SO2 + MgO = MgSO3

SO_2 sulfur dioxide + MgO magnesium oxide ⟶ MgSO3

Balance the chemical equation algebraically: SO_2 + MgO ⟶ MgSO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 MgO ⟶ c_3 MgSO3 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 + c_2 = 3 c_3 S: | c_1 = c_3 Mg: | c_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 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | SO_2 + MgO ⟶ MgSO3

+ ⟶ MgSO3

sulfur dioxide + magnesium oxide ⟶ MgSO3

Construct the equilibrium constant, K, expression for: SO_2 + MgO ⟶ MgSO3 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_2 + MgO ⟶ MgSO3 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 | 1 | -1 MgO | 1 | -1 MgSO3 | 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 | 1 | -1 | ([SO2])^(-1) MgO | 1 | -1 | ([MgO])^(-1) MgSO3 | 1 | 1 | [MgSO3] 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])^(-1) ([MgO])^(-1) [MgSO3] = ([MgSO3])/([SO2] [MgO])

Construct the rate of reaction expression for: SO_2 + MgO ⟶ MgSO3 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_2 + MgO ⟶ MgSO3 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 | 1 | -1 MgO | 1 | -1 MgSO3 | 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 | 1 | -1 | -(Δ[SO2])/(Δt) MgO | 1 | -1 | -(Δ[MgO])/(Δt) MgSO3 | 1 | 1 | (Δ[MgSO3])/(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[SO2])/(Δt) = -(Δ[MgO])/(Δt) = (Δ[MgSO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | magnesium oxide | MgSO3 formula | SO_2 | MgO | MgSO3 Hill formula | O_2S | MgO | MgO3S name | sulfur dioxide | magnesium oxide | IUPAC name | sulfur dioxide | oxomagnesium |

| sulfur dioxide | magnesium oxide | MgSO3 molar mass | 64.06 g/mol | 40.304 g/mol | 104.4 g/mol phase | gas (at STP) | solid (at STP) | melting point | -73 °C | 2852 °C | boiling point | -10 °C | 3600 °C | density | 0.002619 g/cm^3 (at 25 °C) | 3.58 g/cm^3 | surface tension | 0.02859 N/m | | dynamic viscosity | 1.282×10^-5 Pa s (at 25 °C) | | odor | | odorless |