Ti + TiO2 = TiO

Ti titanium + TiO_2 titanium dioxide ⟶ TiO titanium monoxide

Balance the chemical equation algebraically: Ti + TiO_2 ⟶ TiO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ti + c_2 TiO_2 ⟶ c_3 TiO Set the number of atoms in the reactants equal to the number of atoms in the products for Ti and O: Ti: | c_1 + c_2 = c_3 O: | 2 c_2 = c_3 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 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Ti + TiO_2 ⟶ 2 TiO

+ ⟶

titanium + titanium dioxide ⟶ titanium monoxide

| titanium | titanium dioxide | titanium monoxide molecular enthalpy | 0 kJ/mol | -944 kJ/mol | -519.7 kJ/mol total enthalpy | 0 kJ/mol | -944 kJ/mol | -1039 kJ/mol | H_initial = -944 kJ/mol | | H_final = -1039 kJ/mol ΔH_rxn^0 | -1039 kJ/mol - -944 kJ/mol = -95.4 kJ/mol (exothermic) | |

Construct the equilibrium constant, K, expression for: Ti + TiO_2 ⟶ TiO 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: Ti + TiO_2 ⟶ 2 TiO 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 Ti | 1 | -1 TiO_2 | 1 | -1 TiO | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ti | 1 | -1 | ([Ti])^(-1) TiO_2 | 1 | -1 | ([TiO2])^(-1) TiO | 2 | 2 | ([TiO])^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 = ([Ti])^(-1) ([TiO2])^(-1) ([TiO])^2 = ([TiO])^2/([Ti] [TiO2])

Construct the rate of reaction expression for: Ti + TiO_2 ⟶ TiO 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: Ti + TiO_2 ⟶ 2 TiO 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 Ti | 1 | -1 TiO_2 | 1 | -1 TiO | 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 Ti | 1 | -1 | -(Δ[Ti])/(Δt) TiO_2 | 1 | -1 | -(Δ[TiO2])/(Δt) TiO | 2 | 2 | 1/2 (Δ[TiO])/(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[Ti])/(Δt) = -(Δ[TiO2])/(Δt) = 1/2 (Δ[TiO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| titanium | titanium dioxide | titanium monoxide formula | Ti | TiO_2 | TiO Hill formula | Ti | O_2Ti | OTi name | titanium | titanium dioxide | titanium monoxide

| titanium | titanium dioxide | titanium monoxide molar mass | 47.867 g/mol | 79.865 g/mol | 63.866 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1660 °C | 1843 °C | 1770 °C boiling point | 3287 °C | 2900 °C | 3227 °C density | 4.5 g/cm^3 | 4.26 g/cm^3 | 4.95 g/cm^3 solubility in water | insoluble | insoluble |