H2SO4 + KClO3 + K2S = H2O + Cl2 + K2SO4

H_2SO_4 sulfuric acid + KClO_3 potassium chlorate + K2S ⟶ H_2O water + Cl_2 chlorine + K_2SO_4 potassium sulfate

Balance the chemical equation algebraically: H_2SO_4 + KClO_3 + K2S ⟶ H_2O + Cl_2 + K_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KClO_3 + c_3 K2S ⟶ c_4 H_2O + c_5 Cl_2 + c_6 K_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 = c_4 + 4 c_6 S: | c_1 + c_3 = c_6 Cl: | c_2 = 2 c_5 K: | c_2 + 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 5/4 c_4 = 1 c_5 = 1 c_6 = 9/4 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 4 c_2 = 8 c_3 = 5 c_4 = 4 c_5 = 4 c_6 = 9 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 8 KClO_3 + 5 K2S ⟶ 4 H_2O + 4 Cl_2 + 9 K_2SO_4

+ + K2S ⟶ + +

sulfuric acid + potassium chlorate + K2S ⟶ water + chlorine + potassium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + KClO_3 + K2S ⟶ H_2O + Cl_2 + K_2SO_4 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_2SO_4 + 8 KClO_3 + 5 K2S ⟶ 4 H_2O + 4 Cl_2 + 9 K_2SO_4 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 | 4 | -4 KClO_3 | 8 | -8 K2S | 5 | -5 H_2O | 4 | 4 Cl_2 | 4 | 4 K_2SO_4 | 9 | 9 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KClO_3 | 8 | -8 | ([KClO3])^(-8) K2S | 5 | -5 | ([K2S])^(-5) H_2O | 4 | 4 | ([H2O])^4 Cl_2 | 4 | 4 | ([Cl2])^4 K_2SO_4 | 9 | 9 | ([K2SO4])^9 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])^(-4) ([KClO3])^(-8) ([K2S])^(-5) ([H2O])^4 ([Cl2])^4 ([K2SO4])^9 = (([H2O])^4 ([Cl2])^4 ([K2SO4])^9)/(([H2SO4])^4 ([KClO3])^8 ([K2S])^5)

Construct the rate of reaction expression for: H_2SO_4 + KClO_3 + K2S ⟶ H_2O + Cl_2 + K_2SO_4 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_2SO_4 + 8 KClO_3 + 5 K2S ⟶ 4 H_2O + 4 Cl_2 + 9 K_2SO_4 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 | 4 | -4 KClO_3 | 8 | -8 K2S | 5 | -5 H_2O | 4 | 4 Cl_2 | 4 | 4 K_2SO_4 | 9 | 9 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KClO_3 | 8 | -8 | -1/8 (Δ[KClO3])/(Δt) K2S | 5 | -5 | -1/5 (Δ[K2S])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Cl_2 | 4 | 4 | 1/4 (Δ[Cl2])/(Δt) K_2SO_4 | 9 | 9 | 1/9 (Δ[K2SO4])/(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[H2SO4])/(Δt) = -1/8 (Δ[KClO3])/(Δt) = -1/5 (Δ[K2S])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/4 (Δ[Cl2])/(Δt) = 1/9 (Δ[K2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium chlorate | K2S | water | chlorine | potassium sulfate formula | H_2SO_4 | KClO_3 | K2S | H_2O | Cl_2 | K_2SO_4 Hill formula | H_2O_4S | ClKO_3 | K2S | H_2O | Cl_2 | K_2O_4S name | sulfuric acid | potassium chlorate | | water | chlorine | potassium sulfate IUPAC name | sulfuric acid | potassium chlorate | | water | molecular chlorine | dipotassium sulfate

| sulfuric acid | potassium chlorate | K2S | water | chlorine | potassium sulfate molar mass | 98.07 g/mol | 122.5 g/mol | 110.26 g/mol | 18.015 g/mol | 70.9 g/mol | 174.25 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | gas (at STP) | melting point | 10.371 °C | 356 °C | | 0 °C | -101 °C | boiling point | 279.6 °C | | | 99.9839 °C | -34 °C | density | 1.8305 g/cm^3 | 2.34 g/cm^3 | | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | solubility in water | very soluble | 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 | |