Al + ZnBr2 = Zn + Al2Br

Al aluminum + ZnBr_2 zinc bromide ⟶ Zn zinc + Al2Br

Balance the chemical equation algebraically: Al + ZnBr_2 ⟶ Zn + Al2Br Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 ZnBr_2 ⟶ c_3 Zn + c_4 Al2Br Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Br and Zn: Al: | c_1 = 2 c_4 Br: | 2 c_2 = c_4 Zn: | c_2 = c_3 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 = 4 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Al + ZnBr_2 ⟶ Zn + 2 Al2Br

+ ⟶ + Al2Br

aluminum + zinc bromide ⟶ zinc + Al2Br

Construct the equilibrium constant, K, expression for: Al + ZnBr_2 ⟶ Zn + Al2Br 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: 4 Al + ZnBr_2 ⟶ Zn + 2 Al2Br 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 | 4 | -4 ZnBr_2 | 1 | -1 Zn | 1 | 1 Al2Br | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 4 | -4 | ([Al])^(-4) ZnBr_2 | 1 | -1 | ([ZnBr2])^(-1) Zn | 1 | 1 | [Zn] Al2Br | 2 | 2 | ([Al2Br])^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])^(-4) ([ZnBr2])^(-1) [Zn] ([Al2Br])^2 = ([Zn] ([Al2Br])^2)/(([Al])^4 [ZnBr2])

Construct the rate of reaction expression for: Al + ZnBr_2 ⟶ Zn + Al2Br 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: 4 Al + ZnBr_2 ⟶ Zn + 2 Al2Br 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 | 4 | -4 ZnBr_2 | 1 | -1 Zn | 1 | 1 Al2Br | 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 | 4 | -4 | -1/4 (Δ[Al])/(Δt) ZnBr_2 | 1 | -1 | -(Δ[ZnBr2])/(Δt) Zn | 1 | 1 | (Δ[Zn])/(Δt) Al2Br | 2 | 2 | 1/2 (Δ[Al2Br])/(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 = -1/4 (Δ[Al])/(Δt) = -(Δ[ZnBr2])/(Δt) = (Δ[Zn])/(Δt) = 1/2 (Δ[Al2Br])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | zinc bromide | zinc | Al2Br formula | Al | ZnBr_2 | Zn | Al2Br Hill formula | Al | Br_2Zn | Zn | Al2Br name | aluminum | zinc bromide | zinc | IUPAC name | aluminum | dibromozinc | zinc |

| aluminum | zinc bromide | zinc | Al2Br molar mass | 26.9815385 g/mol | 225.2 g/mol | 65.38 g/mol | 133.87 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 660.4 °C | 394 °C | 420 °C | boiling point | 2460 °C | 675 °C | 907 °C | density | 2.7 g/cm^3 | 4.22 g/cm^3 | 7.14 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) | | | odor | odorless | | odorless |