Ca(OH)2 + Br2 = H2O + CaBr2 + Ca(BrO)2

Ca(OH)_2 calcium hydroxide + Br_2 bromine ⟶ H_2O water + CaBr_2 calcium bromide + Ca(BrO)2

Balance the chemical equation algebraically: Ca(OH)_2 + Br_2 ⟶ H_2O + CaBr_2 + Ca(BrO)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca(OH)_2 + c_2 Br_2 ⟶ c_3 H_2O + c_4 CaBr_2 + c_5 Ca(BrO)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, H, O and Br: Ca: | c_1 = c_4 + c_5 H: | 2 c_1 = 2 c_3 O: | 2 c_1 = c_3 + 2 c_5 Br: | 2 c_2 = 2 c_4 + 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Ca(OH)_2 + 2 Br_2 ⟶ 2 H_2O + CaBr_2 + Ca(BrO)2

+ ⟶ + + Ca(BrO)2

calcium hydroxide + bromine ⟶ water + calcium bromide + Ca(BrO)2

Construct the equilibrium constant, K, expression for: Ca(OH)_2 + Br_2 ⟶ H_2O + CaBr_2 + Ca(BrO)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 Ca(OH)_2 + 2 Br_2 ⟶ 2 H_2O + CaBr_2 + Ca(BrO)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 Ca(OH)_2 | 2 | -2 Br_2 | 2 | -2 H_2O | 2 | 2 CaBr_2 | 1 | 1 Ca(BrO)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca(OH)_2 | 2 | -2 | ([Ca(OH)2])^(-2) Br_2 | 2 | -2 | ([Br2])^(-2) H_2O | 2 | 2 | ([H2O])^2 CaBr_2 | 1 | 1 | [CaBr2] Ca(BrO)2 | 1 | 1 | [Ca(BrO)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 = ([Ca(OH)2])^(-2) ([Br2])^(-2) ([H2O])^2 [CaBr2] [Ca(BrO)2] = (([H2O])^2 [CaBr2] [Ca(BrO)2])/(([Ca(OH)2])^2 ([Br2])^2)

Construct the rate of reaction expression for: Ca(OH)_2 + Br_2 ⟶ H_2O + CaBr_2 + Ca(BrO)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 Ca(OH)_2 + 2 Br_2 ⟶ 2 H_2O + CaBr_2 + Ca(BrO)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 Ca(OH)_2 | 2 | -2 Br_2 | 2 | -2 H_2O | 2 | 2 CaBr_2 | 1 | 1 Ca(BrO)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 Ca(OH)_2 | 2 | -2 | -1/2 (Δ[Ca(OH)2])/(Δt) Br_2 | 2 | -2 | -1/2 (Δ[Br2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CaBr_2 | 1 | 1 | (Δ[CaBr2])/(Δt) Ca(BrO)2 | 1 | 1 | (Δ[Ca(BrO)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[Ca(OH)2])/(Δt) = -1/2 (Δ[Br2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[CaBr2])/(Δt) = (Δ[Ca(BrO)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium hydroxide | bromine | water | calcium bromide | Ca(BrO)2 formula | Ca(OH)_2 | Br_2 | H_2O | CaBr_2 | Ca(BrO)2 Hill formula | CaH_2O_2 | Br_2 | H_2O | Br_2Ca | Br2CaO2 name | calcium hydroxide | bromine | water | calcium bromide | IUPAC name | calcium dihydroxide | molecular bromine | water | calcium dibromide |

| calcium hydroxide | bromine | water | calcium bromide | Ca(BrO)2 molar mass | 74.092 g/mol | 159.81 g/mol | 18.015 g/mol | 199.89 g/mol | 231.88 g/mol phase | solid (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) | melting point | 550 °C | -7.2 °C | 0 °C | 730 °C | boiling point | | 58.8 °C | 99.9839 °C | 810 °C | density | 2.24 g/cm^3 | 3.119 g/cm^3 | 1 g/cm^3 | 3.353 g/cm^3 | solubility in water | slightly soluble | insoluble | | soluble | surface tension | | 0.0409 N/m | 0.0728 N/m | | dynamic viscosity | | 9.44×10^-4 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | | odorless | |