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Mg + Fe2(SO4)3 = Fe + MgSO4

Input interpretation

Mg magnesium + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate ⟶ Fe iron + MgSO_4 magnesium sulfate
Mg magnesium + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate ⟶ Fe iron + MgSO_4 magnesium sulfate

Balanced equation

Balance the chemical equation algebraically: Mg + Fe_2(SO_4)_3·xH_2O ⟶ Fe + MgSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 Fe_2(SO_4)_3·xH_2O ⟶ c_3 Fe + c_4 MgSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Fe, O and S: Mg: | c_1 = c_4 Fe: | 2 c_2 = c_3 O: | 12 c_2 = 4 c_4 S: | 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Mg + Fe_2(SO_4)_3·xH_2O ⟶ 2 Fe + 3 MgSO_4
Balance the chemical equation algebraically: Mg + Fe_2(SO_4)_3·xH_2O ⟶ Fe + MgSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 Fe_2(SO_4)_3·xH_2O ⟶ c_3 Fe + c_4 MgSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Fe, O and S: Mg: | c_1 = c_4 Fe: | 2 c_2 = c_3 O: | 12 c_2 = 4 c_4 S: | 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Mg + Fe_2(SO_4)_3·xH_2O ⟶ 2 Fe + 3 MgSO_4

Structures

+ ⟶ +
+ ⟶ +

Names

magnesium + iron(III) sulfate hydrate ⟶ iron + magnesium sulfate
magnesium + iron(III) sulfate hydrate ⟶ iron + magnesium sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: Mg + Fe_2(SO_4)_3·xH_2O ⟶ Fe + MgSO_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: 3 Mg + Fe_2(SO_4)_3·xH_2O ⟶ 2 Fe + 3 MgSO_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 Mg | 3 | -3 Fe_2(SO_4)_3·xH_2O | 1 | -1 Fe | 2 | 2 MgSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 3 | -3 | ([Mg])^(-3) Fe_2(SO_4)_3·xH_2O | 1 | -1 | ([Fe2(SO4)3·xH2O])^(-1) Fe | 2 | 2 | ([Fe])^2 MgSO_4 | 3 | 3 | ([MgSO4])^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 = ([Mg])^(-3) ([Fe2(SO4)3·xH2O])^(-1) ([Fe])^2 ([MgSO4])^3 = (([Fe])^2 ([MgSO4])^3)/(([Mg])^3 [Fe2(SO4)3·xH2O])
Construct the equilibrium constant, K, expression for: Mg + Fe_2(SO_4)_3·xH_2O ⟶ Fe + MgSO_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: 3 Mg + Fe_2(SO_4)_3·xH_2O ⟶ 2 Fe + 3 MgSO_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 Mg | 3 | -3 Fe_2(SO_4)_3·xH_2O | 1 | -1 Fe | 2 | 2 MgSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 3 | -3 | ([Mg])^(-3) Fe_2(SO_4)_3·xH_2O | 1 | -1 | ([Fe2(SO4)3·xH2O])^(-1) Fe | 2 | 2 | ([Fe])^2 MgSO_4 | 3 | 3 | ([MgSO4])^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 = ([Mg])^(-3) ([Fe2(SO4)3·xH2O])^(-1) ([Fe])^2 ([MgSO4])^3 = (([Fe])^2 ([MgSO4])^3)/(([Mg])^3 [Fe2(SO4)3·xH2O])

Rate of reaction

Construct the rate of reaction expression for: Mg + Fe_2(SO_4)_3·xH_2O ⟶ Fe + MgSO_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: 3 Mg + Fe_2(SO_4)_3·xH_2O ⟶ 2 Fe + 3 MgSO_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 Mg | 3 | -3 Fe_2(SO_4)_3·xH_2O | 1 | -1 Fe | 2 | 2 MgSO_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 Mg | 3 | -3 | -1/3 (Δ[Mg])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | -1 | -(Δ[Fe2(SO4)3·xH2O])/(Δt) Fe | 2 | 2 | 1/2 (Δ[Fe])/(Δt) MgSO_4 | 3 | 3 | 1/3 (Δ[MgSO4])/(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[Mg])/(Δt) = -(Δ[Fe2(SO4)3·xH2O])/(Δt) = 1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[MgSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Mg + Fe_2(SO_4)_3·xH_2O ⟶ Fe + MgSO_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: 3 Mg + Fe_2(SO_4)_3·xH_2O ⟶ 2 Fe + 3 MgSO_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 Mg | 3 | -3 Fe_2(SO_4)_3·xH_2O | 1 | -1 Fe | 2 | 2 MgSO_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 Mg | 3 | -3 | -1/3 (Δ[Mg])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | -1 | -(Δ[Fe2(SO4)3·xH2O])/(Δt) Fe | 2 | 2 | 1/2 (Δ[Fe])/(Δt) MgSO_4 | 3 | 3 | 1/3 (Δ[MgSO4])/(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[Mg])/(Δt) = -(Δ[Fe2(SO4)3·xH2O])/(Δt) = 1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[MgSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| magnesium | iron(III) sulfate hydrate | iron | magnesium sulfate formula | Mg | Fe_2(SO_4)_3·xH_2O | Fe | MgSO_4 Hill formula | Mg | Fe_2O_12S_3 | Fe | MgO_4S name | magnesium | iron(III) sulfate hydrate | iron | magnesium sulfate IUPAC name | magnesium | diferric trisulfate | iron | magnesium sulfate
| magnesium | iron(III) sulfate hydrate | iron | magnesium sulfate formula | Mg | Fe_2(SO_4)_3·xH_2O | Fe | MgSO_4 Hill formula | Mg | Fe_2O_12S_3 | Fe | MgO_4S name | magnesium | iron(III) sulfate hydrate | iron | magnesium sulfate IUPAC name | magnesium | diferric trisulfate | iron | magnesium sulfate

Substance properties

| magnesium | iron(III) sulfate hydrate | iron | magnesium sulfate molar mass | 24.305 g/mol | 399.9 g/mol | 55.845 g/mol | 120.4 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 648 °C | | 1535 °C | boiling point | 1090 °C | | 2750 °C | density | 1.738 g/cm^3 | | 7.874 g/cm^3 | solubility in water | reacts | slightly soluble | insoluble | soluble
| magnesium | iron(III) sulfate hydrate | iron | magnesium sulfate molar mass | 24.305 g/mol | 399.9 g/mol | 55.845 g/mol | 120.4 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 648 °C | | 1535 °C | boiling point | 1090 °C | | 2750 °C | density | 1.738 g/cm^3 | | 7.874 g/cm^3 | solubility in water | reacts | slightly soluble | insoluble | soluble

Units

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