KOH + H2S2O7 = H2O + K2S2O7

KOH potassium hydroxide + H_2SO_4SO_3 oleum ⟶ H_2O water + K_2S_2O_7 potassium pyrosulfate

Balance the chemical equation algebraically: KOH + H_2SO_4SO_3 ⟶ H_2O + K_2S_2O_7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 H_2SO_4SO_3 ⟶ c_3 H_2O + c_4 K_2S_2O_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O and S: H: | c_1 + 2 c_2 = 2 c_3 K: | c_1 = 2 c_4 O: | c_1 + 7 c_2 = c_3 + 7 c_4 S: | 2 c_2 = 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + H_2SO_4SO_3 ⟶ 2 H_2O + K_2S_2O_7

+ ⟶ +

potassium hydroxide + oleum ⟶ water + potassium pyrosulfate

Construct the equilibrium constant, K, expression for: KOH + H_2SO_4SO_3 ⟶ H_2O + K_2S_2O_7 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: 2 KOH + H_2SO_4SO_3 ⟶ 2 H_2O + K_2S_2O_7 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 KOH | 2 | -2 H_2SO_4SO_3 | 1 | -1 H_2O | 2 | 2 K_2S_2O_7 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) H_2SO_4SO_3 | 1 | -1 | ([H2SO4SO3])^(-1) H_2O | 2 | 2 | ([H2O])^2 K_2S_2O_7 | 1 | 1 | [K2S2O7] 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 = ([KOH])^(-2) ([H2SO4SO3])^(-1) ([H2O])^2 [K2S2O7] = (([H2O])^2 [K2S2O7])/(([KOH])^2 [H2SO4SO3])

Construct the rate of reaction expression for: KOH + H_2SO_4SO_3 ⟶ H_2O + K_2S_2O_7 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: 2 KOH + H_2SO_4SO_3 ⟶ 2 H_2O + K_2S_2O_7 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 KOH | 2 | -2 H_2SO_4SO_3 | 1 | -1 H_2O | 2 | 2 K_2S_2O_7 | 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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) H_2SO_4SO_3 | 1 | -1 | -(Δ[H2SO4SO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2S_2O_7 | 1 | 1 | (Δ[K2S2O7])/(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 = -1/2 (Δ[KOH])/(Δt) = -(Δ[H2SO4SO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2S2O7])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | oleum | water | potassium pyrosulfate formula | KOH | H_2SO_4SO_3 | H_2O | K_2S_2O_7 Hill formula | HKO | H_2O_7S_2 | H_2O | K_2O_7S_2 name | potassium hydroxide | oleum | water | potassium pyrosulfate IUPAC name | potassium hydroxide | sulfuric acid; sulfur trioxide | water | dipotassium sulfonato sulfate

| potassium hydroxide | oleum | water | potassium pyrosulfate molar mass | 56.105 g/mol | 178.1 g/mol | 18.015 g/mol | 254.31 g/mol phase | solid (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | 406 °C | 1 °C | 0 °C | 325 °C boiling point | 1327 °C | 142 °C | 99.9839 °C | density | 2.044 g/cm^3 | 1.94 g/cm^3 | 1 g/cm^3 | 2.28 g/cm^3 solubility in water | soluble | reacts | | soluble surface tension | | | 0.0728 N/m | dynamic viscosity | 0.001 Pa s (at 550 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |