H2O + S + HClO4 = H2SO4 + HCl

H_2O water + S mixed sulfur + HClO_4 perchloric acid ⟶ H_2SO_4 sulfuric acid + HCl hydrogen chloride

Balance the chemical equation algebraically: H_2O + S + HClO_4 ⟶ H_2SO_4 + HCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 S + c_3 HClO_4 ⟶ c_4 H_2SO_4 + c_5 HCl Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cl: H: | 2 c_1 + c_3 = 2 c_4 + c_5 O: | c_1 + 4 c_3 = 4 c_4 S: | c_2 = c_4 Cl: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4/3 c_2 = 4/3 c_3 = 1 c_4 = 4/3 c_5 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 4 c_2 = 4 c_3 = 3 c_4 = 4 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + 4 S + 3 HClO_4 ⟶ 4 H_2SO_4 + 3 HCl

+ + ⟶ +

water + mixed sulfur + perchloric acid ⟶ sulfuric acid + hydrogen chloride

Construct the equilibrium constant, K, expression for: H_2O + S + HClO_4 ⟶ H_2SO_4 + HCl 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 + 4 S + 3 HClO_4 ⟶ 4 H_2SO_4 + 3 HCl 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 S | 4 | -4 HClO_4 | 3 | -3 H_2SO_4 | 4 | 4 HCl | 3 | 3 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) S | 4 | -4 | ([S])^(-4) HClO_4 | 3 | -3 | ([HClO4])^(-3) H_2SO_4 | 4 | 4 | ([H2SO4])^4 HCl | 3 | 3 | ([HCl])^3 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) ([S])^(-4) ([HClO4])^(-3) ([H2SO4])^4 ([HCl])^3 = (([H2SO4])^4 ([HCl])^3)/(([H2O])^4 ([S])^4 ([HClO4])^3)

Construct the rate of reaction expression for: H_2O + S + HClO_4 ⟶ H_2SO_4 + HCl 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 + 4 S + 3 HClO_4 ⟶ 4 H_2SO_4 + 3 HCl 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 S | 4 | -4 HClO_4 | 3 | -3 H_2SO_4 | 4 | 4 HCl | 3 | 3 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) S | 4 | -4 | -1/4 (Δ[S])/(Δt) HClO_4 | 3 | -3 | -1/3 (Δ[HClO4])/(Δt) H_2SO_4 | 4 | 4 | 1/4 (Δ[H2SO4])/(Δt) HCl | 3 | 3 | 1/3 (Δ[HCl])/(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) = -1/4 (Δ[S])/(Δt) = -1/3 (Δ[HClO4])/(Δt) = 1/4 (Δ[H2SO4])/(Δt) = 1/3 (Δ[HCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | mixed sulfur | perchloric acid | sulfuric acid | hydrogen chloride formula | H_2O | S | HClO_4 | H_2SO_4 | HCl Hill formula | H_2O | S | ClHO_4 | H_2O_4S | ClH name | water | mixed sulfur | perchloric acid | sulfuric acid | hydrogen chloride IUPAC name | water | sulfur | perchloric acid | sulfuric acid | hydrogen chloride

| water | mixed sulfur | perchloric acid | sulfuric acid | hydrogen chloride molar mass | 18.015 g/mol | 32.06 g/mol | 100.5 g/mol | 98.07 g/mol | 36.46 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | gas (at STP) melting point | 0 °C | 112.8 °C | -112 °C | 10.371 °C | -114.17 °C boiling point | 99.9839 °C | 444.7 °C | 90 °C | 279.6 °C | -85 °C density | 1 g/cm^3 | 2.07 g/cm^3 | 1.77 g/cm^3 | 1.8305 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) solubility in water | | | very soluble | very soluble | miscible surface tension | 0.0728 N/m | | | 0.0735 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8×10^-4 Pa s (at 25 °C) | 0.021 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |