H2O + Cl2 + Se = H2SeO4 + HCl2

H_2O water + Cl_2 chlorine + Se gray selenium ⟶ H_2SeO_4 selenic acid + HCl2

Balance the chemical equation algebraically: H_2O + Cl_2 + Se ⟶ H_2SeO_4 + HCl2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cl_2 + c_3 Se ⟶ c_4 H_2SeO_4 + c_5 HCl2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl and Se: H: | 2 c_1 = 2 c_4 + c_5 O: | c_1 = 4 c_4 Cl: | 2 c_2 = 2 c_5 Se: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 6 c_3 = 1 c_4 = 1 c_5 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + 6 Cl_2 + Se ⟶ H_2SeO_4 + 6 HCl2

+ + ⟶ + HCl2

water + chlorine + gray selenium ⟶ selenic acid + HCl2

Construct the equilibrium constant, K, expression for: H_2O + Cl_2 + Se ⟶ H_2SeO_4 + HCl2 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 H_2O + 6 Cl_2 + Se ⟶ H_2SeO_4 + 6 HCl2 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 | 4 | -4 Cl_2 | 6 | -6 Se | 1 | -1 H_2SeO_4 | 1 | 1 HCl2 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 4 | -4 | ([H2O])^(-4) Cl_2 | 6 | -6 | ([Cl2])^(-6) Se | 1 | -1 | ([Se])^(-1) H_2SeO_4 | 1 | 1 | [H2SeO4] HCl2 | 6 | 6 | ([HCl2])^6 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])^(-4) ([Cl2])^(-6) ([Se])^(-1) [H2SeO4] ([HCl2])^6 = ([H2SeO4] ([HCl2])^6)/(([H2O])^4 ([Cl2])^6 [Se])

Construct the rate of reaction expression for: H_2O + Cl_2 + Se ⟶ H_2SeO_4 + HCl2 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 H_2O + 6 Cl_2 + Se ⟶ H_2SeO_4 + 6 HCl2 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 | 4 | -4 Cl_2 | 6 | -6 Se | 1 | -1 H_2SeO_4 | 1 | 1 HCl2 | 6 | 6 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 | 4 | -4 | -1/4 (Δ[H2O])/(Δt) Cl_2 | 6 | -6 | -1/6 (Δ[Cl2])/(Δt) Se | 1 | -1 | -(Δ[Se])/(Δt) H_2SeO_4 | 1 | 1 | (Δ[H2SeO4])/(Δt) HCl2 | 6 | 6 | 1/6 (Δ[HCl2])/(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[H2O])/(Δt) = -1/6 (Δ[Cl2])/(Δt) = -(Δ[Se])/(Δt) = (Δ[H2SeO4])/(Δt) = 1/6 (Δ[HCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | chlorine | gray selenium | selenic acid | HCl2 formula | H_2O | Cl_2 | Se | H_2SeO_4 | HCl2 Hill formula | H_2O | Cl_2 | Se | H_2O_4Se | HCl2 name | water | chlorine | gray selenium | selenic acid | IUPAC name | water | molecular chlorine | selenium | selenic acid |

| water | chlorine | gray selenium | selenic acid | HCl2 molar mass | 18.015 g/mol | 70.9 g/mol | 78.971 g/mol | 144.98 g/mol | 71.91 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | | melting point | 0 °C | -101 °C | 217 °C | | boiling point | 99.9839 °C | -34 °C | 684.9 °C | | density | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 4.81 g/cm^3 | 2.511 g/cm^3 | solubility in water | | | insoluble | | surface tension | 0.0728 N/m | | 0.1055 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 0.221 Pa s (at 220 °C) | | odor | odorless | | | |