O2 + Ga = Ga2O3O

O_2 oxygen + Ga gallium ⟶ Ga2O3O

Balance the chemical equation algebraically: O_2 + Ga ⟶ Ga2O3O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 Ga ⟶ c_3 Ga2O3O Set the number of atoms in the reactants equal to the number of atoms in the products for O and Ga: O: | 2 c_1 = 4 c_3 Ga: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 O_2 + 2 Ga ⟶ Ga2O3O

+ ⟶ Ga2O3O

oxygen + gallium ⟶ Ga2O3O

Construct the equilibrium constant, K, expression for: O_2 + Ga ⟶ Ga2O3O 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 O_2 + 2 Ga ⟶ Ga2O3O 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 O_2 | 2 | -2 Ga | 2 | -2 Ga2O3O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 2 | -2 | ([O2])^(-2) Ga | 2 | -2 | ([Ga])^(-2) Ga2O3O | 1 | 1 | [Ga2O3O] 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 = ([O2])^(-2) ([Ga])^(-2) [Ga2O3O] = ([Ga2O3O])/(([O2])^2 ([Ga])^2)

Construct the rate of reaction expression for: O_2 + Ga ⟶ Ga2O3O 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 O_2 + 2 Ga ⟶ Ga2O3O 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 O_2 | 2 | -2 Ga | 2 | -2 Ga2O3O | 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 O_2 | 2 | -2 | -1/2 (Δ[O2])/(Δt) Ga | 2 | -2 | -1/2 (Δ[Ga])/(Δt) Ga2O3O | 1 | 1 | (Δ[Ga2O3O])/(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[O2])/(Δt) = -1/2 (Δ[Ga])/(Δt) = (Δ[Ga2O3O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | gallium | Ga2O3O formula | O_2 | Ga | Ga2O3O Hill formula | O_2 | Ga | Ga2O4 name | oxygen | gallium | IUPAC name | molecular oxygen | gallium |

| oxygen | gallium | Ga2O3O molar mass | 31.998 g/mol | 69.723 g/mol | 203.44 g/mol phase | gas (at STP) | solid (at STP) | melting point | -218 °C | 29.8 °C | boiling point | -183 °C | 2403 °C | density | 0.001429 g/cm^3 (at 0 °C) | 5.904 g/cm^3 | solubility in water | | insoluble | surface tension | 0.01347 N/m | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | 0.0019 Pa s (at 53 °C) | odor | odorless | |