S + KOH = H2O + K2S + K2SO3

S (mixed sulfur) + KOH (potassium hydroxide) ⟶ H_2O (water) + K2S + K_2SO_3 (potassium sulfite)

Balance the chemical equation algebraically: S + KOH ⟶ H_2O + K2S + K_2SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 KOH ⟶ c_3 H_2O + c_4 K2S + c_5 K_2SO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for S, H, K and O: S: | c_1 = c_4 + c_5 H: | c_2 = 2 c_3 K: | c_2 = 2 c_4 + 2 c_5 O: | c_2 = c_3 + 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 6 c_3 = 3 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 S + 6 KOH ⟶ 3 H_2O + 2 K2S + K_2SO_3

+ ⟶ + K2S +

mixed sulfur + potassium hydroxide ⟶ water + K2S + potassium sulfite

Construct the equilibrium constant, K, expression for: S + KOH ⟶ H_2O + K2S + K_2SO_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: 3 S + 6 KOH ⟶ 3 H_2O + 2 K2S + K_2SO_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 S | 3 | -3 KOH | 6 | -6 H_2O | 3 | 3 K2S | 2 | 2 K_2SO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S | 3 | -3 | ([S])^(-3) KOH | 6 | -6 | ([KOH])^(-6) H_2O | 3 | 3 | ([H2O])^3 K2S | 2 | 2 | ([K2S])^2 K_2SO_3 | 1 | 1 | [K2SO3] 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 = ([S])^(-3) ([KOH])^(-6) ([H2O])^3 ([K2S])^2 [K2SO3] = (([H2O])^3 ([K2S])^2 [K2SO3])/(([S])^3 ([KOH])^6)

Construct the rate of reaction expression for: S + KOH ⟶ H_2O + K2S + K_2SO_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: 3 S + 6 KOH ⟶ 3 H_2O + 2 K2S + K_2SO_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 S | 3 | -3 KOH | 6 | -6 H_2O | 3 | 3 K2S | 2 | 2 K_2SO_3 | 1 | 1 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 S | 3 | -3 | -1/3 (Δ[S])/(Δt) KOH | 6 | -6 | -1/6 (Δ[KOH])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K2S | 2 | 2 | 1/2 (Δ[K2S])/(Δt) K_2SO_3 | 1 | 1 | (Δ[K2SO3])/(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 = -1/3 (Δ[S])/(Δt) = -1/6 (Δ[KOH])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[K2S])/(Δt) = (Δ[K2SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | potassium hydroxide | water | K2S | potassium sulfite formula | S | KOH | H_2O | K2S | K_2SO_3 Hill formula | S | HKO | H_2O | K2S | K_2O_3S name | mixed sulfur | potassium hydroxide | water | | potassium sulfite IUPAC name | sulfur | potassium hydroxide | water | | dipotassium sulfite