TiO2 = O2 + Ti

TiO_2 titanium dioxide ⟶ O_2 oxygen + Ti titanium

Balance the chemical equation algebraically: TiO_2 ⟶ O_2 + Ti Add stoichiometric coefficients, c_i, to the reactants and products: c_1 TiO_2 ⟶ c_2 O_2 + c_3 Ti Set the number of atoms in the reactants equal to the number of atoms in the products for O and Ti: O: | 2 c_1 = 2 c_2 Ti: | c_1 = 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | TiO_2 ⟶ O_2 + Ti

⟶ +

titanium dioxide ⟶ oxygen + titanium

| titanium dioxide | oxygen | titanium molecular enthalpy | -944 kJ/mol | 0 kJ/mol | 0 kJ/mol total enthalpy | -944 kJ/mol | 0 kJ/mol | 0 kJ/mol | H_initial = -944 kJ/mol | H_final = 0 kJ/mol | ΔH_rxn^0 | 0 kJ/mol - -944 kJ/mol = 944 kJ/mol (endothermic) | |

Construct the equilibrium constant, K, expression for: TiO_2 ⟶ O_2 + 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: TiO_2 ⟶ O_2 + 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 TiO_2 | 1 | -1 O_2 | 1 | 1 Ti | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression TiO_2 | 1 | -1 | ([TiO2])^(-1) O_2 | 1 | 1 | [O2] 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 = ([TiO2])^(-1) [O2] [Ti] = ([O2] [Ti])/([TiO2])

Construct the rate of reaction expression for: TiO_2 ⟶ O_2 + 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: TiO_2 ⟶ O_2 + 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 TiO_2 | 1 | -1 O_2 | 1 | 1 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 TiO_2 | 1 | -1 | -(Δ[TiO2])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(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 = -(Δ[TiO2])/(Δt) = (Δ[O2])/(Δt) = (Δ[Ti])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| titanium dioxide | oxygen | titanium formula | TiO_2 | O_2 | Ti Hill formula | O_2Ti | O_2 | Ti name | titanium dioxide | oxygen | titanium IUPAC name | | molecular oxygen | titanium

| titanium dioxide | oxygen | titanium molar mass | 79.865 g/mol | 31.998 g/mol | 47.867 g/mol phase | solid (at STP) | gas (at STP) | solid (at STP) melting point | 1843 °C | -218 °C | 1660 °C boiling point | 2900 °C | -183 °C | 3287 °C density | 4.26 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 4.5 g/cm^3 solubility in water | insoluble | | insoluble surface tension | | 0.01347 N/m | dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | odor | | odorless |