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Al + Cu(SO4) = Cu + Al2(SO4)3

Input interpretation

Al aluminum + CuSO_4 copper(II) sulfate ⟶ 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

Balanced equation

Balance the chemical equation algebraically: Al + CuSO_4 ⟶ Cu + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 CuSO_4 ⟶ c_3 Cu + c_4 Al_2(SO_4)_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 = 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + 3 CuSO_4 ⟶ 3 Cu + Al_2(SO_4)_3
Balance the chemical equation algebraically: Al + CuSO_4 ⟶ Cu + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 CuSO_4 ⟶ c_3 Cu + c_4 Al_2(SO_4)_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 = 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + 3 CuSO_4 ⟶ 3 Cu + Al_2(SO_4)_3

Structures

+ ⟶ +
+ ⟶ +

Names

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

Equilibrium constant

Construct the equilibrium constant, K, expression for: Al + CuSO_4 ⟶ Cu + Al_2(SO_4)_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 CuSO_4 ⟶ 3 Cu + Al_2(SO_4)_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 CuSO_4 | 3 | -3 Cu | 3 | 3 Al_2(SO_4)_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 | 2 | -2 | ([Al])^(-2) CuSO_4 | 3 | -3 | ([CuSO4])^(-3) Cu | 3 | 3 | ([Cu])^3 Al_2(SO_4)_3 | 1 | 1 | [Al2(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])^(-2) ([CuSO4])^(-3) ([Cu])^3 [Al2(SO4)3] = (([Cu])^3 [Al2(SO4)3])/(([Al])^2 ([CuSO4])^3)
Construct the equilibrium constant, K, expression for: Al + CuSO_4 ⟶ Cu + Al_2(SO_4)_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 CuSO_4 ⟶ 3 Cu + Al_2(SO_4)_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 CuSO_4 | 3 | -3 Cu | 3 | 3 Al_2(SO_4)_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 | 2 | -2 | ([Al])^(-2) CuSO_4 | 3 | -3 | ([CuSO4])^(-3) Cu | 3 | 3 | ([Cu])^3 Al_2(SO_4)_3 | 1 | 1 | [Al2(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])^(-2) ([CuSO4])^(-3) ([Cu])^3 [Al2(SO4)3] = (([Cu])^3 [Al2(SO4)3])/(([Al])^2 ([CuSO4])^3)

Rate of reaction

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

Chemical names and formulas

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

Substance properties

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

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