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Cu(NO3)2 + Al(OH)3 = Cu(OH)2 + Al(NO3)3

Input interpretation

Cu(NO_3)_2 copper(II) nitrate + Al(OH)_3 aluminum hydroxide ⟶ Cu(OH)_2 copper hydroxide + Al(NO_3)_3 aluminum nitrate
Cu(NO_3)_2 copper(II) nitrate + Al(OH)_3 aluminum hydroxide ⟶ Cu(OH)_2 copper hydroxide + Al(NO_3)_3 aluminum nitrate

Balanced equation

Balance the chemical equation algebraically: Cu(NO_3)_2 + Al(OH)_3 ⟶ Cu(OH)_2 + Al(NO_3)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu(NO_3)_2 + c_2 Al(OH)_3 ⟶ c_3 Cu(OH)_2 + c_4 Al(NO_3)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, N, O, Al and H: Cu: | c_1 = c_3 N: | 2 c_1 = 3 c_4 O: | 6 c_1 + 3 c_2 = 2 c_3 + 9 c_4 Al: | c_2 = c_4 H: | 3 c_2 = 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 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cu(NO_3)_2 + 2 Al(OH)_3 ⟶ 3 Cu(OH)_2 + 2 Al(NO_3)_3
Balance the chemical equation algebraically: Cu(NO_3)_2 + Al(OH)_3 ⟶ Cu(OH)_2 + Al(NO_3)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu(NO_3)_2 + c_2 Al(OH)_3 ⟶ c_3 Cu(OH)_2 + c_4 Al(NO_3)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, N, O, Al and H: Cu: | c_1 = c_3 N: | 2 c_1 = 3 c_4 O: | 6 c_1 + 3 c_2 = 2 c_3 + 9 c_4 Al: | c_2 = c_4 H: | 3 c_2 = 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 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cu(NO_3)_2 + 2 Al(OH)_3 ⟶ 3 Cu(OH)_2 + 2 Al(NO_3)_3

Structures

+ ⟶ +
+ ⟶ +

Names

copper(II) nitrate + aluminum hydroxide ⟶ copper hydroxide + aluminum nitrate
copper(II) nitrate + aluminum hydroxide ⟶ copper hydroxide + aluminum nitrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: Cu(NO_3)_2 + Al(OH)_3 ⟶ Cu(OH)_2 + 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: 3 Cu(NO_3)_2 + 2 Al(OH)_3 ⟶ 3 Cu(OH)_2 + 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 Cu(NO_3)_2 | 3 | -3 Al(OH)_3 | 2 | -2 Cu(OH)_2 | 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 Cu(NO_3)_2 | 3 | -3 | ([Cu(NO3)2])^(-3) Al(OH)_3 | 2 | -2 | ([Al(OH)3])^(-2) Cu(OH)_2 | 3 | 3 | ([Cu(OH)2])^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 = ([Cu(NO3)2])^(-3) ([Al(OH)3])^(-2) ([Cu(OH)2])^3 ([Al(NO3)3])^2 = (([Cu(OH)2])^3 ([Al(NO3)3])^2)/(([Cu(NO3)2])^3 ([Al(OH)3])^2)
Construct the equilibrium constant, K, expression for: Cu(NO_3)_2 + Al(OH)_3 ⟶ Cu(OH)_2 + 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: 3 Cu(NO_3)_2 + 2 Al(OH)_3 ⟶ 3 Cu(OH)_2 + 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 Cu(NO_3)_2 | 3 | -3 Al(OH)_3 | 2 | -2 Cu(OH)_2 | 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 Cu(NO_3)_2 | 3 | -3 | ([Cu(NO3)2])^(-3) Al(OH)_3 | 2 | -2 | ([Al(OH)3])^(-2) Cu(OH)_2 | 3 | 3 | ([Cu(OH)2])^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 = ([Cu(NO3)2])^(-3) ([Al(OH)3])^(-2) ([Cu(OH)2])^3 ([Al(NO3)3])^2 = (([Cu(OH)2])^3 ([Al(NO3)3])^2)/(([Cu(NO3)2])^3 ([Al(OH)3])^2)

