SO2 + MgSO4 = SO3 + MgSO2

SO_2 sulfur dioxide + MgSO_4 magnesium sulfate ⟶ SO_3 sulfur trioxide + MgSO2

Balance the chemical equation algebraically: SO_2 + MgSO_4 ⟶ SO_3 + MgSO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 MgSO_4 ⟶ c_3 SO_3 + c_4 MgSO2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, S and Mg: O: | 2 c_1 + 4 c_2 = 3 c_3 + 2 c_4 S: | c_1 + c_2 = c_3 + c_4 Mg: | c_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 SO_2 + MgSO_4 ⟶ 2 SO_3 + MgSO2

+ ⟶ + MgSO2

sulfur dioxide + magnesium sulfate ⟶ sulfur trioxide + MgSO2

Construct the equilibrium constant, K, expression for: SO_2 + MgSO_4 ⟶ SO_3 + MgSO2 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 SO_2 + MgSO_4 ⟶ 2 SO_3 + MgSO2 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_2 | 2 | -2 MgSO_4 | 1 | -1 SO_3 | 2 | 2 MgSO2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 2 | -2 | ([SO2])^(-2) MgSO_4 | 1 | -1 | ([MgSO4])^(-1) SO_3 | 2 | 2 | ([SO3])^2 MgSO2 | 1 | 1 | [MgSO2] 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 = ([SO2])^(-2) ([MgSO4])^(-1) ([SO3])^2 [MgSO2] = (([SO3])^2 [MgSO2])/(([SO2])^2 [MgSO4])

Construct the rate of reaction expression for: SO_2 + MgSO_4 ⟶ SO_3 + MgSO2 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 SO_2 + MgSO_4 ⟶ 2 SO_3 + MgSO2 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_2 | 2 | -2 MgSO_4 | 1 | -1 SO_3 | 2 | 2 MgSO2 | 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_2 | 2 | -2 | -1/2 (Δ[SO2])/(Δt) MgSO_4 | 1 | -1 | -(Δ[MgSO4])/(Δt) SO_3 | 2 | 2 | 1/2 (Δ[SO3])/(Δt) MgSO2 | 1 | 1 | (Δ[MgSO2])/(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[SO2])/(Δt) = -(Δ[MgSO4])/(Δt) = 1/2 (Δ[SO3])/(Δt) = (Δ[MgSO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | magnesium sulfate | sulfur trioxide | MgSO2 formula | SO_2 | MgSO_4 | SO_3 | MgSO2 Hill formula | O_2S | MgO_4S | O_3S | MgO2S name | sulfur dioxide | magnesium sulfate | sulfur trioxide |

| sulfur dioxide | magnesium sulfate | sulfur trioxide | MgSO2 molar mass | 64.06 g/mol | 120.4 g/mol | 80.06 g/mol | 88.36 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | melting point | -73 °C | | 16.8 °C | boiling point | -10 °C | | 44.7 °C | density | 0.002619 g/cm^3 (at 25 °C) | | 1.97 g/cm^3 | solubility in water | | soluble | reacts | surface tension | 0.02859 N/m | | | dynamic viscosity | 1.282×10^-5 Pa s (at 25 °C) | | 0.00159 Pa s (at 30 °C) |