H2SO4 + KClO4 + Sb = H2O + KCl + Sb2(SO4)3

H_2SO_4 sulfuric acid + KClO_4 potassium perchlorate + Sb gray antimony ⟶ H_2O water + KCl potassium chloride + O_12S_3Sb_2 antimony(III) sulfate

Balance the chemical equation algebraically: H_2SO_4 + KClO_4 + Sb ⟶ H_2O + KCl + O_12S_3Sb_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KClO_4 + c_3 Sb ⟶ c_4 H_2O + c_5 KCl + c_6 O_12S_3Sb_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl, K and Sb: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 12 c_6 S: | c_1 = 3 c_6 Cl: | c_2 = c_5 K: | c_2 = c_5 Sb: | c_3 = 2 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 = 8/3 c_4 = 4 c_5 = 1 c_6 = 4/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 12 c_2 = 3 c_3 = 8 c_4 = 12 c_5 = 3 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2SO_4 + 3 KClO_4 + 8 Sb ⟶ 12 H_2O + 3 KCl + 4 O_12S_3Sb_2

+ + ⟶ + +

sulfuric acid + potassium perchlorate + gray antimony ⟶ water + potassium chloride + antimony(III) sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + KClO_4 + Sb ⟶ H_2O + KCl + O_12S_3Sb_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: 12 H_2SO_4 + 3 KClO_4 + 8 Sb ⟶ 12 H_2O + 3 KCl + 4 O_12S_3Sb_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_2SO_4 | 12 | -12 KClO_4 | 3 | -3 Sb | 8 | -8 H_2O | 12 | 12 KCl | 3 | 3 O_12S_3Sb_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 12 | -12 | ([H2SO4])^(-12) KClO_4 | 3 | -3 | ([KClO4])^(-3) Sb | 8 | -8 | ([Sb])^(-8) H_2O | 12 | 12 | ([H2O])^12 KCl | 3 | 3 | ([KCl])^3 O_12S_3Sb_2 | 4 | 4 | ([O12S3Sb2])^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 = ([H2SO4])^(-12) ([KClO4])^(-3) ([Sb])^(-8) ([H2O])^12 ([KCl])^3 ([O12S3Sb2])^4 = (([H2O])^12 ([KCl])^3 ([O12S3Sb2])^4)/(([H2SO4])^12 ([KClO4])^3 ([Sb])^8)

Construct the rate of reaction expression for: H_2SO_4 + KClO_4 + Sb ⟶ H_2O + KCl + O_12S_3Sb_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: 12 H_2SO_4 + 3 KClO_4 + 8 Sb ⟶ 12 H_2O + 3 KCl + 4 O_12S_3Sb_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_2SO_4 | 12 | -12 KClO_4 | 3 | -3 Sb | 8 | -8 H_2O | 12 | 12 KCl | 3 | 3 O_12S_3Sb_2 | 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 H_2SO_4 | 12 | -12 | -1/12 (Δ[H2SO4])/(Δt) KClO_4 | 3 | -3 | -1/3 (Δ[KClO4])/(Δt) Sb | 8 | -8 | -1/8 (Δ[Sb])/(Δt) H_2O | 12 | 12 | 1/12 (Δ[H2O])/(Δt) KCl | 3 | 3 | 1/3 (Δ[KCl])/(Δt) O_12S_3Sb_2 | 4 | 4 | 1/4 (Δ[O12S3Sb2])/(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 = -1/12 (Δ[H2SO4])/(Δt) = -1/3 (Δ[KClO4])/(Δt) = -1/8 (Δ[Sb])/(Δt) = 1/12 (Δ[H2O])/(Δt) = 1/3 (Δ[KCl])/(Δt) = 1/4 (Δ[O12S3Sb2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium perchlorate | gray antimony | water | potassium chloride | antimony(III) sulfate formula | H_2SO_4 | KClO_4 | Sb | H_2O | KCl | O_12S_3Sb_2 Hill formula | H_2O_4S | ClKO_4 | Sb | H_2O | ClK | O_12S_3Sb_2 name | sulfuric acid | potassium perchlorate | gray antimony | water | potassium chloride | antimony(III) sulfate IUPAC name | sulfuric acid | potassium perchlorate | antimony | water | potassium chloride | antimony(+3) cation trisulfate

| sulfuric acid | potassium perchlorate | gray antimony | water | potassium chloride | antimony(III) sulfate molar mass | 98.07 g/mol | 138.54 g/mol | 121.76 g/mol | 18.015 g/mol | 74.55 g/mol | 531.7 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | melting point | 10.371 °C | 400 °C | 630 °C | 0 °C | 770 °C | boiling point | 279.6 °C | | 1587 °C | 99.9839 °C | 1420 °C | density | 1.8305 g/cm^3 | 2.5239 g/cm^3 | 6.69 g/cm^3 | 1 g/cm^3 | 1.98 g/cm^3 | 3.6246 g/cm^3 solubility in water | very soluble | | | | soluble | surface tension | 0.0735 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | | | odorless | odorless |