NH4OH + CrSO4 = H2O + [Cr(NH3)6]SO4

NH_4OH ammonium hydroxide + CrSO4 ⟶ H_2O water + Cr(NH3)6SO4

Balance the chemical equation algebraically: NH_4OH + CrSO4 ⟶ H_2O + Cr(NH3)6SO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4OH + c_2 CrSO4 ⟶ c_3 H_2O + c_4 Cr(NH3)6SO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Cr and S: H: | 5 c_1 = 2 c_3 + 18 c_4 N: | c_1 = 6 c_4 O: | c_1 + 4 c_2 = c_3 + 4 c_4 Cr: | c_2 = c_4 S: | 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 = 6 c_2 = 1 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NH_4OH + CrSO4 ⟶ 6 H_2O + Cr(NH3)6SO4

+ CrSO4 ⟶ + Cr(NH3)6SO4

ammonium hydroxide + CrSO4 ⟶ water + Cr(NH3)6SO4

Construct the equilibrium constant, K, expression for: NH_4OH + CrSO4 ⟶ H_2O + Cr(NH3)6SO4 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: 6 NH_4OH + CrSO4 ⟶ 6 H_2O + Cr(NH3)6SO4 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 | 6 | -6 CrSO4 | 1 | -1 H_2O | 6 | 6 Cr(NH3)6SO4 | 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 | 6 | -6 | ([NH4OH])^(-6) CrSO4 | 1 | -1 | ([CrSO4])^(-1) H_2O | 6 | 6 | ([H2O])^6 Cr(NH3)6SO4 | 1 | 1 | [Cr(NH3)6SO4] 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])^(-6) ([CrSO4])^(-1) ([H2O])^6 [Cr(NH3)6SO4] = (([H2O])^6 [Cr(NH3)6SO4])/(([NH4OH])^6 [CrSO4])

Construct the rate of reaction expression for: NH_4OH + CrSO4 ⟶ H_2O + Cr(NH3)6SO4 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: 6 NH_4OH + CrSO4 ⟶ 6 H_2O + Cr(NH3)6SO4 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 | 6 | -6 CrSO4 | 1 | -1 H_2O | 6 | 6 Cr(NH3)6SO4 | 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 | 6 | -6 | -1/6 (Δ[NH4OH])/(Δt) CrSO4 | 1 | -1 | -(Δ[CrSO4])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) Cr(NH3)6SO4 | 1 | 1 | (Δ[Cr(NH3)6SO4])/(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 = -1/6 (Δ[NH4OH])/(Δt) = -(Δ[CrSO4])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[Cr(NH3)6SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonium hydroxide | CrSO4 | water | Cr(NH3)6SO4 formula | NH_4OH | CrSO4 | H_2O | Cr(NH3)6SO4 Hill formula | H_5NO | CrO4S | H_2O | H18CrN6O4S name | ammonium hydroxide | | water |

| ammonium hydroxide | CrSO4 | water | Cr(NH3)6SO4 molar mass | 35.046 g/mol | 148.05 g/mol | 18.015 g/mol | 250.24 g/mol phase | aqueous (at STP) | | liquid (at STP) | melting point | -57.5 °C | | 0 °C | boiling point | 36 °C | | 99.9839 °C | density | 0.9 g/cm^3 | | 1 g/cm^3 | solubility in water | very soluble | | | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |