Input interpretation
Mg (magnesium) + Fe_2O_3 (iron(III) oxide) ⟶ Fe (iron) + MgO (magnesium oxide)
Balanced equation
Balance the chemical equation algebraically: Mg + Fe_2O_3 ⟶ Fe + MgO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 Fe_2O_3 ⟶ c_3 Fe + c_4 MgO Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Fe and O: Mg: | c_1 = c_4 Fe: | 2 c_2 = c_3 O: | 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_2O_3 ⟶ 2 Fe + 3 MgO
Structures
+ ⟶ +
Names
magnesium + iron(III) oxide ⟶ iron + magnesium oxide
Reaction thermodynamics
Enthalpy
| magnesium | iron(III) oxide | iron | magnesium oxide molecular enthalpy | 0 kJ/mol | -826 kJ/mol | 0 kJ/mol | -601.6 kJ/mol total enthalpy | 0 kJ/mol | -826 kJ/mol | 0 kJ/mol | -1805 kJ/mol | H_initial = -826 kJ/mol | | H_final = -1805 kJ/mol | ΔH_rxn^0 | -1805 kJ/mol - -826 kJ/mol = -978.8 kJ/mol (exothermic) | | |
Entropy
| magnesium | iron(III) oxide | iron | magnesium oxide molecular entropy | 33 J/(mol K) | 90 J/(mol K) | 27 J/(mol K) | 27 J/(mol K) total entropy | 99 J/(mol K) | 90 J/(mol K) | 54 J/(mol K) | 81 J/(mol K) | S_initial = 189 J/(mol K) | | S_final = 135 J/(mol K) | ΔS_rxn^0 | 135 J/(mol K) - 189 J/(mol K) = -54 J/(mol K) (exoentropic) | | |
Equilibrium constant
![K_c = ([Fe]^2 [MgO]^3)/([Mg]^3 [Fe2O3])](../image_source/5a194564514bc62f575afeab55cf805f.png)
K_c = ([Fe]^2 [MgO]^3)/([Mg]^3 [Fe2O3])
Rate of reaction
![rate = -1/3 (Δ[Mg])/(Δt) = -(Δ[Fe2O3])/(Δt) = 1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[MgO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/f6628a5cf28a9e8b3faf5bcf43e06e5b.png)
rate = -1/3 (Δ[Mg])/(Δt) = -(Δ[Fe2O3])/(Δt) = 1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[MgO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| magnesium | iron(III) oxide | iron | magnesium oxide formula | Mg | Fe_2O_3 | Fe | MgO name | magnesium | iron(III) oxide | iron | magnesium oxide IUPAC name | magnesium | | iron | oxomagnesium
Substance properties
| magnesium | iron(III) oxide | iron | magnesium oxide molar mass | 24.305 g/mol | 159.69 g/mol | 55.845 g/mol | 40.304 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 648 °C | 1565 °C | 1535 °C | 2852 °C boiling point | 1090 °C | | 2750 °C | 3600 °C density | 1.738 g/cm^3 | 5.26 g/cm^3 | 7.874 g/cm^3 | 3.58 g/cm^3 solubility in water | reacts | insoluble | insoluble | odor | | odorless | | odorless
Units
