BaCl2 + Na2SiO3 = NaCl + BaSiO3

BaCl_2 barium chloride + Na_2SiO_3 sodium metasilicate ⟶ NaCl sodium chloride + BaSiO_3 barium metasilicate

Balance the chemical equation algebraically: BaCl_2 + Na_2SiO_3 ⟶ NaCl + BaSiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 BaCl_2 + c_2 Na_2SiO_3 ⟶ c_3 NaCl + c_4 BaSiO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Ba, Cl, Na, O and Si: Ba: | c_1 = c_4 Cl: | 2 c_1 = c_3 Na: | 2 c_2 = c_3 O: | 3 c_2 = 3 c_4 Si: | c_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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | BaCl_2 + Na_2SiO_3 ⟶ 2 NaCl + BaSiO_3

+ ⟶ +

barium chloride + sodium metasilicate ⟶ sodium chloride + barium metasilicate

Construct the equilibrium constant, K, expression for: BaCl_2 + Na_2SiO_3 ⟶ NaCl + 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: BaCl_2 + Na_2SiO_3 ⟶ 2 NaCl + 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 BaCl_2 | 1 | -1 Na_2SiO_3 | 1 | -1 NaCl | 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 BaCl_2 | 1 | -1 | ([BaCl2])^(-1) Na_2SiO_3 | 1 | -1 | ([Na2SiO3])^(-1) NaCl | 2 | 2 | ([NaCl])^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 = ([BaCl2])^(-1) ([Na2SiO3])^(-1) ([NaCl])^2 [BaSiO3] = (([NaCl])^2 [BaSiO3])/([BaCl2] [Na2SiO3])

Construct the rate of reaction expression for: BaCl_2 + Na_2SiO_3 ⟶ NaCl + 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: BaCl_2 + Na_2SiO_3 ⟶ 2 NaCl + 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 BaCl_2 | 1 | -1 Na_2SiO_3 | 1 | -1 NaCl | 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 BaCl_2 | 1 | -1 | -(Δ[BaCl2])/(Δt) Na_2SiO_3 | 1 | -1 | -(Δ[Na2SiO3])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(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[BaCl2])/(Δt) = -(Δ[Na2SiO3])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = (Δ[BaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| barium chloride | sodium metasilicate | sodium chloride | barium metasilicate formula | BaCl_2 | Na_2SiO_3 | NaCl | BaSiO_3 Hill formula | BaCl_2 | Na_2O_3Si | ClNa | BaO_3Si name | barium chloride | sodium metasilicate | sodium chloride | barium metasilicate IUPAC name | barium(+2) cation dichloride | disodium dioxido-oxosilane | sodium chloride | barium(+2) cation; dioxido-oxosilane

| barium chloride | sodium metasilicate | sodium chloride | barium metasilicate molar mass | 208.2 g/mol | 122.06 g/mol | 58.44 g/mol | 213.41 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 963 °C | 72.2 °C | 801 °C | 1604 °C boiling point | | | 1413 °C | density | 3.856 g/cm^3 | 1.749 g/cm^3 | 2.16 g/cm^3 | 1.67 g/cm^3 solubility in water | | soluble | soluble | dynamic viscosity | | 1 Pa s (at 1088 °C) | | odor | odorless | | odorless |