NaOH + Br2 + CH3COCH3 = H2O + NaBr + CHBr3 + C6H5COONa

NaOH sodium hydroxide + Br_2 bromine + CH_3COCH_3 acetone ⟶ H_2O water + NaBr sodium bromide + CHBr_3 bromoform + C_6H_5COONa sodium benzoate

Balance the chemical equation algebraically: NaOH + Br_2 + CH_3COCH_3 ⟶ H_2O + NaBr + CHBr_3 + C_6H_5COONa Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Br_2 + c_3 CH_3COCH_3 ⟶ c_4 H_2O + c_5 NaBr + c_6 CHBr_3 + c_7 C_6H_5COONa Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Br and C: H: | c_1 + 6 c_3 = 2 c_4 + c_6 + 5 c_7 Na: | c_1 = c_5 + c_7 O: | c_1 + c_3 = c_4 + 2 c_7 Br: | 2 c_2 = c_5 + 3 c_6 C: | 3 c_3 = c_6 + 7 c_7 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_6 = 1 and solve the system of equations for the remaining coefficients: c_2 = (11 c_1)/25 + 38/25 c_3 = (7 c_1)/25 + 6/25 c_4 = (26 c_1)/25 + 8/25 c_5 = (22 c_1)/25 + 1/25 c_6 = 1 c_7 = (3 c_1)/25 - 1/25 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_2 = (11 c_1)/25 + 114/25 c_3 = (7 c_1)/25 + 18/25 c_4 = (26 c_1)/25 + 24/25 c_5 = (22 c_1)/25 + 3/25 c_6 = 3 c_7 = (3 c_1)/25 - 3/25 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 26 and solve for the remaining coefficients: c_1 = 26 c_2 = 16 c_3 = 8 c_4 = 28 c_5 = 23 c_6 = 3 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 26 NaOH + 16 Br_2 + 8 CH_3COCH_3 ⟶ 28 H_2O + 23 NaBr + 3 CHBr_3 + 3 C_6H_5COONa

+ + ⟶ + + +

sodium hydroxide + bromine + acetone ⟶ water + sodium bromide + bromoform + sodium benzoate

Construct the equilibrium constant, K, expression for: NaOH + Br_2 + CH_3COCH_3 ⟶ H_2O + NaBr + CHBr_3 + C_6H_5COONa 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: 26 NaOH + 16 Br_2 + 8 CH_3COCH_3 ⟶ 28 H_2O + 23 NaBr + 3 CHBr_3 + 3 C_6H_5COONa 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 NaOH | 26 | -26 Br_2 | 16 | -16 CH_3COCH_3 | 8 | -8 H_2O | 28 | 28 NaBr | 23 | 23 CHBr_3 | 3 | 3 C_6H_5COONa | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 26 | -26 | ([NaOH])^(-26) Br_2 | 16 | -16 | ([Br2])^(-16) CH_3COCH_3 | 8 | -8 | ([CH3COCH3])^(-8) H_2O | 28 | 28 | ([H2O])^28 NaBr | 23 | 23 | ([NaBr])^23 CHBr_3 | 3 | 3 | ([CHBr3])^3 C_6H_5COONa | 3 | 3 | ([C6H5COONa])^3 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 = ([NaOH])^(-26) ([Br2])^(-16) ([CH3COCH3])^(-8) ([H2O])^28 ([NaBr])^23 ([CHBr3])^3 ([C6H5COONa])^3 = (([H2O])^28 ([NaBr])^23 ([CHBr3])^3 ([C6H5COONa])^3)/(([NaOH])^26 ([Br2])^16 ([CH3COCH3])^8)

Construct the rate of reaction expression for: NaOH + Br_2 + CH_3COCH_3 ⟶ H_2O + NaBr + CHBr_3 + C_6H_5COONa 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: 26 NaOH + 16 Br_2 + 8 CH_3COCH_3 ⟶ 28 H_2O + 23 NaBr + 3 CHBr_3 + 3 C_6H_5COONa 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 NaOH | 26 | -26 Br_2 | 16 | -16 CH_3COCH_3 | 8 | -8 H_2O | 28 | 28 NaBr | 23 | 23 CHBr_3 | 3 | 3 C_6H_5COONa | 3 | 3 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 NaOH | 26 | -26 | -1/26 (Δ[NaOH])/(Δt) Br_2 | 16 | -16 | -1/16 (Δ[Br2])/(Δt) CH_3COCH_3 | 8 | -8 | -1/8 (Δ[CH3COCH3])/(Δt) H_2O | 28 | 28 | 1/28 (Δ[H2O])/(Δt) NaBr | 23 | 23 | 1/23 (Δ[NaBr])/(Δt) CHBr_3 | 3 | 3 | 1/3 (Δ[CHBr3])/(Δt) C_6H_5COONa | 3 | 3 | 1/3 (Δ[C6H5COONa])/(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 = -1/26 (Δ[NaOH])/(Δt) = -1/16 (Δ[Br2])/(Δt) = -1/8 (Δ[CH3COCH3])/(Δt) = 1/28 (Δ[H2O])/(Δt) = 1/23 (Δ[NaBr])/(Δt) = 1/3 (Δ[CHBr3])/(Δt) = 1/3 (Δ[C6H5COONa])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | bromine | acetone | water | sodium bromide | bromoform | sodium benzoate formula | NaOH | Br_2 | CH_3COCH_3 | H_2O | NaBr | CHBr_3 | C_6H_5COONa Hill formula | HNaO | Br_2 | C_3H_6O | H_2O | BrNa | CHBr_3 | C_7H_5NaO_2 name | sodium hydroxide | bromine | acetone | water | sodium bromide | bromoform | sodium benzoate IUPAC name | sodium hydroxide | molecular bromine | acetone | water | sodium bromide | bromoform | sodium benzoate