Si + Mn2O3 = SiO2 + Mn

Si (silicon) + Mn_2O_3 (manganese(III) oxide) ⟶ SiO_2 (silicon dioxide) + Mn (manganese)

Balance the chemical equation algebraically: Si + Mn_2O_3 ⟶ SiO_2 + Mn Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Si + c_2 Mn_2O_3 ⟶ c_3 SiO_2 + c_4 Mn 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 Mn: | 2 c_2 = c_4 O: | 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Si + 2 Mn_2O_3 ⟶ 3 SiO_2 + 4 Mn

+ ⟶ +

silicon + manganese(III) oxide ⟶ silicon dioxide + manganese

| silicon | manganese(III) oxide | silicon dioxide | manganese molecular enthalpy | 0 kJ/mol | -959 kJ/mol | -911 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -1918 kJ/mol | -2733 kJ/mol | 0 kJ/mol | H_initial = -1918 kJ/mol | | H_final = -2733 kJ/mol | ΔH_rxn^0 | -2733 kJ/mol - -1918 kJ/mol = -815 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: Si + Mn_2O_3 ⟶ SiO_2 + Mn 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: 3 Si + 2 Mn_2O_3 ⟶ 3 SiO_2 + 4 Mn 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 | 3 | -3 Mn_2O_3 | 2 | -2 SiO_2 | 3 | 3 Mn | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Si | 3 | -3 | ([Si])^(-3) Mn_2O_3 | 2 | -2 | ([Mn2O3])^(-2) SiO_2 | 3 | 3 | ([SiO2])^3 Mn | 4 | 4 | ([Mn])^4 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])^(-3) ([Mn2O3])^(-2) ([SiO2])^3 ([Mn])^4 = (([SiO2])^3 ([Mn])^4)/(([Si])^3 ([Mn2O3])^2)

Construct the rate of reaction expression for: Si + Mn_2O_3 ⟶ SiO_2 + Mn 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: 3 Si + 2 Mn_2O_3 ⟶ 3 SiO_2 + 4 Mn 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 | 3 | -3 Mn_2O_3 | 2 | -2 SiO_2 | 3 | 3 Mn | 4 | 4 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 | 3 | -3 | -1/3 (Δ[Si])/(Δt) Mn_2O_3 | 2 | -2 | -1/2 (Δ[Mn2O3])/(Δt) SiO_2 | 3 | 3 | 1/3 (Δ[SiO2])/(Δt) Mn | 4 | 4 | 1/4 (Δ[Mn])/(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 = -1/3 (Δ[Si])/(Δt) = -1/2 (Δ[Mn2O3])/(Δt) = 1/3 (Δ[SiO2])/(Δt) = 1/4 (Δ[Mn])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silicon | manganese(III) oxide | silicon dioxide | manganese formula | Si | Mn_2O_3 | SiO_2 | Mn Hill formula | Si | Mn_2O_3 | O_2Si | Mn name | silicon | manganese(III) oxide | silicon dioxide | manganese IUPAC name | silicon | oxo-(oxomanganiooxy)manganese | dioxosilane | manganese

| silicon | manganese(III) oxide | silicon dioxide | manganese molar mass | 28.085 g/mol | 157.873 g/mol | 60.083 g/mol | 54.938044 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1410 °C | 1347 °C | 1713 °C | 1244 °C boiling point | 2355 °C | | 2950 °C | 1962 °C density | 2.33 g/cm^3 | 4.5 g/cm^3 | 2.196 g/cm^3 | 7.3 g/cm^3 solubility in water | insoluble | | insoluble | insoluble odor | | | odorless |