SO3 + K2SO3 = K2SO4 + SO2

SO_3 sulfur trioxide + K_2SO_3 potassium sulfite ⟶ K_2SO_4 potassium sulfate + SO_2 sulfur dioxide

Balance the chemical equation algebraically: SO_3 + K_2SO_3 ⟶ K_2SO_4 + SO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_3 + c_2 K_2SO_3 ⟶ c_3 K_2SO_4 + c_4 SO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, S and K: O: | 3 c_1 + 3 c_2 = 4 c_3 + 2 c_4 S: | c_1 + c_2 = c_3 + c_4 K: | 2 c_2 = 2 c_3 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | SO_3 + K_2SO_3 ⟶ K_2SO_4 + SO_2

+ ⟶ +

sulfur trioxide + potassium sulfite ⟶ potassium sulfate + sulfur dioxide

Construct the equilibrium constant, K, expression for: SO_3 + K_2SO_3 ⟶ K_2SO_4 + SO_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: SO_3 + K_2SO_3 ⟶ K_2SO_4 + SO_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 SO_3 | 1 | -1 K_2SO_3 | 1 | -1 K_2SO_4 | 1 | 1 SO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_3 | 1 | -1 | ([SO3])^(-1) K_2SO_3 | 1 | -1 | ([K2SO3])^(-1) K_2SO_4 | 1 | 1 | [K2SO4] SO_2 | 1 | 1 | [SO2] 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 = ([SO3])^(-1) ([K2SO3])^(-1) [K2SO4] [SO2] = ([K2SO4] [SO2])/([SO3] [K2SO3])

Construct the rate of reaction expression for: SO_3 + K_2SO_3 ⟶ K_2SO_4 + SO_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: SO_3 + K_2SO_3 ⟶ K_2SO_4 + SO_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 SO_3 | 1 | -1 K_2SO_3 | 1 | -1 K_2SO_4 | 1 | 1 SO_2 | 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 SO_3 | 1 | -1 | -(Δ[SO3])/(Δt) K_2SO_3 | 1 | -1 | -(Δ[K2SO3])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(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[SO3])/(Δt) = -(Δ[K2SO3])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[SO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur trioxide | potassium sulfite | potassium sulfate | sulfur dioxide formula | SO_3 | K_2SO_3 | K_2SO_4 | SO_2 Hill formula | O_3S | K_2O_3S | K_2O_4S | O_2S name | sulfur trioxide | potassium sulfite | potassium sulfate | sulfur dioxide IUPAC name | sulfur trioxide | dipotassium sulfite | dipotassium sulfate | sulfur dioxide

| sulfur trioxide | potassium sulfite | potassium sulfate | sulfur dioxide molar mass | 80.06 g/mol | 158.25 g/mol | 174.25 g/mol | 64.06 g/mol phase | liquid (at STP) | | | gas (at STP) melting point | 16.8 °C | | | -73 °C boiling point | 44.7 °C | | | -10 °C density | 1.97 g/cm^3 | | | 0.002619 g/cm^3 (at 25 °C) solubility in water | reacts | | soluble | surface tension | | | | 0.02859 N/m dynamic viscosity | 0.00159 Pa s (at 30 °C) | | | 1.282×10^-5 Pa s (at 25 °C)