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H2O + NH3 + CuSO4 = Cu(OH)2 + (NH4)2SO4

Input interpretation

H_2O water + NH_3 ammonia + CuSO_4 copper(II) sulfate ⟶ Cu(OH)_2 copper hydroxide + (NH_4)_2SO_4 ammonium sulfate
H_2O water + NH_3 ammonia + CuSO_4 copper(II) sulfate ⟶ Cu(OH)_2 copper hydroxide + (NH_4)_2SO_4 ammonium sulfate

Balanced equation

Balance the chemical equation algebraically: H_2O + NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 + c_3 CuSO_4 ⟶ c_4 Cu(OH)_2 + c_5 (NH_4)_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N, Cu and S: H: | 2 c_1 + 3 c_2 = 2 c_4 + 8 c_5 O: | c_1 + 4 c_3 = 2 c_4 + 4 c_5 N: | c_2 = 2 c_5 Cu: | c_3 = c_4 S: | c_3 = c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_4
Balance the chemical equation algebraically: H_2O + NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 + c_3 CuSO_4 ⟶ c_4 Cu(OH)_2 + c_5 (NH_4)_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N, Cu and S: H: | 2 c_1 + 3 c_2 = 2 c_4 + 8 c_5 O: | c_1 + 4 c_3 = 2 c_4 + 4 c_5 N: | c_2 = 2 c_5 Cu: | c_3 = c_4 S: | c_3 = c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_4

Structures

+ + ⟶ +
+ + ⟶ +

Names

water + ammonia + copper(II) sulfate ⟶ copper hydroxide + ammonium sulfate
water + ammonia + copper(II) sulfate ⟶ copper hydroxide + ammonium sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_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: 2 H_2O + 2 NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_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 H_2O | 2 | -2 NH_3 | 2 | -2 CuSO_4 | 1 | -1 Cu(OH)_2 | 1 | 1 (NH_4)_2SO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) NH_3 | 2 | -2 | ([NH3])^(-2) CuSO_4 | 1 | -1 | ([CuSO4])^(-1) Cu(OH)_2 | 1 | 1 | [Cu(OH)2] (NH_4)_2SO_4 | 1 | 1 | [(NH4)2SO4] 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 = ([H2O])^(-2) ([NH3])^(-2) ([CuSO4])^(-1) [Cu(OH)2] [(NH4)2SO4] = ([Cu(OH)2] [(NH4)2SO4])/(([H2O])^2 ([NH3])^2 [CuSO4])
Construct the equilibrium constant, K, expression for: H_2O + NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_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: 2 H_2O + 2 NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_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 H_2O | 2 | -2 NH_3 | 2 | -2 CuSO_4 | 1 | -1 Cu(OH)_2 | 1 | 1 (NH_4)_2SO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) NH_3 | 2 | -2 | ([NH3])^(-2) CuSO_4 | 1 | -1 | ([CuSO4])^(-1) Cu(OH)_2 | 1 | 1 | [Cu(OH)2] (NH_4)_2SO_4 | 1 | 1 | [(NH4)2SO4] 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 = ([H2O])^(-2) ([NH3])^(-2) ([CuSO4])^(-1) [Cu(OH)2] [(NH4)2SO4] = ([Cu(OH)2] [(NH4)2SO4])/(([H2O])^2 ([NH3])^2 [CuSO4])

Rate of reaction

Construct the rate of reaction expression for: H_2O + NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_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: 2 H_2O + 2 NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_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 H_2O | 2 | -2 NH_3 | 2 | -2 CuSO_4 | 1 | -1 Cu(OH)_2 | 1 | 1 (NH_4)_2SO_4 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) CuSO_4 | 1 | -1 | -(Δ[CuSO4])/(Δt) Cu(OH)_2 | 1 | 1 | (Δ[Cu(OH)2])/(Δt) (NH_4)_2SO_4 | 1 | 1 | (Δ[(NH4)2SO4])/(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[H2O])/(Δt) = -1/2 (Δ[NH3])/(Δt) = -(Δ[CuSO4])/(Δt) = (Δ[Cu(OH)2])/(Δt) = (Δ[(NH4)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_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: 2 H_2O + 2 NH_3 + CuSO_4 ⟶ Cu(OH)_2 + (NH_4)_2SO_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 H_2O | 2 | -2 NH_3 | 2 | -2 CuSO_4 | 1 | -1 Cu(OH)_2 | 1 | 1 (NH_4)_2SO_4 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) CuSO_4 | 1 | -1 | -(Δ[CuSO4])/(Δt) Cu(OH)_2 | 1 | 1 | (Δ[Cu(OH)2])/(Δt) (NH_4)_2SO_4 | 1 | 1 | (Δ[(NH4)2SO4])/(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[H2O])/(Δt) = -1/2 (Δ[NH3])/(Δt) = -(Δ[CuSO4])/(Δt) = (Δ[Cu(OH)2])/(Δt) = (Δ[(NH4)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | ammonia | copper(II) sulfate | copper hydroxide | ammonium sulfate formula | H_2O | NH_3 | CuSO_4 | Cu(OH)_2 | (NH_4)_2SO_4 Hill formula | H_2O | H_3N | CuO_4S | CuH_2O_2 | H_8N_2O_4S name | water | ammonia | copper(II) sulfate | copper hydroxide | ammonium sulfate IUPAC name | water | ammonia | copper sulfate | copper dihydroxide |
| water | ammonia | copper(II) sulfate | copper hydroxide | ammonium sulfate formula | H_2O | NH_3 | CuSO_4 | Cu(OH)_2 | (NH_4)_2SO_4 Hill formula | H_2O | H_3N | CuO_4S | CuH_2O_2 | H_8N_2O_4S name | water | ammonia | copper(II) sulfate | copper hydroxide | ammonium sulfate IUPAC name | water | ammonia | copper sulfate | copper dihydroxide |

Substance properties

| water | ammonia | copper(II) sulfate | copper hydroxide | ammonium sulfate molar mass | 18.015 g/mol | 17.031 g/mol | 159.6 g/mol | 97.56 g/mol | 132.1 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | | solid (at STP) melting point | 0 °C | -77.73 °C | 200 °C | | 280 °C boiling point | 99.9839 °C | -33.33 °C | | | density | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 3.603 g/cm^3 | | 1.77 g/cm^3 surface tension | 0.0728 N/m | 0.0234 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | | | odor | odorless | | | | odorless
| water | ammonia | copper(II) sulfate | copper hydroxide | ammonium sulfate molar mass | 18.015 g/mol | 17.031 g/mol | 159.6 g/mol | 97.56 g/mol | 132.1 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | | solid (at STP) melting point | 0 °C | -77.73 °C | 200 °C | | 280 °C boiling point | 99.9839 °C | -33.33 °C | | | density | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 3.603 g/cm^3 | | 1.77 g/cm^3 surface tension | 0.0728 N/m | 0.0234 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | | | odor | odorless | | | | odorless

Units

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