Si + BaO = Ba + BaSiO3

Si silicon + BaO barium oxide ⟶ Ba barium + BaSiO_3 barium metasilicate

Balance the chemical equation algebraically: Si + BaO ⟶ Ba + BaSiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Si + c_2 BaO ⟶ c_3 Ba + c_4 BaSiO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Si, Ba and O: Si: | c_1 = c_4 Ba: | c_2 = c_3 + c_4 O: | c_2 = 3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Si + 3 BaO ⟶ 2 Ba + BaSiO_3

+ ⟶ +

silicon + barium oxide ⟶ barium + barium metasilicate

Construct the equilibrium constant, K, expression for: Si + BaO ⟶ Ba + BaSiO_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: Si + 3 BaO ⟶ 2 Ba + BaSiO_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 Si | 1 | -1 BaO | 3 | -3 Ba | 2 | 2 BaSiO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Si | 1 | -1 | ([Si])^(-1) BaO | 3 | -3 | ([BaO])^(-3) Ba | 2 | 2 | ([Ba])^2 BaSiO_3 | 1 | 1 | [BaSiO3] 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 = ([Si])^(-1) ([BaO])^(-3) ([Ba])^2 [BaSiO3] = (([Ba])^2 [BaSiO3])/([Si] ([BaO])^3)

Construct the rate of reaction expression for: Si + BaO ⟶ Ba + BaSiO_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: Si + 3 BaO ⟶ 2 Ba + BaSiO_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 Si | 1 | -1 BaO | 3 | -3 Ba | 2 | 2 BaSiO_3 | 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 Si | 1 | -1 | -(Δ[Si])/(Δt) BaO | 3 | -3 | -1/3 (Δ[BaO])/(Δt) Ba | 2 | 2 | 1/2 (Δ[Ba])/(Δt) BaSiO_3 | 1 | 1 | (Δ[BaSiO3])/(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[Si])/(Δt) = -1/3 (Δ[BaO])/(Δt) = 1/2 (Δ[Ba])/(Δt) = (Δ[BaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silicon | barium oxide | barium | barium metasilicate formula | Si | BaO | Ba | BaSiO_3 Hill formula | Si | BaO | Ba | BaO_3Si name | silicon | barium oxide | barium | barium metasilicate IUPAC name | silicon | oxobarium | barium | barium(+2) cation; dioxido-oxosilane

| silicon | barium oxide | barium | barium metasilicate molar mass | 28.085 g/mol | 153.326 g/mol | 137.327 g/mol | 213.41 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1410 °C | 1920 °C | 725 °C | 1604 °C boiling point | 2355 °C | | 1640 °C | density | 2.33 g/cm^3 | 5.72 g/cm^3 | 3.6 g/cm^3 | 1.67 g/cm^3 solubility in water | insoluble | | insoluble | surface tension | | | 0.224 N/m |