([CaSO4])^3)/([Ca3(PO4)2] ([Na2SO4])^3)

Rate of reaction

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Construct the rate of reaction expression for: Ca_3(PO_4)_2 + Na_2SO_4 ⟶ Na_3PO_4 + CaSO_4 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: Ca_3(PO_4)_2 + 3 Na_2SO_4 ⟶ 2 Na_3PO_4 + 3 CaSO_4 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 Ca_3(PO_4)_2 | 1 | -1 Na_2SO_4 | 3 | -3 Na_3PO_4 | 2 | 2 CaSO_4 | 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 Ca_3(PO_4)_2 | 1 | -1 | -(Δ[Ca3(PO4)2])/(Δt) Na_2SO_4 | 3 | -3 | -1/3 (Δ[Na2SO4])/(Δt) Na_3PO_4 | 2 | 2 | 1/2 (Δ[Na3PO4])/(Δt) CaSO_4 | 3 | 3 | 1/3 (Δ[CaSO4])/(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[Ca3(PO4)2])/(Δt) = -1/3 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[Na3PO4])/(Δt) = 1/3 (Δ[CaSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)