KOH + Br2 + Fe(OH)2 = KBr + Fe(OH)3

KOH potassium hydroxide + Br_2 bromine + Fe(OH)_2 iron(II) hydroxide ⟶ KBr potassium bromide + Fe(OH)_3 iron(III) hydroxide

Balance the chemical equation algebraically: KOH + Br_2 + Fe(OH)_2 ⟶ KBr + Fe(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Br_2 + c_3 Fe(OH)_2 ⟶ c_4 KBr + c_5 Fe(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Br and Fe: H: | c_1 + 2 c_3 = 3 c_5 K: | c_1 = c_4 O: | c_1 + 2 c_3 = 3 c_5 Br: | 2 c_2 = c_4 Fe: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + Br_2 + 2 Fe(OH)_2 ⟶ 2 KBr + 2 Fe(OH)_3

+ + ⟶ +

potassium hydroxide + bromine + iron(II) hydroxide ⟶ potassium bromide + iron(III) hydroxide

Construct the equilibrium constant, K, expression for: KOH + Br_2 + Fe(OH)_2 ⟶ KBr + Fe(OH)_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 KOH + Br_2 + 2 Fe(OH)_2 ⟶ 2 KBr + 2 Fe(OH)_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 KOH | 2 | -2 Br_2 | 1 | -1 Fe(OH)_2 | 2 | -2 KBr | 2 | 2 Fe(OH)_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) Br_2 | 1 | -1 | ([Br2])^(-1) Fe(OH)_2 | 2 | -2 | ([Fe(OH)2])^(-2) KBr | 2 | 2 | ([KBr])^2 Fe(OH)_3 | 2 | 2 | ([Fe(OH)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 = ([KOH])^(-2) ([Br2])^(-1) ([Fe(OH)2])^(-2) ([KBr])^2 ([Fe(OH)3])^2 = (([KBr])^2 ([Fe(OH)3])^2)/(([KOH])^2 [Br2] ([Fe(OH)2])^2)

Construct the rate of reaction expression for: KOH + Br_2 + Fe(OH)_2 ⟶ KBr + Fe(OH)_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 KOH + Br_2 + 2 Fe(OH)_2 ⟶ 2 KBr + 2 Fe(OH)_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 KOH | 2 | -2 Br_2 | 1 | -1 Fe(OH)_2 | 2 | -2 KBr | 2 | 2 Fe(OH)_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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) Br_2 | 1 | -1 | -(Δ[Br2])/(Δt) Fe(OH)_2 | 2 | -2 | -1/2 (Δ[Fe(OH)2])/(Δt) KBr | 2 | 2 | 1/2 (Δ[KBr])/(Δt) Fe(OH)_3 | 2 | 2 | 1/2 (Δ[Fe(OH)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[KOH])/(Δt) = -(Δ[Br2])/(Δt) = -1/2 (Δ[Fe(OH)2])/(Δt) = 1/2 (Δ[KBr])/(Δt) = 1/2 (Δ[Fe(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | bromine | iron(II) hydroxide | potassium bromide | iron(III) hydroxide formula | KOH | Br_2 | Fe(OH)_2 | KBr | Fe(OH)_3 Hill formula | HKO | Br_2 | FeH_2O_2 | BrK | FeH_3O_3 name | potassium hydroxide | bromine | iron(II) hydroxide | potassium bromide | iron(III) hydroxide IUPAC name | potassium hydroxide | molecular bromine | ferrous dihydroxide | potassium bromide | ferric trihydroxide

| potassium hydroxide | bromine | iron(II) hydroxide | potassium bromide | iron(III) hydroxide molar mass | 56.105 g/mol | 159.81 g/mol | 89.86 g/mol | 119 g/mol | 106.87 g/mol phase | solid (at STP) | liquid (at STP) | | solid (at STP) | melting point | 406 °C | -7.2 °C | | 734 °C | boiling point | 1327 °C | 58.8 °C | | 1435 °C | density | 2.044 g/cm^3 | 3.119 g/cm^3 | | 2.75 g/cm^3 | solubility in water | soluble | insoluble | | soluble | surface tension | | 0.0409 N/m | | | dynamic viscosity | 0.001 Pa s (at 550 °C) | 9.44×10^-4 Pa s (at 25 °C) | | |