HCl + AuCl3 = HAuCl4

HCl (hydrogen chloride) + AuCl_3 (gold(III) chloride) ⟶ HAuCl_4·xH_2O (gold(III) chloride hydrate)

Balance the chemical equation algebraically: HCl + AuCl_3 ⟶ HAuCl_4·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 AuCl_3 ⟶ c_3 HAuCl_4·xH_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H and Au: Cl: | c_1 + 3 c_2 = 4 c_3 H: | c_1 = c_3 Au: | 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | HCl + AuCl_3 ⟶ HAuCl_4·xH_2O

+ ⟶

hydrogen chloride + gold(III) chloride ⟶ gold(III) chloride hydrate

Construct the equilibrium constant, K, expression for: HCl + AuCl_3 ⟶ HAuCl_4·xH_2O 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: HCl + AuCl_3 ⟶ HAuCl_4·xH_2O 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 | 1 | -1 AuCl_3 | 1 | -1 HAuCl_4·xH_2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 1 | -1 | ([HCl])^(-1) AuCl_3 | 1 | -1 | ([AuCl3])^(-1) HAuCl_4·xH_2O | 1 | 1 | [HAuCl4·xH2O] 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])^(-1) ([AuCl3])^(-1) [HAuCl4·xH2O] = ([HAuCl4·xH2O])/([HCl] [AuCl3])

Construct the rate of reaction expression for: HCl + AuCl_3 ⟶ HAuCl_4·xH_2O 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: HCl + AuCl_3 ⟶ HAuCl_4·xH_2O 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 | 1 | -1 AuCl_3 | 1 | -1 HAuCl_4·xH_2O | 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 HCl | 1 | -1 | -(Δ[HCl])/(Δt) AuCl_3 | 1 | -1 | -(Δ[AuCl3])/(Δt) HAuCl_4·xH_2O | 1 | 1 | (Δ[HAuCl4·xH2O])/(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[HCl])/(Δt) = -(Δ[AuCl3])/(Δt) = (Δ[HAuCl4·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | gold(III) chloride | gold(III) chloride hydrate formula | HCl | AuCl_3 | HAuCl_4·xH_2O Hill formula | ClH | AuCl_3 | AuCl_4H name | hydrogen chloride | gold(III) chloride | gold(III) chloride hydrate IUPAC name | hydrogen chloride | trichlorogold | hydron; tetrachlorogold

| hydrogen chloride | gold(III) chloride | gold(III) chloride hydrate molar mass | 36.46 g/mol | 303.3 g/mol | 339.8 g/mol phase | gas (at STP) | | melting point | -114.17 °C | | boiling point | -85 °C | | density | 0.00149 g/cm^3 (at 25 °C) | | 3.9 g/cm^3 solubility in water | miscible | |