NaOH + Br2 + C3H6O = H2O + NaBr + CH3COONa + CHBr3

NaOH sodium hydroxide + Br_2 bromine + CH_3COCH_3 acetone ⟶ H_2O water + NaBr sodium bromide + CH_3COONa sodium acetate + CHBr_3 bromoform

Balance the chemical equation algebraically: NaOH + Br_2 + CH_3COCH_3 ⟶ H_2O + NaBr + CH_3COONa + CHBr_3 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 CH_3COONa + c_7 CHBr_3 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 + 3 c_6 + c_7 Na: | c_1 = c_5 + c_6 O: | c_1 + c_3 = c_4 + 2 c_6 Br: | 2 c_2 = c_5 + 3 c_7 C: | 3 c_3 = 2 c_6 + 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = 17/3 - (2 c_1)/3 c_3 = 1 c_4 = c_1/3 + 5/3 c_5 = (2 c_1)/3 + 1/3 c_6 = c_1/3 - 1/3 c_7 = 11/3 - (2 c_1)/3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 3 c_3 = 1 c_4 = 3 c_5 = 3 c_6 = 1 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 NaOH + 3 Br_2 + CH_3COCH_3 ⟶ 3 H_2O + 3 NaBr + CH_3COONa + CHBr_3

+ + ⟶ + + +

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

Construct the equilibrium constant, K, expression for: NaOH + Br_2 + CH_3COCH_3 ⟶ H_2O + NaBr + CH_3COONa + CHBr_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: 4 NaOH + 3 Br_2 + CH_3COCH_3 ⟶ 3 H_2O + 3 NaBr + CH_3COONa + CHBr_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 NaOH | 4 | -4 Br_2 | 3 | -3 CH_3COCH_3 | 1 | -1 H_2O | 3 | 3 NaBr | 3 | 3 CH_3COONa | 1 | 1 CHBr_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 4 | -4 | ([NaOH])^(-4) Br_2 | 3 | -3 | ([Br2])^(-3) CH_3COCH_3 | 1 | -1 | ([CH3COCH3])^(-1) H_2O | 3 | 3 | ([H2O])^3 NaBr | 3 | 3 | ([NaBr])^3 CH_3COONa | 1 | 1 | [CH3COONa] CHBr_3 | 1 | 1 | [CHBr3] 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])^(-4) ([Br2])^(-3) ([CH3COCH3])^(-1) ([H2O])^3 ([NaBr])^3 [CH3COONa] [CHBr3] = (([H2O])^3 ([NaBr])^3 [CH3COONa] [CHBr3])/(([NaOH])^4 ([Br2])^3 [CH3COCH3])

Construct the rate of reaction expression for: NaOH + Br_2 + CH_3COCH_3 ⟶ H_2O + NaBr + CH_3COONa + CHBr_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: 4 NaOH + 3 Br_2 + CH_3COCH_3 ⟶ 3 H_2O + 3 NaBr + CH_3COONa + CHBr_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 NaOH | 4 | -4 Br_2 | 3 | -3 CH_3COCH_3 | 1 | -1 H_2O | 3 | 3 NaBr | 3 | 3 CH_3COONa | 1 | 1 CHBr_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 NaOH | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) Br_2 | 3 | -3 | -1/3 (Δ[Br2])/(Δt) CH_3COCH_3 | 1 | -1 | -(Δ[CH3COCH3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) NaBr | 3 | 3 | 1/3 (Δ[NaBr])/(Δt) CH_3COONa | 1 | 1 | (Δ[CH3COONa])/(Δt) CHBr_3 | 1 | 1 | (Δ[CHBr3])/(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 = -1/4 (Δ[NaOH])/(Δt) = -1/3 (Δ[Br2])/(Δt) = -(Δ[CH3COCH3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[NaBr])/(Δt) = (Δ[CH3COONa])/(Δt) = (Δ[CHBr3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | bromine | acetone | water | sodium bromide | sodium acetate | bromoform formula | NaOH | Br_2 | CH_3COCH_3 | H_2O | NaBr | CH_3COONa | CHBr_3 Hill formula | HNaO | Br_2 | C_3H_6O | H_2O | BrNa | C_2H_3NaO_2 | CHBr_3 name | sodium hydroxide | bromine | acetone | water | sodium bromide | sodium acetate | bromoform IUPAC name | sodium hydroxide | molecular bromine | acetone | water | sodium bromide | sodium acetate | bromoform