Rate of reaction

Construct the rate of reaction expression for: Cu(NO_3)_2 + Al(OH)_3 ⟶ Cu(OH)_2 + 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: 3 Cu(NO_3)_2 + 2 Al(OH)_3 ⟶ 3 Cu(OH)_2 + 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 Cu(NO_3)_2 | 3 | -3 Al(OH)_3 | 2 | -2 Cu(OH)_2 | 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 Cu(NO_3)_2 | 3 | -3 | -1/3 (Δ[Cu(NO3)2])/(Δt) Al(OH)_3 | 2 | -2 | -1/2 (Δ[Al(OH)3])/(Δt) Cu(OH)_2 | 3 | 3 | 1/3 (Δ[Cu(OH)2])/(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 = -1/3 (Δ[Cu(NO3)2])/(Δt) = -1/2 (Δ[Al(OH)3])/(Δt) = 1/3 (Δ[Cu(OH)2])/(Δt) = 1/2 (Δ[Al(NO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Cu(NO_3)_2 + Al(OH)_3 ⟶ Cu(OH)_2 + 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: 3 Cu(NO_3)_2 + 2 Al(OH)_3 ⟶ 3 Cu(OH)_2 + 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 Cu(NO_3)_2 | 3 | -3 Al(OH)_3 | 2 | -2 Cu(OH)_2 | 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 Cu(NO_3)_2 | 3 | -3 | -1/3 (Δ[Cu(NO3)2])/(Δt) Al(OH)_3 | 2 | -2 | -1/2 (Δ[Al(OH)3])/(Δt) Cu(OH)_2 | 3 | 3 | 1/3 (Δ[Cu(OH)2])/(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 = -1/3 (Δ[Cu(NO3)2])/(Δt) = -1/2 (Δ[Al(OH)3])/(Δt) = 1/3 (Δ[Cu(OH)2])/(Δt) = 1/2 (Δ[Al(NO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| copper(II) nitrate | aluminum hydroxide | copper hydroxide | aluminum nitrate formula | Cu(NO_3)_2 | Al(OH)_3 | Cu(OH)_2 | Al(NO_3)_3 Hill formula | CuN_2O_6 | AlH_3O_3 | CuH_2O_2 | AlN_3O_9 name | copper(II) nitrate | aluminum hydroxide | copper hydroxide | aluminum nitrate IUPAC name | copper(II) nitrate | aluminum hydroxide | copper dihydroxide | aluminum(+3) cation trinitrate
| copper(II) nitrate | aluminum hydroxide | copper hydroxide | aluminum nitrate formula | Cu(NO_3)_2 | Al(OH)_3 | Cu(OH)_2 | Al(NO_3)_3 Hill formula | CuN_2O_6 | AlH_3O_3 | CuH_2O_2 | AlN_3O_9 name | copper(II) nitrate | aluminum hydroxide | copper hydroxide | aluminum nitrate IUPAC name | copper(II) nitrate | aluminum hydroxide | copper dihydroxide | aluminum(+3) cation trinitrate

Substance properties

| copper(II) nitrate | aluminum hydroxide | copper hydroxide | aluminum nitrate molar mass | 187.55 g/mol | 78.003 g/mol | 97.56 g/mol | 212.99 g/mol phase | | | | solid (at STP) melting point | | | | 72.8 °C density | | | | 1.401 g/cm^3 dynamic viscosity | | | | 0.001338 Pa s (at 22 °C)
| copper(II) nitrate | aluminum hydroxide | copper hydroxide | aluminum nitrate molar mass | 187.55 g/mol | 78.003 g/mol | 97.56 g/mol | 212.99 g/mol phase | | | | solid (at STP) melting point | | | | 72.8 °C density | | | | 1.401 g/cm^3 dynamic viscosity | | | | 0.001338 Pa s (at 22 °C)

Units

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