Mg + Fe(NO3)3 = Fe + Mg(NO3)3

Mg magnesium + Fe(NO_3)_3 ferric nitrate ⟶ Fe iron + Mg(NO3)3

Balance the chemical equation algebraically: Mg + Fe(NO_3)_3 ⟶ Fe + Mg(NO3)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 Fe(NO_3)_3 ⟶ c_3 Fe + c_4 Mg(NO3)3 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Fe, N and O: Mg: | c_1 = c_4 Fe: | c_2 = c_3 N: | 3 c_2 = 3 c_4 O: | 9 c_2 = 9 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Mg + Fe(NO_3)_3 ⟶ Fe + Mg(NO3)3

+ ⟶ + Mg(NO3)3

magnesium + ferric nitrate ⟶ iron + Mg(NO3)3

Construct the equilibrium constant, K, expression for: Mg + Fe(NO_3)_3 ⟶ Fe + Mg(NO3)3 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: Mg + Fe(NO_3)_3 ⟶ Fe + Mg(NO3)3 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 | 1 | -1 Fe(NO_3)_3 | 1 | -1 Fe | 1 | 1 Mg(NO3)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 1 | -1 | ([Mg])^(-1) Fe(NO_3)_3 | 1 | -1 | ([Fe(NO3)3])^(-1) Fe | 1 | 1 | [Fe] Mg(NO3)3 | 1 | 1 | [Mg(NO3)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])^(-1) ([Fe(NO3)3])^(-1) [Fe] [Mg(NO3)3] = ([Fe] [Mg(NO3)3])/([Mg] [Fe(NO3)3])

Construct the rate of reaction expression for: Mg + Fe(NO_3)_3 ⟶ Fe + Mg(NO3)3 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: Mg + Fe(NO_3)_3 ⟶ Fe + Mg(NO3)3 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 | 1 | -1 Fe(NO_3)_3 | 1 | -1 Fe | 1 | 1 Mg(NO3)3 | 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 Mg | 1 | -1 | -(Δ[Mg])/(Δt) Fe(NO_3)_3 | 1 | -1 | -(Δ[Fe(NO3)3])/(Δt) Fe | 1 | 1 | (Δ[Fe])/(Δt) Mg(NO3)3 | 1 | 1 | (Δ[Mg(NO3)3])/(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[Mg])/(Δt) = -(Δ[Fe(NO3)3])/(Δt) = (Δ[Fe])/(Δt) = (Δ[Mg(NO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | ferric nitrate | iron | Mg(NO3)3 formula | Mg | Fe(NO_3)_3 | Fe | Mg(NO3)3 Hill formula | Mg | FeN_3O_9 | Fe | MgN3O9 name | magnesium | ferric nitrate | iron | IUPAC name | magnesium | iron(+3) cation trinitrate | iron |

| magnesium | ferric nitrate | iron | Mg(NO3)3 molar mass | 24.305 g/mol | 241.86 g/mol | 55.845 g/mol | 210.32 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 648 °C | 35 °C | 1535 °C | boiling point | 1090 °C | | 2750 °C | density | 1.738 g/cm^3 | 1.7 g/cm^3 | 7.874 g/cm^3 | solubility in water | reacts | very soluble | insoluble |