Na + B + TiCl4 = NaCl + TiB2

Na sodium + B boron + TiCl_4 titanium tetrachloride ⟶ NaCl sodium chloride + TiB_2 titanium boride

Balance the chemical equation algebraically: Na + B + TiCl_4 ⟶ NaCl + TiB_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 B + c_3 TiCl_4 ⟶ c_4 NaCl + c_5 TiB_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Na, B, Cl and Ti: Na: | c_1 = c_4 B: | c_2 = 2 c_5 Cl: | 4 c_3 = c_4 Ti: | c_3 = c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 1 c_4 = 4 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Na + 2 B + TiCl_4 ⟶ 4 NaCl + TiB_2

+ + ⟶ + TiB_2

sodium + boron + titanium tetrachloride ⟶ sodium chloride + titanium boride

Construct the equilibrium constant, K, expression for: Na + B + TiCl_4 ⟶ NaCl + TiB_2 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: 4 Na + 2 B + TiCl_4 ⟶ 4 NaCl + TiB_2 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 Na | 4 | -4 B | 2 | -2 TiCl_4 | 1 | -1 NaCl | 4 | 4 TiB_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na | 4 | -4 | ([Na])^(-4) B | 2 | -2 | ([B])^(-2) TiCl_4 | 1 | -1 | ([TiCl4])^(-1) NaCl | 4 | 4 | ([NaCl])^4 TiB_2 | 1 | 1 | [TiB2] 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 = ([Na])^(-4) ([B])^(-2) ([TiCl4])^(-1) ([NaCl])^4 [TiB2] = (([NaCl])^4 [TiB2])/(([Na])^4 ([B])^2 [TiCl4])

Construct the rate of reaction expression for: Na + B + TiCl_4 ⟶ NaCl + TiB_2 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: 4 Na + 2 B + TiCl_4 ⟶ 4 NaCl + TiB_2 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 Na | 4 | -4 B | 2 | -2 TiCl_4 | 1 | -1 NaCl | 4 | 4 TiB_2 | 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 Na | 4 | -4 | -1/4 (Δ[Na])/(Δt) B | 2 | -2 | -1/2 (Δ[B])/(Δt) TiCl_4 | 1 | -1 | -(Δ[TiCl4])/(Δt) NaCl | 4 | 4 | 1/4 (Δ[NaCl])/(Δt) TiB_2 | 1 | 1 | (Δ[TiB2])/(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 = -1/4 (Δ[Na])/(Δt) = -1/2 (Δ[B])/(Δt) = -(Δ[TiCl4])/(Δt) = 1/4 (Δ[NaCl])/(Δt) = (Δ[TiB2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium | boron | titanium tetrachloride | sodium chloride | titanium boride formula | Na | B | TiCl_4 | NaCl | TiB_2 Hill formula | Na | B | Cl_4Ti | ClNa | B_2Ti_1 name | sodium | boron | titanium tetrachloride | sodium chloride | titanium boride IUPAC name | sodium | boron | tetrachlorotitanium | sodium chloride |