H3BO3 = H2O + HBO2

B(OH)_3 boric acid ⟶ H_2O water + HBO_2 metaboric acid

Balance the chemical equation algebraically: B(OH)_3 ⟶ H_2O + HBO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 B(OH)_3 ⟶ c_2 H_2O + c_3 HBO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for B, H and O: B: | c_1 = c_3 H: | 3 c_1 = 2 c_2 + c_3 O: | 3 c_1 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | B(OH)_3 ⟶ H_2O + HBO_2

⟶ +

boric acid ⟶ water + metaboric acid

Construct the equilibrium constant, K, expression for: B(OH)_3 ⟶ H_2O + HBO_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: B(OH)_3 ⟶ H_2O + HBO_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 B(OH)_3 | 1 | -1 H_2O | 1 | 1 HBO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression B(OH)_3 | 1 | -1 | ([B(OH)3])^(-1) H_2O | 1 | 1 | [H2O] HBO_2 | 1 | 1 | [HBO2] 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 = ([B(OH)3])^(-1) [H2O] [HBO2] = ([H2O] [HBO2])/([B(OH)3])

Construct the rate of reaction expression for: B(OH)_3 ⟶ H_2O + HBO_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: B(OH)_3 ⟶ H_2O + HBO_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 B(OH)_3 | 1 | -1 H_2O | 1 | 1 HBO_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 B(OH)_3 | 1 | -1 | -(Δ[B(OH)3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) HBO_2 | 1 | 1 | (Δ[HBO2])/(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 = -(Δ[B(OH)3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[HBO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| boric acid | water | metaboric acid formula | B(OH)_3 | H_2O | HBO_2 Hill formula | BH_3O_3 | H_2O | BHO_2 name | boric acid | water | metaboric acid IUPAC name | boric acid | water | oxoborinic acid

| boric acid | water | metaboric acid molar mass | 61.83 g/mol | 18.015 g/mol | 43.82 g/mol phase | solid (at STP) | liquid (at STP) | melting point | 160 °C | 0 °C | boiling point | | 99.9839 °C | density | | 1 g/cm^3 | 2.49 g/cm^3 surface tension | | 0.0728 N/m | dynamic viscosity | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | odorless |