HCl + Ti = H2 + TiCl3

HCl hydrogen chloride + Ti titanium ⟶ H_2 hydrogen + TiCl_3 titanium trichloride

Balance the chemical equation algebraically: HCl + Ti ⟶ H_2 + TiCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Ti ⟶ c_3 H_2 + c_4 TiCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H and Ti: Cl: | c_1 = 3 c_4 H: | c_1 = 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 = 3 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + 2 Ti ⟶ 3 H_2 + 2 TiCl_3

+ ⟶ +

hydrogen chloride + titanium ⟶ hydrogen + titanium trichloride

| hydrogen chloride | titanium | hydrogen | titanium trichloride molecular enthalpy | -92.3 kJ/mol | 0 kJ/mol | 0 kJ/mol | -720.9 kJ/mol total enthalpy | -553.8 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1442 kJ/mol | H_initial = -553.8 kJ/mol | | H_final = -1442 kJ/mol | ΔH_rxn^0 | -1442 kJ/mol - -553.8 kJ/mol = -888 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: HCl + Ti ⟶ H_2 + TiCl_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: 6 HCl + 2 Ti ⟶ 3 H_2 + 2 TiCl_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 HCl | 6 | -6 Ti | 2 | -2 H_2 | 3 | 3 TiCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) Ti | 2 | -2 | ([Ti])^(-2) H_2 | 3 | 3 | ([H2])^3 TiCl_3 | 2 | 2 | ([TiCl3])^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 = ([HCl])^(-6) ([Ti])^(-2) ([H2])^3 ([TiCl3])^2 = (([H2])^3 ([TiCl3])^2)/(([HCl])^6 ([Ti])^2)

Construct the rate of reaction expression for: HCl + Ti ⟶ H_2 + TiCl_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: 6 HCl + 2 Ti ⟶ 3 H_2 + 2 TiCl_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 HCl | 6 | -6 Ti | 2 | -2 H_2 | 3 | 3 TiCl_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 HCl | 6 | -6 | -1/6 (Δ[HCl])/(Δt) Ti | 2 | -2 | -1/2 (Δ[Ti])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) TiCl_3 | 2 | 2 | 1/2 (Δ[TiCl3])/(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 = -1/6 (Δ[HCl])/(Δt) = -1/2 (Δ[Ti])/(Δt) = 1/3 (Δ[H2])/(Δt) = 1/2 (Δ[TiCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | titanium | hydrogen | titanium trichloride formula | HCl | Ti | H_2 | TiCl_3 Hill formula | ClH | Ti | H_2 | Cl_3Ti name | hydrogen chloride | titanium | hydrogen | titanium trichloride IUPAC name | hydrogen chloride | titanium | molecular hydrogen | trichlorotitanium

| hydrogen chloride | titanium | hydrogen | titanium trichloride molar mass | 36.46 g/mol | 47.867 g/mol | 2.016 g/mol | 154.2 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -114.17 °C | 1660 °C | -259.2 °C | 440 °C boiling point | -85 °C | 3287 °C | -252.8 °C | 960 °C density | 0.00149 g/cm^3 (at 25 °C) | 4.5 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 1.32 g/cm^3 solubility in water | miscible | insoluble | | very soluble dynamic viscosity | | | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless |