NaOH + Br2 + Ni(OH)2 = NaBr + Ni(OH)3

NaOH sodium hydroxide + Br_2 bromine + Ni(OH)_2 nickel(II) hydroxide ⟶ NaBr sodium bromide + Ni(OH)3

Balance the chemical equation algebraically: NaOH + Br_2 + Ni(OH)_2 ⟶ NaBr + Ni(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Br_2 + c_3 Ni(OH)_2 ⟶ c_4 NaBr + c_5 Ni(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Br and Ni: H: | c_1 + 2 c_3 = 3 c_5 Na: | c_1 = c_4 O: | c_1 + 2 c_3 = 3 c_5 Br: | 2 c_2 = c_4 Ni: | 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 NaOH + Br_2 + 2 Ni(OH)_2 ⟶ 2 NaBr + 2 Ni(OH)3

+ + ⟶ + Ni(OH)3

sodium hydroxide + bromine + nickel(II) hydroxide ⟶ sodium bromide + Ni(OH)3

Construct the equilibrium constant, K, expression for: NaOH + Br_2 + Ni(OH)_2 ⟶ NaBr + Ni(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 NaOH + Br_2 + 2 Ni(OH)_2 ⟶ 2 NaBr + 2 Ni(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 NaOH | 2 | -2 Br_2 | 1 | -1 Ni(OH)_2 | 2 | -2 NaBr | 2 | 2 Ni(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 NaOH | 2 | -2 | ([NaOH])^(-2) Br_2 | 1 | -1 | ([Br2])^(-1) Ni(OH)_2 | 2 | -2 | ([Ni(OH)2])^(-2) NaBr | 2 | 2 | ([NaBr])^2 Ni(OH)3 | 2 | 2 | ([Ni(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 = ([NaOH])^(-2) ([Br2])^(-1) ([Ni(OH)2])^(-2) ([NaBr])^2 ([Ni(OH)3])^2 = (([NaBr])^2 ([Ni(OH)3])^2)/(([NaOH])^2 [Br2] ([Ni(OH)2])^2)

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

| sodium hydroxide | bromine | nickel(II) hydroxide | sodium bromide | Ni(OH)3 formula | NaOH | Br_2 | Ni(OH)_2 | NaBr | Ni(OH)3 Hill formula | HNaO | Br_2 | H_2NiO_2 | BrNa | H3NiO3 name | sodium hydroxide | bromine | nickel(II) hydroxide | sodium bromide | IUPAC name | sodium hydroxide | molecular bromine | | sodium bromide |

| sodium hydroxide | bromine | nickel(II) hydroxide | sodium bromide | Ni(OH)3 molar mass | 39.997 g/mol | 159.81 g/mol | 92.707 g/mol | 102.89 g/mol | 109.71 g/mol phase | solid (at STP) | liquid (at STP) | | solid (at STP) | melting point | 323 °C | -7.2 °C | | 755 °C | boiling point | 1390 °C | 58.8 °C | | 1396 °C | density | 2.13 g/cm^3 | 3.119 g/cm^3 | | 3.2 g/cm^3 | solubility in water | soluble | insoluble | | soluble | surface tension | 0.07435 N/m | 0.0409 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | 9.44×10^-4 Pa s (at 25 °C) | | |