O2 + Na = Na2O5

O_2 (oxygen) + Na (sodium) ⟶ Na2O5

Balance the chemical equation algebraically: O_2 + Na ⟶ Na2O5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 Na ⟶ c_3 Na2O5 Set the number of atoms in the reactants equal to the number of atoms in the products for O and Na: O: | 2 c_1 = 5 c_3 Na: | 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 = 5/2 c_2 = 2 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 4 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 O_2 + 4 Na ⟶ 2 Na2O5

+ ⟶ Na2O5

oxygen + sodium ⟶ Na2O5

Construct the equilibrium constant, K, expression for: O_2 + Na ⟶ Na2O5 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: 5 O_2 + 4 Na ⟶ 2 Na2O5 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 | 5 | -5 Na | 4 | -4 Na2O5 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 5 | -5 | ([O2])^(-5) Na | 4 | -4 | ([Na])^(-4) Na2O5 | 2 | 2 | ([Na2O5])^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 = ([O2])^(-5) ([Na])^(-4) ([Na2O5])^2 = ([Na2O5])^2/(([O2])^5 ([Na])^4)

Construct the rate of reaction expression for: O_2 + Na ⟶ Na2O5 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: 5 O_2 + 4 Na ⟶ 2 Na2O5 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 | 5 | -5 Na | 4 | -4 Na2O5 | 2 | 2 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 | 5 | -5 | -1/5 (Δ[O2])/(Δt) Na | 4 | -4 | -1/4 (Δ[Na])/(Δt) Na2O5 | 2 | 2 | 1/2 (Δ[Na2O5])/(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 = -1/5 (Δ[O2])/(Δt) = -1/4 (Δ[Na])/(Δt) = 1/2 (Δ[Na2O5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | sodium | Na2O5 formula | O_2 | Na | Na2O5 name | oxygen | sodium | IUPAC name | molecular oxygen | sodium |

| oxygen | sodium | Na2O5 molar mass | 31.998 g/mol | 22.98976928 g/mol | 125.97 g/mol phase | gas (at STP) | solid (at STP) | melting point | -218 °C | 97.8 °C | boiling point | -183 °C | 883 °C | density | 0.001429 g/cm^3 (at 0 °C) | 0.968 g/cm^3 | solubility in water | | decomposes | surface tension | 0.01347 N/m | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | 1.413×10^-5 Pa s (at 527 °C) | odor | odorless | |