Mg + B2O3 = MgO + Mg3B2

Mg magnesium + B_2O_3 boron oxide ⟶ MgO magnesium oxide + Mg3B2

Balance the chemical equation algebraically: Mg + B_2O_3 ⟶ MgO + Mg3B2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 B_2O_3 ⟶ c_3 MgO + c_4 Mg3B2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, B and O: Mg: | c_1 = c_3 + 3 c_4 B: | 2 c_2 = 2 c_4 O: | 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 Mg + B_2O_3 ⟶ 3 MgO + Mg3B2

+ ⟶ + Mg3B2

magnesium + boron oxide ⟶ magnesium oxide + Mg3B2

Construct the equilibrium constant, K, expression for: Mg + B_2O_3 ⟶ MgO + Mg3B2 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: 6 Mg + B_2O_3 ⟶ 3 MgO + Mg3B2 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 Mg | 6 | -6 B_2O_3 | 1 | -1 MgO | 3 | 3 Mg3B2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 6 | -6 | ([Mg])^(-6) B_2O_3 | 1 | -1 | ([B2O3])^(-1) MgO | 3 | 3 | ([MgO])^3 Mg3B2 | 1 | 1 | [Mg3B2] 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 = ([Mg])^(-6) ([B2O3])^(-1) ([MgO])^3 [Mg3B2] = (([MgO])^3 [Mg3B2])/(([Mg])^6 [B2O3])

Construct the rate of reaction expression for: Mg + B_2O_3 ⟶ MgO + Mg3B2 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: 6 Mg + B_2O_3 ⟶ 3 MgO + Mg3B2 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 Mg | 6 | -6 B_2O_3 | 1 | -1 MgO | 3 | 3 Mg3B2 | 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 Mg | 6 | -6 | -1/6 (Δ[Mg])/(Δt) B_2O_3 | 1 | -1 | -(Δ[B2O3])/(Δt) MgO | 3 | 3 | 1/3 (Δ[MgO])/(Δt) Mg3B2 | 1 | 1 | (Δ[Mg3B2])/(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 = -1/6 (Δ[Mg])/(Δt) = -(Δ[B2O3])/(Δt) = 1/3 (Δ[MgO])/(Δt) = (Δ[Mg3B2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | boron oxide | magnesium oxide | Mg3B2 formula | Mg | B_2O_3 | MgO | Mg3B2 Hill formula | Mg | B_2O_3 | MgO | B2Mg3 name | magnesium | boron oxide | magnesium oxide | IUPAC name | magnesium | | oxomagnesium |

| magnesium | boron oxide | magnesium oxide | Mg3B2 molar mass | 24.305 g/mol | 69.62 g/mol | 40.304 g/mol | 94.53 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 648 °C | 450 °C | 2852 °C | boiling point | 1090 °C | 1860 °C | 3600 °C | density | 1.738 g/cm^3 | 2.46 g/cm^3 | 3.58 g/cm^3 | solubility in water | reacts | | | dynamic viscosity | | 85 Pa s (at 700 °C) | | odor | | | odorless |