Ca + H3BO3 = Ca(OH)2 + B2

Ca calcium + B(OH)_3 boric acid ⟶ Ca(OH)_2 calcium hydroxide + B2

Balance the chemical equation algebraically: Ca + B(OH)_3 ⟶ Ca(OH)_2 + B2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca + c_2 B(OH)_3 ⟶ c_3 Ca(OH)_2 + c_4 B2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, B, H and O: Ca: | c_1 = c_3 B: | c_2 = 2 c_4 H: | 3 c_2 = 2 c_3 O: | 3 c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Ca + 2 B(OH)_3 ⟶ 3 Ca(OH)_2 + B2

+ ⟶ + B2

calcium + boric acid ⟶ calcium hydroxide + B2

Construct the equilibrium constant, K, expression for: Ca + B(OH)_3 ⟶ Ca(OH)_2 + B2 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 Ca + 2 B(OH)_3 ⟶ 3 Ca(OH)_2 + B2 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 | 3 | -3 B(OH)_3 | 2 | -2 Ca(OH)_2 | 3 | 3 B2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca | 3 | -3 | ([Ca])^(-3) B(OH)_3 | 2 | -2 | ([B(OH)3])^(-2) Ca(OH)_2 | 3 | 3 | ([Ca(OH)2])^3 B2 | 1 | 1 | [B2] 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])^(-3) ([B(OH)3])^(-2) ([Ca(OH)2])^3 [B2] = (([Ca(OH)2])^3 [B2])/(([Ca])^3 ([B(OH)3])^2)

Construct the rate of reaction expression for: Ca + B(OH)_3 ⟶ Ca(OH)_2 + B2 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 Ca + 2 B(OH)_3 ⟶ 3 Ca(OH)_2 + B2 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 | 3 | -3 B(OH)_3 | 2 | -2 Ca(OH)_2 | 3 | 3 B2 | 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 | 3 | -3 | -1/3 (Δ[Ca])/(Δt) B(OH)_3 | 2 | -2 | -1/2 (Δ[B(OH)3])/(Δt) Ca(OH)_2 | 3 | 3 | 1/3 (Δ[Ca(OH)2])/(Δt) B2 | 1 | 1 | (Δ[B2])/(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[Ca])/(Δt) = -1/2 (Δ[B(OH)3])/(Δt) = 1/3 (Δ[Ca(OH)2])/(Δt) = (Δ[B2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium | boric acid | calcium hydroxide | B2 formula | Ca | B(OH)_3 | Ca(OH)_2 | B2 Hill formula | Ca | BH_3O_3 | CaH_2O_2 | B2 name | calcium | boric acid | calcium hydroxide | IUPAC name | calcium | boric acid | calcium dihydroxide |

| calcium | boric acid | calcium hydroxide | B2 molar mass | 40.078 g/mol | 61.83 g/mol | 74.092 g/mol | 21.62 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 850 °C | 160 °C | 550 °C | boiling point | 1484 °C | | | density | 1.54 g/cm^3 | | 2.24 g/cm^3 | solubility in water | decomposes | | slightly soluble | odor | | odorless | odorless |