HCl + HIO4 + CeCl3 = H2O + HIO2 + CeCl4

HCl hydrogen chloride + HIO4 + CeCl_3 cerous chloride ⟶ H_2O water + HIO2 + CeCl4

Balance the chemical equation algebraically: HCl + HIO4 + CeCl_3 ⟶ H_2O + HIO2 + CeCl4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 HIO4 + c_3 CeCl_3 ⟶ c_4 H_2O + c_5 HIO2 + c_6 CeCl4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, I, O and Ce: Cl: | c_1 + 3 c_3 = 4 c_6 H: | c_1 + c_2 = 2 c_4 + c_5 I: | c_2 = c_5 O: | 4 c_2 = c_4 + 2 c_5 Ce: | c_3 = c_6 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 = 4 c_2 = 1 c_3 = 4 c_4 = 2 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HCl + HIO4 + 4 CeCl_3 ⟶ 2 H_2O + HIO2 + 4 CeCl4

+ HIO4 + ⟶ + HIO2 + CeCl4

hydrogen chloride + HIO4 + cerous chloride ⟶ water + HIO2 + CeCl4

Construct the equilibrium constant, K, expression for: HCl + HIO4 + CeCl_3 ⟶ H_2O + HIO2 + CeCl4 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: 4 HCl + HIO4 + 4 CeCl_3 ⟶ 2 H_2O + HIO2 + 4 CeCl4 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 | 4 | -4 HIO4 | 1 | -1 CeCl_3 | 4 | -4 H_2O | 2 | 2 HIO2 | 1 | 1 CeCl4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 4 | -4 | ([HCl])^(-4) HIO4 | 1 | -1 | ([HIO4])^(-1) CeCl_3 | 4 | -4 | ([CeCl3])^(-4) H_2O | 2 | 2 | ([H2O])^2 HIO2 | 1 | 1 | [HIO2] CeCl4 | 4 | 4 | ([CeCl4])^4 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])^(-4) ([HIO4])^(-1) ([CeCl3])^(-4) ([H2O])^2 [HIO2] ([CeCl4])^4 = (([H2O])^2 [HIO2] ([CeCl4])^4)/(([HCl])^4 [HIO4] ([CeCl3])^4)

Construct the rate of reaction expression for: HCl + HIO4 + CeCl_3 ⟶ H_2O + HIO2 + CeCl4 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: 4 HCl + HIO4 + 4 CeCl_3 ⟶ 2 H_2O + HIO2 + 4 CeCl4 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 | 4 | -4 HIO4 | 1 | -1 CeCl_3 | 4 | -4 H_2O | 2 | 2 HIO2 | 1 | 1 CeCl4 | 4 | 4 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 | 4 | -4 | -1/4 (Δ[HCl])/(Δt) HIO4 | 1 | -1 | -(Δ[HIO4])/(Δt) CeCl_3 | 4 | -4 | -1/4 (Δ[CeCl3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) HIO2 | 1 | 1 | (Δ[HIO2])/(Δt) CeCl4 | 4 | 4 | 1/4 (Δ[CeCl4])/(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 = -1/4 (Δ[HCl])/(Δt) = -(Δ[HIO4])/(Δt) = -1/4 (Δ[CeCl3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[HIO2])/(Δt) = 1/4 (Δ[CeCl4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | HIO4 | cerous chloride | water | HIO2 | CeCl4 formula | HCl | HIO4 | CeCl_3 | H_2O | HIO2 | CeCl4 Hill formula | ClH | HIO4 | CeCl_3 | H_2O | HIO2 | CeCl4 name | hydrogen chloride | | cerous chloride | water | | IUPAC name | hydrogen chloride | | trichlorocerium | water | |

| hydrogen chloride | HIO4 | cerous chloride | water | HIO2 | CeCl4 molar mass | 36.46 g/mol | 191.91 g/mol | 246.5 g/mol | 18.015 g/mol | 159.91 g/mol | 281.9 g/mol phase | gas (at STP) | | solid (at STP) | liquid (at STP) | | melting point | -114.17 °C | | 848 °C | 0 °C | | boiling point | -85 °C | | | 99.9839 °C | | density | 0.00149 g/cm^3 (at 25 °C) | | 3.97 g/cm^3 | 1 g/cm^3 | | solubility in water | miscible | | | | | surface tension | | | | 0.0728 N/m | | dynamic viscosity | | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | | odorless | |