Si + MnO = SiO2 + Mn3Si

Si silicon + MnO manganese monoxide ⟶ SiO_2 silicon dioxide + Mn3Si

Balance the chemical equation algebraically: Si + MnO ⟶ SiO_2 + Mn3Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Si + c_2 MnO ⟶ c_3 SiO_2 + c_4 Mn3Si Set the number of atoms in the reactants equal to the number of atoms in the products for Si, Mn and O: Si: | c_1 = c_3 + c_4 Mn: | c_2 = 3 c_4 O: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5/2 c_2 = 3 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 6 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 Si + 6 MnO ⟶ 3 SiO_2 + 2 Mn3Si

+ ⟶ + Mn3Si

silicon + manganese monoxide ⟶ silicon dioxide + Mn3Si

Construct the equilibrium constant, K, expression for: Si + MnO ⟶ SiO_2 + Mn3Si 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: 5 Si + 6 MnO ⟶ 3 SiO_2 + 2 Mn3Si 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 Si | 5 | -5 MnO | 6 | -6 SiO_2 | 3 | 3 Mn3Si | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Si | 5 | -5 | ([Si])^(-5) MnO | 6 | -6 | ([MnO])^(-6) SiO_2 | 3 | 3 | ([SiO2])^3 Mn3Si | 2 | 2 | ([Mn3Si])^2 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 = ([Si])^(-5) ([MnO])^(-6) ([SiO2])^3 ([Mn3Si])^2 = (([SiO2])^3 ([Mn3Si])^2)/(([Si])^5 ([MnO])^6)

Construct the rate of reaction expression for: Si + MnO ⟶ SiO_2 + Mn3Si 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: 5 Si + 6 MnO ⟶ 3 SiO_2 + 2 Mn3Si 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 Si | 5 | -5 MnO | 6 | -6 SiO_2 | 3 | 3 Mn3Si | 2 | 2 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 Si | 5 | -5 | -1/5 (Δ[Si])/(Δt) MnO | 6 | -6 | -1/6 (Δ[MnO])/(Δt) SiO_2 | 3 | 3 | 1/3 (Δ[SiO2])/(Δt) Mn3Si | 2 | 2 | 1/2 (Δ[Mn3Si])/(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 = -1/5 (Δ[Si])/(Δt) = -1/6 (Δ[MnO])/(Δt) = 1/3 (Δ[SiO2])/(Δt) = 1/2 (Δ[Mn3Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silicon | manganese monoxide | silicon dioxide | Mn3Si formula | Si | MnO | SiO_2 | Mn3Si Hill formula | Si | MnO | O_2Si | Mn3Si name | silicon | manganese monoxide | silicon dioxide | IUPAC name | silicon | oxomanganese | dioxosilane |

| silicon | manganese monoxide | silicon dioxide | Mn3Si molar mass | 28.085 g/mol | 70.937 g/mol | 60.083 g/mol | 192.899 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 1410 °C | 1840 °C | 1713 °C | boiling point | 2355 °C | | 2950 °C | density | 2.33 g/cm^3 | 5.45 g/cm^3 | 2.196 g/cm^3 | solubility in water | insoluble | insoluble | insoluble | odor | | | odorless |