SiO2 + B = Si + B2O3

SiO_2 silicon dioxide + B boron ⟶ Si silicon + B_2O_3 boron oxide

Balance the chemical equation algebraically: SiO_2 + B ⟶ Si + B_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SiO_2 + c_2 B ⟶ c_3 Si + c_4 B_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Si and B: O: | 2 c_1 = 3 c_4 Si: | c_1 = c_3 B: | c_2 = 2 c_4 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 = 3/2 c_2 = 2 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 4 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 SiO_2 + 4 B ⟶ 3 Si + 2 B_2O_3

+ ⟶ +

silicon dioxide + boron ⟶ silicon + boron oxide

| silicon dioxide | boron | silicon | boron oxide molecular enthalpy | -911 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1274 kJ/mol total enthalpy | -2733 kJ/mol | 0 kJ/mol | 0 kJ/mol | -2547 kJ/mol | H_initial = -2733 kJ/mol | | H_final = -2547 kJ/mol | ΔH_rxn^0 | -2547 kJ/mol - -2733 kJ/mol = 186 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: SiO_2 + B ⟶ Si + B_2O_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 SiO_2 + 4 B ⟶ 3 Si + 2 B_2O_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 SiO_2 | 3 | -3 B | 4 | -4 Si | 3 | 3 B_2O_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SiO_2 | 3 | -3 | ([SiO2])^(-3) B | 4 | -4 | ([B])^(-4) Si | 3 | 3 | ([Si])^3 B_2O_3 | 2 | 2 | ([B2O3])^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 = ([SiO2])^(-3) ([B])^(-4) ([Si])^3 ([B2O3])^2 = (([Si])^3 ([B2O3])^2)/(([SiO2])^3 ([B])^4)

Construct the rate of reaction expression for: SiO_2 + B ⟶ Si + B_2O_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 SiO_2 + 4 B ⟶ 3 Si + 2 B_2O_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 SiO_2 | 3 | -3 B | 4 | -4 Si | 3 | 3 B_2O_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 SiO_2 | 3 | -3 | -1/3 (Δ[SiO2])/(Δt) B | 4 | -4 | -1/4 (Δ[B])/(Δt) Si | 3 | 3 | 1/3 (Δ[Si])/(Δt) B_2O_3 | 2 | 2 | 1/2 (Δ[B2O3])/(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[SiO2])/(Δt) = -1/4 (Δ[B])/(Δt) = 1/3 (Δ[Si])/(Δt) = 1/2 (Δ[B2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silicon dioxide | boron | silicon | boron oxide formula | SiO_2 | B | Si | B_2O_3 Hill formula | O_2Si | B | Si | B_2O_3 name | silicon dioxide | boron | silicon | boron oxide IUPAC name | dioxosilane | boron | silicon |

| silicon dioxide | boron | silicon | boron oxide molar mass | 60.083 g/mol | 10.81 g/mol | 28.085 g/mol | 69.62 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1713 °C | 2075 °C | 1410 °C | 450 °C boiling point | 2950 °C | 4000 °C | 2355 °C | 1860 °C density | 2.196 g/cm^3 | 2.34 g/cm^3 | 2.33 g/cm^3 | 2.46 g/cm^3 solubility in water | insoluble | insoluble | insoluble | dynamic viscosity | | | | 85 Pa s (at 700 °C) odor | odorless | | |