Na + C2H5OH = H2 + C2H5ONa

Na sodium + CH_3CH_2OH ethanol ⟶ H_2 hydrogen + CH_3CH_2ONa sodium ethylate

Balance the chemical equation algebraically: Na + CH_3CH_2OH ⟶ H_2 + CH_3CH_2ONa Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 CH_3CH_2OH ⟶ c_3 H_2 + c_4 CH_3CH_2ONa Set the number of atoms in the reactants equal to the number of atoms in the products for Na, C, H and O: Na: | c_1 = c_4 C: | 2 c_2 = 2 c_4 H: | 6 c_2 = 2 c_3 + 5 c_4 O: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Na + 2 CH_3CH_2OH ⟶ H_2 + 2 CH_3CH_2ONa

+ ⟶ +

sodium + ethanol ⟶ hydrogen + sodium ethylate

Construct the equilibrium constant, K, expression for: Na + CH_3CH_2OH ⟶ H_2 + CH_3CH_2ONa 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 Na + 2 CH_3CH_2OH ⟶ H_2 + 2 CH_3CH_2ONa 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 Na | 2 | -2 CH_3CH_2OH | 2 | -2 H_2 | 1 | 1 CH_3CH_2ONa | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na | 2 | -2 | ([Na])^(-2) CH_3CH_2OH | 2 | -2 | ([CH3CH2OH])^(-2) H_2 | 1 | 1 | [H2] CH_3CH_2ONa | 2 | 2 | ([CH3CH2ONa])^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 = ([Na])^(-2) ([CH3CH2OH])^(-2) [H2] ([CH3CH2ONa])^2 = ([H2] ([CH3CH2ONa])^2)/(([Na])^2 ([CH3CH2OH])^2)

Construct the rate of reaction expression for: Na + CH_3CH_2OH ⟶ H_2 + CH_3CH_2ONa 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 Na + 2 CH_3CH_2OH ⟶ H_2 + 2 CH_3CH_2ONa 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 Na | 2 | -2 CH_3CH_2OH | 2 | -2 H_2 | 1 | 1 CH_3CH_2ONa | 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 Na | 2 | -2 | -1/2 (Δ[Na])/(Δt) CH_3CH_2OH | 2 | -2 | -1/2 (Δ[CH3CH2OH])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) CH_3CH_2ONa | 2 | 2 | 1/2 (Δ[CH3CH2ONa])/(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[Na])/(Δt) = -1/2 (Δ[CH3CH2OH])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[CH3CH2ONa])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium | ethanol | hydrogen | sodium ethylate formula | Na | CH_3CH_2OH | H_2 | CH_3CH_2ONa Hill formula | Na | C_2H_6O | H_2 | C_2H_5NaO name | sodium | ethanol | hydrogen | sodium ethylate IUPAC name | sodium | ethanol | molecular hydrogen | sodium ethanolate