Na + TiCl4 = NaCl + Ti

Na sodium + TiCl_4 titanium tetrachloride ⟶ NaCl sodium chloride + Ti titanium

Balance the chemical equation algebraically: Na + TiCl_4 ⟶ NaCl + Ti Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 TiCl_4 ⟶ c_3 NaCl + c_4 Ti Set the number of atoms in the reactants equal to the number of atoms in the products for Na, Cl and Ti: Na: | c_1 = c_3 Cl: | 4 c_2 = c_3 Ti: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 4 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Na + TiCl_4 ⟶ 4 NaCl + Ti

+ ⟶ +

sodium + titanium tetrachloride ⟶ sodium chloride + titanium

Construct the equilibrium constant, K, expression for: Na + TiCl_4 ⟶ NaCl + Ti 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 + TiCl_4 ⟶ 4 NaCl + Ti 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 TiCl_4 | 1 | -1 NaCl | 4 | 4 Ti | 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) TiCl_4 | 1 | -1 | ([TiCl4])^(-1) NaCl | 4 | 4 | ([NaCl])^4 Ti | 1 | 1 | [Ti] 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) ([TiCl4])^(-1) ([NaCl])^4 [Ti] = (([NaCl])^4 [Ti])/(([Na])^4 [TiCl4])

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

| sodium | titanium tetrachloride | sodium chloride | titanium formula | Na | TiCl_4 | NaCl | Ti Hill formula | Na | Cl_4Ti | ClNa | Ti name | sodium | titanium tetrachloride | sodium chloride | titanium IUPAC name | sodium | tetrachlorotitanium | sodium chloride | titanium

| sodium | titanium tetrachloride | sodium chloride | titanium molar mass | 22.98976928 g/mol | 189.7 g/mol | 58.44 g/mol | 47.867 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 97.8 °C | -25 °C | 801 °C | 1660 °C boiling point | 883 °C | 135.5 °C | 1413 °C | 3287 °C density | 0.968 g/cm^3 | 1.73 g/cm^3 | 2.16 g/cm^3 | 4.5 g/cm^3 solubility in water | decomposes | reacts | soluble | insoluble dynamic viscosity | 1.413×10^-5 Pa s (at 527 °C) | 8.27×10^-4 Pa s (at 20 °C) | | odor | | | odorless |