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MgSO4 + Na3PO4 = Na2SO4 + Mg3(PO4)2

Input interpretation

MgSO_4 magnesium sulfate + Na_3PO_4 trisodium phosphate ⟶ Na_2SO_4 sodium sulfate + Mg_3(PO_4)_2·5H_2O Trimagnesium diphosphate pentahydrate
MgSO_4 magnesium sulfate + Na_3PO_4 trisodium phosphate ⟶ Na_2SO_4 sodium sulfate + Mg_3(PO_4)_2·5H_2O Trimagnesium diphosphate pentahydrate

Balanced equation

Balance the chemical equation algebraically: MgSO_4 + Na_3PO_4 ⟶ Na_2SO_4 + Mg_3(PO_4)_2·5H_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MgSO_4 + c_2 Na_3PO_4 ⟶ c_3 Na_2SO_4 + c_4 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, S, Na and P: Mg: | c_1 = 3 c_4 O: | 4 c_1 + 4 c_2 = 4 c_3 + 8 c_4 S: | c_1 = c_3 Na: | 3 c_2 = 2 c_3 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 MgSO_4 + 2 Na_3PO_4 ⟶ 3 Na_2SO_4 + Mg_3(PO_4)_2·5H_2O
Balance the chemical equation algebraically: MgSO_4 + Na_3PO_4 ⟶ Na_2SO_4 + Mg_3(PO_4)_2·5H_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MgSO_4 + c_2 Na_3PO_4 ⟶ c_3 Na_2SO_4 + c_4 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, S, Na and P: Mg: | c_1 = 3 c_4 O: | 4 c_1 + 4 c_2 = 4 c_3 + 8 c_4 S: | c_1 = c_3 Na: | 3 c_2 = 2 c_3 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 MgSO_4 + 2 Na_3PO_4 ⟶ 3 Na_2SO_4 + Mg_3(PO_4)_2·5H_2O

Structures

+ ⟶ +
+ ⟶ +

Names

magnesium sulfate + trisodium phosphate ⟶ sodium sulfate + Trimagnesium diphosphate pentahydrate
magnesium sulfate + trisodium phosphate ⟶ sodium sulfate + Trimagnesium diphosphate pentahydrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: MgSO_4 + Na_3PO_4 ⟶ Na_2SO_4 + 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 MgSO_4 + 2 Na_3PO_4 ⟶ 3 Na_2SO_4 + 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 MgSO_4 | 3 | -3 Na_3PO_4 | 2 | -2 Na_2SO_4 | 3 | 3 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 MgSO_4 | 3 | -3 | ([MgSO4])^(-3) Na_3PO_4 | 2 | -2 | ([Na3PO4])^(-2) Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 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 = ([MgSO4])^(-3) ([Na3PO4])^(-2) ([Na2SO4])^3 [Mg3(PO4)2·5H2O] = (([Na2SO4])^3 [Mg3(PO4)2·5H2O])/(([MgSO4])^3 ([Na3PO4])^2)
Construct the equilibrium constant, K, expression for: MgSO_4 + Na_3PO_4 ⟶ Na_2SO_4 + 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 MgSO_4 + 2 Na_3PO_4 ⟶ 3 Na_2SO_4 + 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 MgSO_4 | 3 | -3 Na_3PO_4 | 2 | -2 Na_2SO_4 | 3 | 3 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 MgSO_4 | 3 | -3 | ([MgSO4])^(-3) Na_3PO_4 | 2 | -2 | ([Na3PO4])^(-2) Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 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 = ([MgSO4])^(-3) ([Na3PO4])^(-2) ([Na2SO4])^3 [Mg3(PO4)2·5H2O] = (([Na2SO4])^3 [Mg3(PO4)2·5H2O])/(([MgSO4])^3 ([Na3PO4])^2)

Rate of reaction

Construct the rate of reaction expression for: MgSO_4 + Na_3PO_4 ⟶ Na_2SO_4 + 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 MgSO_4 + 2 Na_3PO_4 ⟶ 3 Na_2SO_4 + 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 MgSO_4 | 3 | -3 Na_3PO_4 | 2 | -2 Na_2SO_4 | 3 | 3 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 MgSO_4 | 3 | -3 | -1/3 (Δ[MgSO4])/(Δt) Na_3PO_4 | 2 | -2 | -1/2 (Δ[Na3PO4])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(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[MgSO4])/(Δt) = -1/2 (Δ[Na3PO4])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = (Δ[Mg3(PO4)2·5H2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: MgSO_4 + Na_3PO_4 ⟶ Na_2SO_4 + 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 MgSO_4 + 2 Na_3PO_4 ⟶ 3 Na_2SO_4 + 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 MgSO_4 | 3 | -3 Na_3PO_4 | 2 | -2 Na_2SO_4 | 3 | 3 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 MgSO_4 | 3 | -3 | -1/3 (Δ[MgSO4])/(Δt) Na_3PO_4 | 2 | -2 | -1/2 (Δ[Na3PO4])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(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[MgSO4])/(Δt) = -1/2 (Δ[Na3PO4])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = (Δ[Mg3(PO4)2·5H2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| magnesium sulfate | trisodium phosphate | sodium sulfate | Trimagnesium diphosphate pentahydrate formula | MgSO_4 | Na_3PO_4 | Na_2SO_4 | Mg_3(PO_4)_2·5H_2O Hill formula | MgO_4S | Na_3O_4P | Na_2O_4S | Mg_3O_8P_2 name | magnesium sulfate | trisodium phosphate | sodium sulfate | Trimagnesium diphosphate pentahydrate IUPAC name | magnesium sulfate | trisodium phosphate | disodium sulfate | trimagnesium diphosphate
| magnesium sulfate | trisodium phosphate | sodium sulfate | Trimagnesium diphosphate pentahydrate formula | MgSO_4 | Na_3PO_4 | Na_2SO_4 | Mg_3(PO_4)_2·5H_2O Hill formula | MgO_4S | Na_3O_4P | Na_2O_4S | Mg_3O_8P_2 name | magnesium sulfate | trisodium phosphate | sodium sulfate | Trimagnesium diphosphate pentahydrate IUPAC name | magnesium sulfate | trisodium phosphate | disodium sulfate | trimagnesium diphosphate

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