Mg + WO3 = MgO + W

Mg magnesium + WO_3 tungsten trioxide ⟶ MgO magnesium oxide + W tungsten

Balance the chemical equation algebraically: Mg + WO_3 ⟶ MgO + W Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 WO_3 ⟶ c_3 MgO + c_4 W Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, O and W: Mg: | c_1 = c_3 O: | 3 c_2 = c_3 W: | 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 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Mg + WO_3 ⟶ 3 MgO + W

+ ⟶ +

magnesium + tungsten trioxide ⟶ magnesium oxide + tungsten

| magnesium | tungsten trioxide | magnesium oxide | tungsten molecular enthalpy | 0 kJ/mol | -842.9 kJ/mol | -601.6 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -842.9 kJ/mol | -1805 kJ/mol | 0 kJ/mol | H_initial = -842.9 kJ/mol | | H_final = -1805 kJ/mol | ΔH_rxn^0 | -1805 kJ/mol - -842.9 kJ/mol = -961.9 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: Mg + WO_3 ⟶ MgO + W 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 Mg + WO_3 ⟶ 3 MgO + W 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 | 3 | -3 WO_3 | 1 | -1 MgO | 3 | 3 W | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 3 | -3 | ([Mg])^(-3) WO_3 | 1 | -1 | ([WO3])^(-1) MgO | 3 | 3 | ([MgO])^3 W | 1 | 1 | [W] 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])^(-3) ([WO3])^(-1) ([MgO])^3 [W] = (([MgO])^3 [W])/(([Mg])^3 [WO3])

Construct the rate of reaction expression for: Mg + WO_3 ⟶ MgO + W 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 Mg + WO_3 ⟶ 3 MgO + W 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 | 3 | -3 WO_3 | 1 | -1 MgO | 3 | 3 W | 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 | 3 | -3 | -1/3 (Δ[Mg])/(Δt) WO_3 | 1 | -1 | -(Δ[WO3])/(Δt) MgO | 3 | 3 | 1/3 (Δ[MgO])/(Δt) W | 1 | 1 | (Δ[W])/(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[Mg])/(Δt) = -(Δ[WO3])/(Δt) = 1/3 (Δ[MgO])/(Δt) = (Δ[W])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | tungsten trioxide | magnesium oxide | tungsten formula | Mg | WO_3 | MgO | W Hill formula | Mg | O_3W | MgO | W name | magnesium | tungsten trioxide | magnesium oxide | tungsten IUPAC name | magnesium | | oxomagnesium | tungsten

| magnesium | tungsten trioxide | magnesium oxide | tungsten molar mass | 24.305 g/mol | 231.84 g/mol | 40.304 g/mol | 183.84 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 648 °C | 1473 °C | 2852 °C | 3410 °C boiling point | 1090 °C | | 3600 °C | 5660 °C density | 1.738 g/cm^3 | 7.16 g/cm^3 | 3.58 g/cm^3 | 19.3 g/cm^3 solubility in water | reacts | insoluble | | insoluble odor | | | odorless |