AuCl3 + TiCl3 = Au + TiCl4

AuCl_3 gold(III) chloride + TiCl_3 titanium trichloride ⟶ Au gold + TiCl_4 titanium tetrachloride

Balance the chemical equation algebraically: AuCl_3 + TiCl_3 ⟶ Au + TiCl_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AuCl_3 + c_2 TiCl_3 ⟶ c_3 Au + c_4 TiCl_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Au, Cl and Ti: Au: | c_1 = c_3 Cl: | 3 c_1 + 3 c_2 = 4 c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | AuCl_3 + 3 TiCl_3 ⟶ Au + 3 TiCl_4

+ ⟶ +

gold(III) chloride + titanium trichloride ⟶ gold + titanium tetrachloride

Construct the equilibrium constant, K, expression for: AuCl_3 + TiCl_3 ⟶ Au + 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: AuCl_3 + 3 TiCl_3 ⟶ Au + 3 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 AuCl_3 | 1 | -1 TiCl_3 | 3 | -3 Au | 1 | 1 TiCl_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AuCl_3 | 1 | -1 | ([AuCl3])^(-1) TiCl_3 | 3 | -3 | ([TiCl3])^(-3) Au | 1 | 1 | [Au] TiCl_4 | 3 | 3 | ([TiCl4])^3 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 = ([AuCl3])^(-1) ([TiCl3])^(-3) [Au] ([TiCl4])^3 = ([Au] ([TiCl4])^3)/([AuCl3] ([TiCl3])^3)

Construct the rate of reaction expression for: AuCl_3 + TiCl_3 ⟶ Au + 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: AuCl_3 + 3 TiCl_3 ⟶ Au + 3 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 AuCl_3 | 1 | -1 TiCl_3 | 3 | -3 Au | 1 | 1 TiCl_4 | 3 | 3 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 AuCl_3 | 1 | -1 | -(Δ[AuCl3])/(Δt) TiCl_3 | 3 | -3 | -1/3 (Δ[TiCl3])/(Δt) Au | 1 | 1 | (Δ[Au])/(Δt) TiCl_4 | 3 | 3 | 1/3 (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 = -(Δ[AuCl3])/(Δt) = -1/3 (Δ[TiCl3])/(Δt) = (Δ[Au])/(Δt) = 1/3 (Δ[TiCl4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| gold(III) chloride | titanium trichloride | gold | titanium tetrachloride formula | AuCl_3 | TiCl_3 | Au | TiCl_4 Hill formula | AuCl_3 | Cl_3Ti | Au | Cl_4Ti name | gold(III) chloride | titanium trichloride | gold | titanium tetrachloride IUPAC name | trichlorogold | trichlorotitanium | gold | tetrachlorotitanium

| gold(III) chloride | titanium trichloride | gold | titanium tetrachloride molar mass | 303.3 g/mol | 154.2 g/mol | 196.966569 g/mol | 189.7 g/mol phase | | solid (at STP) | solid (at STP) | liquid (at STP) melting point | | 440 °C | 1063 °C | -25 °C boiling point | | 960 °C | 2856 °C | 135.5 °C density | | 1.32 g/cm^3 | 19.3 g/cm^3 | 1.73 g/cm^3 solubility in water | | very soluble | insoluble | reacts dynamic viscosity | | | | 8.27×10^-4 Pa s (at 20 °C)