Zn + Fe(NO3)3 = Fe + Zn(NO3)2

Zn zinc + Fe(NO_3)_3 ferric nitrate ⟶ Fe iron + Zn(NO3)2

Balance the chemical equation algebraically: Zn + Fe(NO_3)_3 ⟶ Fe + Zn(NO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Zn + c_2 Fe(NO_3)_3 ⟶ c_3 Fe + c_4 Zn(NO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Zn, Fe, N and O: Zn: | c_1 = c_4 Fe: | c_2 = c_3 N: | 3 c_2 = 2 c_4 O: | 9 c_2 = 6 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 = 3/2 c_2 = 1 c_3 = 1 c_4 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Zn + 2 Fe(NO_3)_3 ⟶ 2 Fe + 3 Zn(NO3)2

+ ⟶ + Zn(NO3)2

zinc + ferric nitrate ⟶ iron + Zn(NO3)2

Construct the equilibrium constant, K, expression for: Zn + Fe(NO_3)_3 ⟶ Fe + Zn(NO3)2 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 Zn + 2 Fe(NO_3)_3 ⟶ 2 Fe + 3 Zn(NO3)2 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 Zn | 3 | -3 Fe(NO_3)_3 | 2 | -2 Fe | 2 | 2 Zn(NO3)2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Zn | 3 | -3 | ([Zn])^(-3) Fe(NO_3)_3 | 2 | -2 | ([Fe(NO3)3])^(-2) Fe | 2 | 2 | ([Fe])^2 Zn(NO3)2 | 3 | 3 | ([Zn(NO3)2])^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 = ([Zn])^(-3) ([Fe(NO3)3])^(-2) ([Fe])^2 ([Zn(NO3)2])^3 = (([Fe])^2 ([Zn(NO3)2])^3)/(([Zn])^3 ([Fe(NO3)3])^2)

Construct the rate of reaction expression for: Zn + Fe(NO_3)_3 ⟶ Fe + Zn(NO3)2 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 Zn + 2 Fe(NO_3)_3 ⟶ 2 Fe + 3 Zn(NO3)2 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 Zn | 3 | -3 Fe(NO_3)_3 | 2 | -2 Fe | 2 | 2 Zn(NO3)2 | 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 Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) Fe(NO_3)_3 | 2 | -2 | -1/2 (Δ[Fe(NO3)3])/(Δt) Fe | 2 | 2 | 1/2 (Δ[Fe])/(Δt) Zn(NO3)2 | 3 | 3 | 1/3 (Δ[Zn(NO3)2])/(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[Zn])/(Δt) = -1/2 (Δ[Fe(NO3)3])/(Δt) = 1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[Zn(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| zinc | ferric nitrate | iron | Zn(NO3)2 formula | Zn | Fe(NO_3)_3 | Fe | Zn(NO3)2 Hill formula | Zn | FeN_3O_9 | Fe | N2O6Zn name | zinc | ferric nitrate | iron | IUPAC name | zinc | iron(+3) cation trinitrate | iron |

| zinc | ferric nitrate | iron | Zn(NO3)2 molar mass | 65.38 g/mol | 241.86 g/mol | 55.845 g/mol | 189.4 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 420 °C | 35 °C | 1535 °C | boiling point | 907 °C | | 2750 °C | density | 7.14 g/cm^3 | 1.7 g/cm^3 | 7.874 g/cm^3 | solubility in water | insoluble | very soluble | insoluble | odor | odorless | | |