MgO + Si = Mg + SiO2

MgO magnesium oxide + Si silicon ⟶ Mg magnesium + SiO_2 silicon dioxide

Balance the chemical equation algebraically: MgO + Si ⟶ Mg + SiO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MgO + c_2 Si ⟶ c_3 Mg + c_4 SiO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, O and Si: Mg: | c_1 = c_3 O: | c_1 = 2 c_4 Si: | 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 MgO + Si ⟶ 2 Mg + SiO_2

+ ⟶ +

magnesium oxide + silicon ⟶ magnesium + silicon dioxide

| magnesium oxide | silicon | magnesium | silicon dioxide molecular enthalpy | -601.6 kJ/mol | 0 kJ/mol | 0 kJ/mol | -911 kJ/mol total enthalpy | -1203 kJ/mol | 0 kJ/mol | 0 kJ/mol | -911 kJ/mol | H_initial = -1203 kJ/mol | | H_final = -911 kJ/mol | ΔH_rxn^0 | -911 kJ/mol - -1203 kJ/mol = 292.2 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: MgO + Si ⟶ Mg + SiO_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: 2 MgO + Si ⟶ 2 Mg + SiO_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 MgO | 2 | -2 Si | 1 | -1 Mg | 2 | 2 SiO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MgO | 2 | -2 | ([MgO])^(-2) Si | 1 | -1 | ([Si])^(-1) Mg | 2 | 2 | ([Mg])^2 SiO_2 | 1 | 1 | [SiO2] 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 = ([MgO])^(-2) ([Si])^(-1) ([Mg])^2 [SiO2] = (([Mg])^2 [SiO2])/(([MgO])^2 [Si])

Construct the rate of reaction expression for: MgO + Si ⟶ Mg + SiO_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: 2 MgO + Si ⟶ 2 Mg + SiO_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 MgO | 2 | -2 Si | 1 | -1 Mg | 2 | 2 SiO_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 MgO | 2 | -2 | -1/2 (Δ[MgO])/(Δt) Si | 1 | -1 | -(Δ[Si])/(Δt) Mg | 2 | 2 | 1/2 (Δ[Mg])/(Δt) SiO_2 | 1 | 1 | (Δ[SiO2])/(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[MgO])/(Δt) = -(Δ[Si])/(Δt) = 1/2 (Δ[Mg])/(Δt) = (Δ[SiO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium oxide | silicon | magnesium | silicon dioxide formula | MgO | Si | Mg | SiO_2 Hill formula | MgO | Si | Mg | O_2Si name | magnesium oxide | silicon | magnesium | silicon dioxide IUPAC name | oxomagnesium | silicon | magnesium | dioxosilane

| magnesium oxide | silicon | magnesium | silicon dioxide molar mass | 40.304 g/mol | 28.085 g/mol | 24.305 g/mol | 60.083 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 2852 °C | 1410 °C | 648 °C | 1713 °C boiling point | 3600 °C | 2355 °C | 1090 °C | 2950 °C density | 3.58 g/cm^3 | 2.33 g/cm^3 | 1.738 g/cm^3 | 2.196 g/cm^3 solubility in water | | insoluble | reacts | insoluble odor | odorless | | | odorless