KOH + AlBr3 = KBr + Al(OH)3

KOH potassium hydroxide + AlBr_3 aluminum tribromide ⟶ KBr potassium bromide + Al(OH)_3 aluminum hydroxide

Balance the chemical equation algebraically: KOH + AlBr_3 ⟶ KBr + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 AlBr_3 ⟶ c_3 KBr + c_4 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Al and Br: H: | c_1 = 3 c_4 K: | c_1 = c_3 O: | c_1 = 3 c_4 Al: | c_2 = c_4 Br: | 3 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 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 KOH + AlBr_3 ⟶ 3 KBr + Al(OH)_3

+ ⟶ +

potassium hydroxide + aluminum tribromide ⟶ potassium bromide + aluminum hydroxide

Construct the equilibrium constant, K, expression for: KOH + AlBr_3 ⟶ KBr + Al(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: 3 KOH + AlBr_3 ⟶ 3 KBr + Al(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 | 3 | -3 AlBr_3 | 1 | -1 KBr | 3 | 3 Al(OH)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 3 | -3 | ([KOH])^(-3) AlBr_3 | 1 | -1 | ([AlBr3])^(-1) KBr | 3 | 3 | ([KBr])^3 Al(OH)_3 | 1 | 1 | [Al(OH)3] 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])^(-3) ([AlBr3])^(-1) ([KBr])^3 [Al(OH)3] = (([KBr])^3 [Al(OH)3])/(([KOH])^3 [AlBr3])

Construct the rate of reaction expression for: KOH + AlBr_3 ⟶ KBr + Al(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: 3 KOH + AlBr_3 ⟶ 3 KBr + Al(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 | 3 | -3 AlBr_3 | 1 | -1 KBr | 3 | 3 Al(OH)_3 | 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 KOH | 3 | -3 | -1/3 (Δ[KOH])/(Δt) AlBr_3 | 1 | -1 | -(Δ[AlBr3])/(Δt) KBr | 3 | 3 | 1/3 (Δ[KBr])/(Δt) Al(OH)_3 | 1 | 1 | (Δ[Al(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 = -1/3 (Δ[KOH])/(Δt) = -(Δ[AlBr3])/(Δt) = 1/3 (Δ[KBr])/(Δt) = (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | aluminum tribromide | potassium bromide | aluminum hydroxide formula | KOH | AlBr_3 | KBr | Al(OH)_3 Hill formula | HKO | AlBr_3 | BrK | AlH_3O_3 name | potassium hydroxide | aluminum tribromide | potassium bromide | aluminum hydroxide IUPAC name | potassium hydroxide | tribromoalumane | potassium bromide | aluminum hydroxide

| potassium hydroxide | aluminum tribromide | potassium bromide | aluminum hydroxide molar mass | 56.105 g/mol | 266.69 g/mol | 119 g/mol | 78.003 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 406 °C | 96 °C | 734 °C | boiling point | 1327 °C | 265 °C | 1435 °C | density | 2.044 g/cm^3 | 3.205 g/cm^3 | 2.75 g/cm^3 | solubility in water | soluble | reacts | soluble | dynamic viscosity | 0.001 Pa s (at 550 °C) | | |