Na + C2H5Cl = NaCl + C4H10

Na sodium + C_2H_5Cl chloroethane ⟶ NaCl sodium chloride + CH_3CH_2CH_2CH_3 butane

Balance the chemical equation algebraically: Na + C_2H_5Cl ⟶ NaCl + CH_3CH_2CH_2CH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 C_2H_5Cl ⟶ c_3 NaCl + c_4 CH_3CH_2CH_2CH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Na, C, Cl and H: Na: | c_1 = c_3 C: | 2 c_2 = 4 c_4 Cl: | c_2 = c_3 H: | 5 c_2 = 10 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Na + 2 C_2H_5Cl ⟶ 2 NaCl + CH_3CH_2CH_2CH_3

+ ⟶ +

sodium + chloroethane ⟶ sodium chloride + butane

Construct the equilibrium constant, K, expression for: Na + C_2H_5Cl ⟶ NaCl + CH_3CH_2CH_2CH_3 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 C_2H_5Cl ⟶ 2 NaCl + CH_3CH_2CH_2CH_3 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 C_2H_5Cl | 2 | -2 NaCl | 2 | 2 CH_3CH_2CH_2CH_3 | 1 | 1 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) C_2H_5Cl | 2 | -2 | ([C2H5Cl])^(-2) NaCl | 2 | 2 | ([NaCl])^2 CH_3CH_2CH_2CH_3 | 1 | 1 | [CH3CH2CH2CH3] 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) ([C2H5Cl])^(-2) ([NaCl])^2 [CH3CH2CH2CH3] = (([NaCl])^2 [CH3CH2CH2CH3])/(([Na])^2 ([C2H5Cl])^2)

Construct the rate of reaction expression for: Na + C_2H_5Cl ⟶ NaCl + CH_3CH_2CH_2CH_3 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 C_2H_5Cl ⟶ 2 NaCl + CH_3CH_2CH_2CH_3 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 C_2H_5Cl | 2 | -2 NaCl | 2 | 2 CH_3CH_2CH_2CH_3 | 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 Na | 2 | -2 | -1/2 (Δ[Na])/(Δt) C_2H_5Cl | 2 | -2 | -1/2 (Δ[C2H5Cl])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) CH_3CH_2CH_2CH_3 | 1 | 1 | (Δ[CH3CH2CH2CH3])/(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[C2H5Cl])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = (Δ[CH3CH2CH2CH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium | chloroethane | sodium chloride | butane formula | Na | C_2H_5Cl | NaCl | CH_3CH_2CH_2CH_3 Hill formula | Na | C_2H_5Cl | ClNa | C_4H_10 name | sodium | chloroethane | sodium chloride | butane