Al + CuSO4 = Cu + Al(SO4)3

Al aluminum + CuSO_4 copper(II) sulfate ⟶ Cu copper + Al(SO4)3

Balance the chemical equation algebraically: Al + CuSO_4 ⟶ Cu + Al(SO4)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 CuSO_4 ⟶ c_3 Cu + c_4 Al(SO4)3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Cu, O and S: Al: | c_1 = c_4 Cu: | c_2 = c_3 O: | 4 c_2 = 12 c_4 S: | c_2 = 3 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 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al + 3 CuSO_4 ⟶ 3 Cu + Al(SO4)3

+ ⟶ + Al(SO4)3

aluminum + copper(II) sulfate ⟶ copper + Al(SO4)3

Construct the equilibrium constant, K, expression for: Al + CuSO_4 ⟶ Cu + Al(SO4)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: Al + 3 CuSO_4 ⟶ 3 Cu + Al(SO4)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 | 1 | -1 CuSO_4 | 3 | -3 Cu | 3 | 3 Al(SO4)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 1 | -1 | ([Al])^(-1) CuSO_4 | 3 | -3 | ([CuSO4])^(-3) Cu | 3 | 3 | ([Cu])^3 Al(SO4)3 | 1 | 1 | [Al(SO4)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 = ([Al])^(-1) ([CuSO4])^(-3) ([Cu])^3 [Al(SO4)3] = (([Cu])^3 [Al(SO4)3])/([Al] ([CuSO4])^3)

Construct the rate of reaction expression for: Al + CuSO_4 ⟶ Cu + Al(SO4)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: Al + 3 CuSO_4 ⟶ 3 Cu + Al(SO4)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 | 1 | -1 CuSO_4 | 3 | -3 Cu | 3 | 3 Al(SO4)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 Al | 1 | -1 | -(Δ[Al])/(Δt) CuSO_4 | 3 | -3 | -1/3 (Δ[CuSO4])/(Δt) Cu | 3 | 3 | 1/3 (Δ[Cu])/(Δt) Al(SO4)3 | 1 | 1 | (Δ[Al(SO4)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[Al])/(Δt) = -1/3 (Δ[CuSO4])/(Δt) = 1/3 (Δ[Cu])/(Δt) = (Δ[Al(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | copper(II) sulfate | copper | Al(SO4)3 formula | Al | CuSO_4 | Cu | Al(SO4)3 Hill formula | Al | CuO_4S | Cu | AlO12S3 name | aluminum | copper(II) sulfate | copper | IUPAC name | aluminum | copper sulfate | copper |

| aluminum | copper(II) sulfate | copper | Al(SO4)3 molar mass | 26.9815385 g/mol | 159.6 g/mol | 63.546 g/mol | 315.1 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 660.4 °C | 200 °C | 1083 °C | boiling point | 2460 °C | | 2567 °C | density | 2.7 g/cm^3 | 3.603 g/cm^3 | 8.96 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 |