MgO + Cr2O3 = Mg(CrO2)2

MgO magnesium oxide + Cr_2O_3 chromium(III) oxide ⟶ Mg(CrO2)2

Balance the chemical equation algebraically: MgO + Cr_2O_3 ⟶ Mg(CrO2)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MgO + c_2 Cr_2O_3 ⟶ c_3 Mg(CrO2)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, O and Cr: Mg: | c_1 = c_3 O: | c_1 + 3 c_2 = 4 c_3 Cr: | 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MgO + Cr_2O_3 ⟶ Mg(CrO2)2

+ ⟶ Mg(CrO2)2

magnesium oxide + chromium(III) oxide ⟶ Mg(CrO2)2

Construct the equilibrium constant, K, expression for: MgO + Cr_2O_3 ⟶ Mg(CrO2)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: MgO + Cr_2O_3 ⟶ Mg(CrO2)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 | 1 | -1 Cr_2O_3 | 1 | -1 Mg(CrO2)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 | 1 | -1 | ([MgO])^(-1) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) Mg(CrO2)2 | 1 | 1 | [Mg(CrO2)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 = ([MgO])^(-1) ([Cr2O3])^(-1) [Mg(CrO2)2] = ([Mg(CrO2)2])/([MgO] [Cr2O3])

Construct the rate of reaction expression for: MgO + Cr_2O_3 ⟶ Mg(CrO2)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: MgO + Cr_2O_3 ⟶ Mg(CrO2)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 | 1 | -1 Cr_2O_3 | 1 | -1 Mg(CrO2)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 | 1 | -1 | -(Δ[MgO])/(Δt) Cr_2O_3 | 1 | -1 | -(Δ[Cr2O3])/(Δt) Mg(CrO2)2 | 1 | 1 | (Δ[Mg(CrO2)2])/(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 = -(Δ[MgO])/(Δt) = -(Δ[Cr2O3])/(Δt) = (Δ[Mg(CrO2)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium oxide | chromium(III) oxide | Mg(CrO2)2 formula | MgO | Cr_2O_3 | Mg(CrO2)2 Hill formula | MgO | Cr_2O_3 | Cr2MgO4 name | magnesium oxide | chromium(III) oxide | IUPAC name | oxomagnesium | |

| magnesium oxide | chromium(III) oxide | Mg(CrO2)2 molar mass | 40.304 g/mol | 151.99 g/mol | 192.29 g/mol phase | solid (at STP) | solid (at STP) | melting point | 2852 °C | 2435 °C | boiling point | 3600 °C | 4000 °C | density | 3.58 g/cm^3 | 4.8 g/cm^3 | solubility in water | | insoluble | odor | odorless | |