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

Al aluminum + Zn(NO3)2 ⟶ Zn zinc + Al(NO_3)_3 aluminum nitrate

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

+ Zn(NO3)2 ⟶ +

aluminum + Zn(NO3)2 ⟶ zinc + aluminum nitrate

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

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

| aluminum | Zn(NO3)2 | zinc | aluminum nitrate formula | Al | Zn(NO3)2 | Zn | Al(NO_3)_3 Hill formula | Al | N2O6Zn | Zn | AlN_3O_9 name | aluminum | | zinc | aluminum nitrate IUPAC name | aluminum | | zinc | aluminum(+3) cation trinitrate

| aluminum | Zn(NO3)2 | zinc | aluminum nitrate molar mass | 26.9815385 g/mol | 189.4 g/mol | 65.38 g/mol | 212.99 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 660.4 °C | | 420 °C | 72.8 °C boiling point | 2460 °C | | 907 °C | density | 2.7 g/cm^3 | | 7.14 g/cm^3 | 1.401 g/cm^3 solubility in water | insoluble | | insoluble | surface tension | 0.817 N/m | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | | 0.001338 Pa s (at 22 °C) odor | odorless | | odorless |