Cl2 + C + TiO2 = CO + TiCl4

Cl_2 chlorine + C activated charcoal + TiO_2 titanium dioxide ⟶ CO carbon monoxide + TiCl_4 titanium tetrachloride

Balance the chemical equation algebraically: Cl_2 + C + TiO_2 ⟶ CO + TiCl_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 C + c_3 TiO_2 ⟶ c_4 CO + c_5 TiCl_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, C, O and Ti: Cl: | 2 c_1 = 4 c_5 C: | c_2 = c_4 O: | 2 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 = 2 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Cl_2 + 2 C + TiO_2 ⟶ 2 CO + TiCl_4

+ + ⟶ +

chlorine + activated charcoal + titanium dioxide ⟶ carbon monoxide + titanium tetrachloride

Construct the equilibrium constant, K, expression for: Cl_2 + C + TiO_2 ⟶ CO + TiCl_4 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: 2 Cl_2 + 2 C + TiO_2 ⟶ 2 CO + TiCl_4 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 Cl_2 | 2 | -2 C | 2 | -2 TiO_2 | 1 | -1 CO | 2 | 2 TiCl_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 2 | -2 | ([Cl2])^(-2) C | 2 | -2 | ([C])^(-2) TiO_2 | 1 | -1 | ([TiO2])^(-1) CO | 2 | 2 | ([CO])^2 TiCl_4 | 1 | 1 | [TiCl4] 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 = ([Cl2])^(-2) ([C])^(-2) ([TiO2])^(-1) ([CO])^2 [TiCl4] = (([CO])^2 [TiCl4])/(([Cl2])^2 ([C])^2 [TiO2])

Construct the rate of reaction expression for: Cl_2 + C + TiO_2 ⟶ CO + TiCl_4 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: 2 Cl_2 + 2 C + TiO_2 ⟶ 2 CO + TiCl_4 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 Cl_2 | 2 | -2 C | 2 | -2 TiO_2 | 1 | -1 CO | 2 | 2 TiCl_4 | 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 Cl_2 | 2 | -2 | -1/2 (Δ[Cl2])/(Δt) C | 2 | -2 | -1/2 (Δ[C])/(Δt) TiO_2 | 1 | -1 | -(Δ[TiO2])/(Δt) CO | 2 | 2 | 1/2 (Δ[CO])/(Δt) TiCl_4 | 1 | 1 | (Δ[TiCl4])/(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 = -1/2 (Δ[Cl2])/(Δt) = -1/2 (Δ[C])/(Δt) = -(Δ[TiO2])/(Δt) = 1/2 (Δ[CO])/(Δt) = (Δ[TiCl4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | activated charcoal | titanium dioxide | carbon monoxide | titanium tetrachloride formula | Cl_2 | C | TiO_2 | CO | TiCl_4 Hill formula | Cl_2 | C | O_2Ti | CO | Cl_4Ti name | chlorine | activated charcoal | titanium dioxide | carbon monoxide | titanium tetrachloride IUPAC name | molecular chlorine | carbon | | carbon monoxide | tetrachlorotitanium

| chlorine | activated charcoal | titanium dioxide | carbon monoxide | titanium tetrachloride molar mass | 70.9 g/mol | 12.011 g/mol | 79.865 g/mol | 28.01 g/mol | 189.7 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | liquid (at STP) melting point | -101 °C | 3550 °C | 1843 °C | -205 °C | -25 °C boiling point | -34 °C | 4027 °C | 2900 °C | -191.5 °C | 135.5 °C density | 0.003214 g/cm^3 (at 0 °C) | 2.26 g/cm^3 | 4.26 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) | 1.73 g/cm^3 solubility in water | | insoluble | insoluble | | reacts dynamic viscosity | | | | 1.772×10^-5 Pa s (at 25 °C) | 8.27×10^-4 Pa s (at 20 °C) odor | | | | odorless |