NH4OH + CoSO4 = H2SO4 + [Co(NH3)2](OH)2

NH_4OH ammonium hydroxide + CoSO_4 cobalt(II) sulfate ⟶ H_2SO_4 sulfuric acid + Co(NH3)2(OH)2

Balance the chemical equation algebraically: NH_4OH + CoSO_4 ⟶ H_2SO_4 + Co(NH3)2(OH)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4OH + c_2 CoSO_4 ⟶ c_3 H_2SO_4 + c_4 Co(NH3)2(OH)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Co and S: H: | 5 c_1 = 2 c_3 + 8 c_4 N: | c_1 = 2 c_4 O: | c_1 + 4 c_2 = 4 c_3 + 2 c_4 Co: | c_2 = c_4 S: | c_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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_4OH + CoSO_4 ⟶ H_2SO_4 + Co(NH3)2(OH)2

+ ⟶ + Co(NH3)2(OH)2

ammonium hydroxide + cobalt(II) sulfate ⟶ sulfuric acid + Co(NH3)2(OH)2

Construct the equilibrium constant, K, expression for: NH_4OH + CoSO_4 ⟶ H_2SO_4 + Co(NH3)2(OH)2 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 NH_4OH + CoSO_4 ⟶ H_2SO_4 + Co(NH3)2(OH)2 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 NH_4OH | 2 | -2 CoSO_4 | 1 | -1 H_2SO_4 | 1 | 1 Co(NH3)2(OH)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_4OH | 2 | -2 | ([NH4OH])^(-2) CoSO_4 | 1 | -1 | ([CoSO4])^(-1) H_2SO_4 | 1 | 1 | [H2SO4] Co(NH3)2(OH)2 | 1 | 1 | [Co(NH3)2(OH)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 = ([NH4OH])^(-2) ([CoSO4])^(-1) [H2SO4] [Co(NH3)2(OH)2] = ([H2SO4] [Co(NH3)2(OH)2])/(([NH4OH])^2 [CoSO4])

Construct the rate of reaction expression for: NH_4OH + CoSO_4 ⟶ H_2SO_4 + Co(NH3)2(OH)2 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 NH_4OH + CoSO_4 ⟶ H_2SO_4 + Co(NH3)2(OH)2 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 NH_4OH | 2 | -2 CoSO_4 | 1 | -1 H_2SO_4 | 1 | 1 Co(NH3)2(OH)2 | 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 NH_4OH | 2 | -2 | -1/2 (Δ[NH4OH])/(Δt) CoSO_4 | 1 | -1 | -(Δ[CoSO4])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) Co(NH3)2(OH)2 | 1 | 1 | (Δ[Co(NH3)2(OH)2])/(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[NH4OH])/(Δt) = -(Δ[CoSO4])/(Δt) = (Δ[H2SO4])/(Δt) = (Δ[Co(NH3)2(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonium hydroxide | cobalt(II) sulfate | sulfuric acid | Co(NH3)2(OH)2 formula | NH_4OH | CoSO_4 | H_2SO_4 | Co(NH3)2(OH)2 Hill formula | H_5NO | CoO_4S | H_2O_4S | H8CoN2O2 name | ammonium hydroxide | cobalt(II) sulfate | sulfuric acid | IUPAC name | ammonium hydroxide | cobalt(+2) cation sulfate | sulfuric acid |

| ammonium hydroxide | cobalt(II) sulfate | sulfuric acid | Co(NH3)2(OH)2 molar mass | 35.046 g/mol | 154.99 g/mol | 98.07 g/mol | 127.01 g/mol phase | aqueous (at STP) | | liquid (at STP) | melting point | -57.5 °C | | 10.371 °C | boiling point | 36 °C | | 279.6 °C | density | 0.9 g/cm^3 | 1.948 g/cm^3 | 1.8305 g/cm^3 | solubility in water | very soluble | | very soluble | surface tension | | | 0.0735 N/m | dynamic viscosity | | | 0.021 Pa s (at 25 °C) | odor | | | odorless |