H2SO4 + SO3 + KHF2 = K2SO4 + HSO3F

Input interpretation

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H_2SO_4 sulfuric acid + SO_3 sulfur trioxide + KHF_2 potassium bifluoride ⟶ K_2SO_4 potassium sulfate + FSO_3H fluorosulfonic acid

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + SO_3 + KHF_2 ⟶ K_2SO_4 + FSO_3H Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 SO_3 + c_3 KHF_2 ⟶ c_4 K_2SO_4 + c_5 FSO_3H Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, F and K: H: | 2 c_1 + c_3 = c_5 O: | 4 c_1 + 3 c_2 = 4 c_4 + 3 c_5 S: | c_1 + c_2 = c_4 + c_5 F: | 2 c_3 = c_5 K: | c_3 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 2 c_4 = 1 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + 4 SO_3 + 2 KHF_2 ⟶ K_2SO_4 + 4 FSO_3H

+ + ⟶ +

Names

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sulfuric acid + sulfur trioxide + potassium bifluoride ⟶ potassium sulfate + fluorosulfonic acid

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + SO_3 + KHF_2 ⟶ K_2SO_4 + FSO_3H 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: H_2SO_4 + 4 SO_3 + 2 KHF_2 ⟶ K_2SO_4 + 4 FSO_3H 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 | 1 | -1 SO_3 | 4 | -4 KHF_2 | 2 | -2 K_2SO_4 | 1 | 1 FSO_3H | 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 | 1 | -1 | ([H2SO4])^(-1) SO_3 | 4 | -4 | ([SO3])^(-4) KHF_2 | 2 | -2 | ([KHF2])^(-2) K_2SO_4 | 1 | 1 | [K2SO4] FSO_3H | 4 | 4 | ([FSO3H])^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])^(-1) ([SO3])^(-4) ([KHF2])^(-2) [K2SO4] ([FSO3H])^4 = ([K2SO4] ([FSO3H])^4)/([H2SO4] ([SO3])^4 ([KHF2])^2)

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + SO_3 + KHF_2 ⟶ K_2SO_4 + FSO_3H 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: H_2SO_4 + 4 SO_3 + 2 KHF_2 ⟶ K_2SO_4 + 4 FSO_3H 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 | 1 | -1 SO_3 | 4 | -4 KHF_2 | 2 | -2 K_2SO_4 | 1 | 1 FSO_3H | 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 | 1 | -1 | -(Δ[H2SO4])/(Δt) SO_3 | 4 | -4 | -1/4 (Δ[SO3])/(Δt) KHF_2 | 2 | -2 | -1/2 (Δ[KHF2])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) FSO_3H | 4 | 4 | 1/4 (Δ[FSO3H])/(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 = -(Δ[H2SO4])/(Δt) = -1/4 (Δ[SO3])/(Δt) = -1/2 (Δ[KHF2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/4 (Δ[FSO3H])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)