HCl + Fe + H2O2 = H2O + FeCl3

HCl hydrogen chloride + Fe iron + H_2O_2 hydrogen peroxide ⟶ H_2O water + FeCl_3 iron(III) chloride

Balance the chemical equation algebraically: HCl + Fe + H_2O_2 ⟶ H_2O + FeCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Fe + c_3 H_2O_2 ⟶ c_4 H_2O + c_5 FeCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Fe and O: Cl: | c_1 = 3 c_5 H: | c_1 + 2 c_3 = 2 c_4 Fe: | c_2 = c_5 O: | 2 c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3/2 c_4 = 3 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 6 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + 2 Fe + 3 H_2O_2 ⟶ 6 H_2O + 2 FeCl_3

+ + ⟶ +

hydrogen chloride + iron + hydrogen peroxide ⟶ water + iron(III) chloride

Construct the equilibrium constant, K, expression for: HCl + Fe + H_2O_2 ⟶ H_2O + FeCl_3 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: 6 HCl + 2 Fe + 3 H_2O_2 ⟶ 6 H_2O + 2 FeCl_3 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 | 6 | -6 Fe | 2 | -2 H_2O_2 | 3 | -3 H_2O | 6 | 6 FeCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) Fe | 2 | -2 | ([Fe])^(-2) H_2O_2 | 3 | -3 | ([H2O2])^(-3) H_2O | 6 | 6 | ([H2O])^6 FeCl_3 | 2 | 2 | ([FeCl3])^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 = ([HCl])^(-6) ([Fe])^(-2) ([H2O2])^(-3) ([H2O])^6 ([FeCl3])^2 = (([H2O])^6 ([FeCl3])^2)/(([HCl])^6 ([Fe])^2 ([H2O2])^3)

Construct the rate of reaction expression for: HCl + Fe + H_2O_2 ⟶ H_2O + FeCl_3 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: 6 HCl + 2 Fe + 3 H_2O_2 ⟶ 6 H_2O + 2 FeCl_3 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 | 6 | -6 Fe | 2 | -2 H_2O_2 | 3 | -3 H_2O | 6 | 6 FeCl_3 | 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 HCl | 6 | -6 | -1/6 (Δ[HCl])/(Δt) Fe | 2 | -2 | -1/2 (Δ[Fe])/(Δt) H_2O_2 | 3 | -3 | -1/3 (Δ[H2O2])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) FeCl_3 | 2 | 2 | 1/2 (Δ[FeCl3])/(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 = -1/6 (Δ[HCl])/(Δt) = -1/2 (Δ[Fe])/(Δt) = -1/3 (Δ[H2O2])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/2 (Δ[FeCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | iron | hydrogen peroxide | water | iron(III) chloride formula | HCl | Fe | H_2O_2 | H_2O | FeCl_3 Hill formula | ClH | Fe | H_2O_2 | H_2O | Cl_3Fe name | hydrogen chloride | iron | hydrogen peroxide | water | iron(III) chloride IUPAC name | hydrogen chloride | iron | hydrogen peroxide | water | trichloroiron

| hydrogen chloride | iron | hydrogen peroxide | water | iron(III) chloride molar mass | 36.46 g/mol | 55.845 g/mol | 34.014 g/mol | 18.015 g/mol | 162.2 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | -114.17 °C | 1535 °C | -0.43 °C | 0 °C | 304 °C boiling point | -85 °C | 2750 °C | 150.2 °C | 99.9839 °C | density | 0.00149 g/cm^3 (at 25 °C) | 7.874 g/cm^3 | 1.44 g/cm^3 | 1 g/cm^3 | solubility in water | miscible | insoluble | miscible | | surface tension | | | 0.0804 N/m | 0.0728 N/m | dynamic viscosity | | | 0.001249 Pa s (at 20 °C) | 8.9×10^-4 Pa s (at 25 °C) | odor | | | | odorless |