Cr2O3 + Si = SiO2 + Cr

Cr_2O_3 chromium(III) oxide + Si silicon ⟶ SiO_2 silicon dioxide + Cr chromium

Balance the chemical equation algebraically: Cr_2O_3 + Si ⟶ SiO_2 + Cr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cr_2O_3 + c_2 Si ⟶ c_3 SiO_2 + c_4 Cr Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, O and Si: Cr: | 2 c_1 = c_4 O: | 3 c_1 = 2 c_3 Si: | 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 = 3/2 c_3 = 3/2 c_4 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Cr_2O_3 + 3 Si ⟶ 3 SiO_2 + 4 Cr

+ ⟶ +

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

| chromium(III) oxide | silicon | silicon dioxide | chromium molecular enthalpy | -1140 kJ/mol | 0 kJ/mol | -911 kJ/mol | 0 kJ/mol total enthalpy | -2279 kJ/mol | 0 kJ/mol | -2733 kJ/mol | 0 kJ/mol | H_initial = -2279 kJ/mol | | H_final = -2733 kJ/mol | ΔH_rxn^0 | -2733 kJ/mol - -2279 kJ/mol = -453.6 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: Cr_2O_3 + Si ⟶ SiO_2 + Cr 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 Cr_2O_3 + 3 Si ⟶ 3 SiO_2 + 4 Cr 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 Cr_2O_3 | 2 | -2 Si | 3 | -3 SiO_2 | 3 | 3 Cr | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cr_2O_3 | 2 | -2 | ([Cr2O3])^(-2) Si | 3 | -3 | ([Si])^(-3) SiO_2 | 3 | 3 | ([SiO2])^3 Cr | 4 | 4 | ([Cr])^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 = ([Cr2O3])^(-2) ([Si])^(-3) ([SiO2])^3 ([Cr])^4 = (([SiO2])^3 ([Cr])^4)/(([Cr2O3])^2 ([Si])^3)

Construct the rate of reaction expression for: Cr_2O_3 + Si ⟶ SiO_2 + Cr 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 Cr_2O_3 + 3 Si ⟶ 3 SiO_2 + 4 Cr 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 Cr_2O_3 | 2 | -2 Si | 3 | -3 SiO_2 | 3 | 3 Cr | 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 Cr_2O_3 | 2 | -2 | -1/2 (Δ[Cr2O3])/(Δt) Si | 3 | -3 | -1/3 (Δ[Si])/(Δt) SiO_2 | 3 | 3 | 1/3 (Δ[SiO2])/(Δt) Cr | 4 | 4 | 1/4 (Δ[Cr])/(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[Cr2O3])/(Δt) = -1/3 (Δ[Si])/(Δt) = 1/3 (Δ[SiO2])/(Δt) = 1/4 (Δ[Cr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromium(III) oxide | silicon | silicon dioxide | chromium formula | Cr_2O_3 | Si | SiO_2 | Cr Hill formula | Cr_2O_3 | Si | O_2Si | Cr name | chromium(III) oxide | silicon | silicon dioxide | chromium IUPAC name | | silicon | dioxosilane | chromium

| chromium(III) oxide | silicon | silicon dioxide | chromium molar mass | 151.99 g/mol | 28.085 g/mol | 60.083 g/mol | 51.9961 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 2435 °C | 1410 °C | 1713 °C | 1857 °C boiling point | 4000 °C | 2355 °C | 2950 °C | 2672 °C density | 4.8 g/cm^3 | 2.33 g/cm^3 | 2.196 g/cm^3 | 7.14 g/cm^3 solubility in water | insoluble | insoluble | insoluble | insoluble odor | | | odorless | odorless