Mg + TiO2 = MgO + Ti

Mg magnesium + TiO_2 titanium dioxide ⟶ MgO magnesium oxide + Ti titanium

Balance the chemical equation algebraically: Mg + TiO_2 ⟶ MgO + Ti Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 TiO_2 ⟶ c_3 MgO + c_4 Ti Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, O and Ti: Mg: | c_1 = c_3 O: | 2 c_2 = c_3 Ti: | c_2 = c_4 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 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Mg + TiO_2 ⟶ 2 MgO + Ti

+ ⟶ +

magnesium + titanium dioxide ⟶ magnesium oxide + titanium

| magnesium | titanium dioxide | magnesium oxide | titanium molecular enthalpy | 0 kJ/mol | -944 kJ/mol | -601.6 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -944 kJ/mol | -1203 kJ/mol | 0 kJ/mol | H_initial = -944 kJ/mol | | H_final = -1203 kJ/mol | ΔH_rxn^0 | -1203 kJ/mol - -944 kJ/mol = -259.2 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: Mg + TiO_2 ⟶ MgO + Ti 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 Mg + TiO_2 ⟶ 2 MgO + Ti 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 | 2 | -2 TiO_2 | 1 | -1 MgO | 2 | 2 Ti | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 2 | -2 | ([Mg])^(-2) TiO_2 | 1 | -1 | ([TiO2])^(-1) MgO | 2 | 2 | ([MgO])^2 Ti | 1 | 1 | [Ti] 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])^(-2) ([TiO2])^(-1) ([MgO])^2 [Ti] = (([MgO])^2 [Ti])/(([Mg])^2 [TiO2])

Construct the rate of reaction expression for: Mg + TiO_2 ⟶ MgO + Ti 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 Mg + TiO_2 ⟶ 2 MgO + Ti 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 | 2 | -2 TiO_2 | 1 | -1 MgO | 2 | 2 Ti | 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 | 2 | -2 | -1/2 (Δ[Mg])/(Δt) TiO_2 | 1 | -1 | -(Δ[TiO2])/(Δt) MgO | 2 | 2 | 1/2 (Δ[MgO])/(Δt) Ti | 1 | 1 | (Δ[Ti])/(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[Mg])/(Δt) = -(Δ[TiO2])/(Δt) = 1/2 (Δ[MgO])/(Δt) = (Δ[Ti])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | titanium dioxide | magnesium oxide | titanium formula | Mg | TiO_2 | MgO | Ti Hill formula | Mg | O_2Ti | MgO | Ti name | magnesium | titanium dioxide | magnesium oxide | titanium IUPAC name | magnesium | | oxomagnesium | titanium

| magnesium | titanium dioxide | magnesium oxide | titanium molar mass | 24.305 g/mol | 79.865 g/mol | 40.304 g/mol | 47.867 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 648 °C | 1843 °C | 2852 °C | 1660 °C boiling point | 1090 °C | 2900 °C | 3600 °C | 3287 °C density | 1.738 g/cm^3 | 4.26 g/cm^3 | 3.58 g/cm^3 | 4.5 g/cm^3 solubility in water | reacts | insoluble | | insoluble odor | | | odorless |