HF + B2O3 = H2O + BF3

HF hydrogen fluoride + B_2O_3 boron oxide ⟶ H_2O water + BF_3 boron trifluoride

Balance the chemical equation algebraically: HF + B_2O_3 ⟶ H_2O + BF_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HF + c_2 B_2O_3 ⟶ c_3 H_2O + c_4 BF_3 Set the number of atoms in the reactants equal to the number of atoms in the products for F, H, B and O: F: | c_1 = 3 c_4 H: | c_1 = 2 c_3 B: | 2 c_2 = c_4 O: | 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 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HF + B_2O_3 ⟶ 3 H_2O + 2 BF_3

+ ⟶ +

hydrogen fluoride + boron oxide ⟶ water + boron trifluoride

| hydrogen fluoride | boron oxide | water | boron trifluoride molecular enthalpy | -273.3 kJ/mol | -1274 kJ/mol | -285.8 kJ/mol | -1136 kJ/mol total enthalpy | -1640 kJ/mol | -1274 kJ/mol | -857.5 kJ/mol | -2272 kJ/mol | H_initial = -2913 kJ/mol | | H_final = -3129 kJ/mol | ΔH_rxn^0 | -3129 kJ/mol - -2913 kJ/mol = -216.2 kJ/mol (exothermic) | | |

| hydrogen fluoride | boron oxide | water | boron trifluoride molecular free energy | -275.4 kJ/mol | -1194 kJ/mol | -237.1 kJ/mol | -1119 kJ/mol total free energy | -1652 kJ/mol | -1194 kJ/mol | -711.3 kJ/mol | -2239 kJ/mol | G_initial = -2847 kJ/mol | | G_final = -2950 kJ/mol | ΔG_rxn^0 | -2950 kJ/mol - -2847 kJ/mol = -103.4 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: HF + B_2O_3 ⟶ H_2O + BF_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: 6 HF + B_2O_3 ⟶ 3 H_2O + 2 BF_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 HF | 6 | -6 B_2O_3 | 1 | -1 H_2O | 3 | 3 BF_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HF | 6 | -6 | ([HF])^(-6) B_2O_3 | 1 | -1 | ([B2O3])^(-1) H_2O | 3 | 3 | ([H2O])^3 BF_3 | 2 | 2 | ([BF3])^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 = ([HF])^(-6) ([B2O3])^(-1) ([H2O])^3 ([BF3])^2 = (([H2O])^3 ([BF3])^2)/(([HF])^6 [B2O3])

Construct the rate of reaction expression for: HF + B_2O_3 ⟶ H_2O + BF_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: 6 HF + B_2O_3 ⟶ 3 H_2O + 2 BF_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 HF | 6 | -6 B_2O_3 | 1 | -1 H_2O | 3 | 3 BF_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 HF | 6 | -6 | -1/6 (Δ[HF])/(Δt) B_2O_3 | 1 | -1 | -(Δ[B2O3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) BF_3 | 2 | 2 | 1/2 (Δ[BF3])/(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 = -1/6 (Δ[HF])/(Δt) = -(Δ[B2O3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[BF3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen fluoride | boron oxide | water | boron trifluoride formula | HF | B_2O_3 | H_2O | BF_3 Hill formula | FH | B_2O_3 | H_2O | BF_3 name | hydrogen fluoride | boron oxide | water | boron trifluoride IUPAC name | hydrogen fluoride | | water | trifluoroborane