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Cu + Al2(SO4)3 = Al + CuSO4

Input interpretation

Cu copper + Al_2(SO_4)_3 aluminum sulfate ⟶ Al aluminum + CuSO_4 copper(II) sulfate
Cu copper + Al_2(SO_4)_3 aluminum sulfate ⟶ Al aluminum + CuSO_4 copper(II) sulfate

Balanced equation

Balance the chemical equation algebraically: Cu + Al_2(SO_4)_3 ⟶ Al + CuSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 Al_2(SO_4)_3 ⟶ c_3 Al + c_4 CuSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, Al, O and S: Cu: | c_1 = c_4 Al: | 2 c_2 = c_3 O: | 12 c_2 = 4 c_4 S: | 3 c_2 = 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 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: |   | 3 Cu + Al_2(SO_4)_3 ⟶ 2 Al + 3 CuSO_4
Balance the chemical equation algebraically: Cu + Al_2(SO_4)_3 ⟶ Al + CuSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 Al_2(SO_4)_3 ⟶ c_3 Al + c_4 CuSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, Al, O and S: Cu: | c_1 = c_4 Al: | 2 c_2 = c_3 O: | 12 c_2 = 4 c_4 S: | 3 c_2 = 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 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cu + Al_2(SO_4)_3 ⟶ 2 Al + 3 CuSO_4

Structures

 + ⟶ +
+ ⟶ +

Names

copper + aluminum sulfate ⟶ aluminum + copper(II) sulfate
copper + aluminum sulfate ⟶ aluminum + copper(II) sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: Cu + Al_2(SO_4)_3 ⟶ Al + CuSO_4 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 Cu + Al_2(SO_4)_3 ⟶ 2 Al + 3 CuSO_4 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 Cu | 3 | -3 Al_2(SO_4)_3 | 1 | -1 Al | 2 | 2 CuSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 3 | -3 | ([Cu])^(-3) Al_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) Al | 2 | 2 | ([Al])^2 CuSO_4 | 3 | 3 | ([CuSO4])^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 = ([Cu])^(-3) ([Al2(SO4)3])^(-1) ([Al])^2 ([CuSO4])^3 = (([Al])^2 ([CuSO4])^3)/(([Cu])^3 [Al2(SO4)3])
Construct the equilibrium constant, K, expression for: Cu + Al_2(SO_4)_3 ⟶ Al + CuSO_4 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 Cu + Al_2(SO_4)_3 ⟶ 2 Al + 3 CuSO_4 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 Cu | 3 | -3 Al_2(SO_4)_3 | 1 | -1 Al | 2 | 2 CuSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 3 | -3 | ([Cu])^(-3) Al_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) Al | 2 | 2 | ([Al])^2 CuSO_4 | 3 | 3 | ([CuSO4])^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 = ([Cu])^(-3) ([Al2(SO4)3])^(-1) ([Al])^2 ([CuSO4])^3 = (([Al])^2 ([CuSO4])^3)/(([Cu])^3 [Al2(SO4)3])

Rate of reaction

Construct the rate of reaction expression for: Cu + Al_2(SO_4)_3 ⟶ Al + CuSO_4 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 Cu + Al_2(SO_4)_3 ⟶ 2 Al + 3 CuSO_4 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 Cu | 3 | -3 Al_2(SO_4)_3 | 1 | -1 Al | 2 | 2 CuSO_4 | 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 Cu | 3 | -3 | -1/3 (Δ[Cu])/(Δt) Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) Al | 2 | 2 | 1/2 (Δ[Al])/(Δt) CuSO_4 | 3 | 3 | 1/3 (Δ[CuSO4])/(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[Cu])/(Δt) = -(Δ[Al2(SO4)3])/(Δt) = 1/2 (Δ[Al])/(Δt) = 1/3 (Δ[CuSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Cu + Al_2(SO_4)_3 ⟶ Al + CuSO_4 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 Cu + Al_2(SO_4)_3 ⟶ 2 Al + 3 CuSO_4 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 Cu | 3 | -3 Al_2(SO_4)_3 | 1 | -1 Al | 2 | 2 CuSO_4 | 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 Cu | 3 | -3 | -1/3 (Δ[Cu])/(Δt) Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) Al | 2 | 2 | 1/2 (Δ[Al])/(Δt) CuSO_4 | 3 | 3 | 1/3 (Δ[CuSO4])/(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[Cu])/(Δt) = -(Δ[Al2(SO4)3])/(Δt) = 1/2 (Δ[Al])/(Δt) = 1/3 (Δ[CuSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

 | copper | aluminum sulfate | aluminum | copper(II) sulfate formula | Cu | Al_2(SO_4)_3 | Al | CuSO_4 Hill formula | Cu | Al_2O_12S_3 | Al | CuO_4S name | copper | aluminum sulfate | aluminum | copper(II) sulfate IUPAC name | copper | dialuminum trisulfate | aluminum | copper sulfate
| copper | aluminum sulfate | aluminum | copper(II) sulfate formula | Cu | Al_2(SO_4)_3 | Al | CuSO_4 Hill formula | Cu | Al_2O_12S_3 | Al | CuO_4S name | copper | aluminum sulfate | aluminum | copper(II) sulfate IUPAC name | copper | dialuminum trisulfate | aluminum | copper sulfate

Substance properties

 | copper | aluminum sulfate | aluminum | copper(II) sulfate molar mass | 63.546 g/mol | 342.1 g/mol | 26.9815385 g/mol | 159.6 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1083 °C | 770 °C | 660.4 °C | 200 °C boiling point | 2567 °C | | 2460 °C |  density | 8.96 g/cm^3 | 2.71 g/cm^3 | 2.7 g/cm^3 | 3.603 g/cm^3 solubility in water | insoluble | soluble | insoluble |  surface tension | | | 0.817 N/m |  dynamic viscosity | | | 1.5×10^-4 Pa s (at 760 °C) |  odor | odorless | | odorless |
| copper | aluminum sulfate | aluminum | copper(II) sulfate molar mass | 63.546 g/mol | 342.1 g/mol | 26.9815385 g/mol | 159.6 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1083 °C | 770 °C | 660.4 °C | 200 °C boiling point | 2567 °C | | 2460 °C | density | 8.96 g/cm^3 | 2.71 g/cm^3 | 2.7 g/cm^3 | 3.603 g/cm^3 solubility in water | insoluble | soluble | insoluble | surface tension | | | 0.817 N/m | dynamic viscosity | | | 1.5×10^-4 Pa s (at 760 °C) | odor | odorless | | odorless |

Units