H2SO4 + B2O3 + CaF2 = H2O + CaSO4 + BF3

H_2SO_4 sulfuric acid + B_2O_3 boron oxide + CaF_2 calcium fluoride ⟶ H_2O water + CaSO_4 calcium sulfate + BF_3 boron trifluoride

Balance the chemical equation algebraically: H_2SO_4 + B_2O_3 + CaF_2 ⟶ H_2O + CaSO_4 + BF_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 B_2O_3 + c_3 CaF_2 ⟶ c_4 H_2O + c_5 CaSO_4 + c_6 BF_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, B, Ca and F: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 = c_4 + 4 c_5 S: | c_1 = c_5 B: | 2 c_2 = c_6 Ca: | c_3 = c_5 F: | 2 c_3 = 3 c_6 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 = 3 c_2 = 1 c_3 = 3 c_4 = 3 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + B_2O_3 + 3 CaF_2 ⟶ 3 H_2O + 3 CaSO_4 + 2 BF_3

+ + ⟶ + +

sulfuric acid + boron oxide + calcium fluoride ⟶ water + calcium sulfate + boron trifluoride

Construct the equilibrium constant, K, expression for: H_2SO_4 + B_2O_3 + CaF_2 ⟶ H_2O + CaSO_4 + 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: 3 H_2SO_4 + B_2O_3 + 3 CaF_2 ⟶ 3 H_2O + 3 CaSO_4 + 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 H_2SO_4 | 3 | -3 B_2O_3 | 1 | -1 CaF_2 | 3 | -3 H_2O | 3 | 3 CaSO_4 | 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 H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) B_2O_3 | 1 | -1 | ([B2O3])^(-1) CaF_2 | 3 | -3 | ([CaF2])^(-3) H_2O | 3 | 3 | ([H2O])^3 CaSO_4 | 3 | 3 | ([CaSO4])^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 = ([H2SO4])^(-3) ([B2O3])^(-1) ([CaF2])^(-3) ([H2O])^3 ([CaSO4])^3 ([BF3])^2 = (([H2O])^3 ([CaSO4])^3 ([BF3])^2)/(([H2SO4])^3 [B2O3] ([CaF2])^3)

Construct the rate of reaction expression for: H_2SO_4 + B_2O_3 + CaF_2 ⟶ H_2O + CaSO_4 + 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: 3 H_2SO_4 + B_2O_3 + 3 CaF_2 ⟶ 3 H_2O + 3 CaSO_4 + 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 H_2SO_4 | 3 | -3 B_2O_3 | 1 | -1 CaF_2 | 3 | -3 H_2O | 3 | 3 CaSO_4 | 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) B_2O_3 | 1 | -1 | -(Δ[B2O3])/(Δt) CaF_2 | 3 | -3 | -1/3 (Δ[CaF2])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) CaSO_4 | 3 | 3 | 1/3 (Δ[CaSO4])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -(Δ[B2O3])/(Δt) = -1/3 (Δ[CaF2])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[CaSO4])/(Δt) = 1/2 (Δ[BF3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | boron oxide | calcium fluoride | water | calcium sulfate | boron trifluoride formula | H_2SO_4 | B_2O_3 | CaF_2 | H_2O | CaSO_4 | BF_3 Hill formula | H_2O_4S | B_2O_3 | CaF_2 | H_2O | CaO_4S | BF_3 name | sulfuric acid | boron oxide | calcium fluoride | water | calcium sulfate | boron trifluoride IUPAC name | sulfuric acid | | calcium difluoride | water | calcium sulfate | trifluoroborane

| sulfuric acid | boron oxide | calcium fluoride | water | calcium sulfate | boron trifluoride molar mass | 98.07 g/mol | 69.62 g/mol | 78.075 g/mol | 18.015 g/mol | 136.13 g/mol | 67.81 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | | gas (at STP) melting point | 10.371 °C | 450 °C | 1418 °C | 0 °C | | -127 °C boiling point | 279.6 °C | 1860 °C | 2500 °C | 99.9839 °C | | -100 °C density | 1.8305 g/cm^3 | 2.46 g/cm^3 | 3.18 g/cm^3 | 1 g/cm^3 | | 0.002772 g/cm^3 (at 25 °C) solubility in water | very soluble | | | | slightly soluble | surface tension | 0.0735 N/m | | | 0.0728 N/m | | 0.0172 N/m dynamic viscosity | 0.021 Pa s (at 25 °C) | 85 Pa s (at 700 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | 1.701×10^-5 Pa s (at 25 °C) odor | odorless | | | odorless | odorless |