H2O + O2 + UCl4 = HCl + UO2Cl2

H_2O water + O_2 oxygen + UCl_4 uranium(IV) chloride ⟶ HCl hydrogen chloride + UO_2Cl_2 uranyl chloride

Balance the chemical equation algebraically: H_2O + O_2 + UCl_4 ⟶ HCl + UO_2Cl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 UCl_4 ⟶ c_4 HCl + c_5 UO_2Cl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl and U: H: | 2 c_1 = c_4 O: | c_1 + 2 c_2 = 2 c_5 Cl: | 4 c_3 = c_4 + 2 c_5 U: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 4 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + O_2 + 2 UCl_4 ⟶ 4 HCl + 2 UO_2Cl_2

+ + ⟶ +

water + oxygen + uranium(IV) chloride ⟶ hydrogen chloride + uranyl chloride

Construct the equilibrium constant, K, expression for: H_2O + O_2 + UCl_4 ⟶ HCl + UO_2Cl_2 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 H_2O + O_2 + 2 UCl_4 ⟶ 4 HCl + 2 UO_2Cl_2 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 H_2O | 2 | -2 O_2 | 1 | -1 UCl_4 | 2 | -2 HCl | 4 | 4 UO_2Cl_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) O_2 | 1 | -1 | ([O2])^(-1) UCl_4 | 2 | -2 | ([UCl4])^(-2) HCl | 4 | 4 | ([HCl])^4 UO_2Cl_2 | 2 | 2 | ([UO2Cl2])^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 = ([H2O])^(-2) ([O2])^(-1) ([UCl4])^(-2) ([HCl])^4 ([UO2Cl2])^2 = (([HCl])^4 ([UO2Cl2])^2)/(([H2O])^2 [O2] ([UCl4])^2)

Construct the rate of reaction expression for: H_2O + O_2 + UCl_4 ⟶ HCl + UO_2Cl_2 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 H_2O + O_2 + 2 UCl_4 ⟶ 4 HCl + 2 UO_2Cl_2 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 H_2O | 2 | -2 O_2 | 1 | -1 UCl_4 | 2 | -2 HCl | 4 | 4 UO_2Cl_2 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) UCl_4 | 2 | -2 | -1/2 (Δ[UCl4])/(Δt) HCl | 4 | 4 | 1/4 (Δ[HCl])/(Δt) UO_2Cl_2 | 2 | 2 | 1/2 (Δ[UO2Cl2])/(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[H2O])/(Δt) = -(Δ[O2])/(Δt) = -1/2 (Δ[UCl4])/(Δt) = 1/4 (Δ[HCl])/(Δt) = 1/2 (Δ[UO2Cl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | oxygen | uranium(IV) chloride | hydrogen chloride | uranyl chloride formula | H_2O | O_2 | UCl_4 | HCl | UO_2Cl_2 Hill formula | H_2O | O_2 | Cl_4U | ClH | Cl_2O_2U_1 name | water | oxygen | uranium(IV) chloride | hydrogen chloride | uranyl chloride IUPAC name | water | molecular oxygen | tetrachlorouranium | hydrogen chloride |