NaHCO3 + CH2(COOH)2 = H2O + CO2 + CH3COONa

NaHCO_3 sodium bicarbonate + C_3H_4O_4 malonyl ⟶ H_2O water + CO_2 carbon dioxide + CH_3COONa sodium acetate

Balance the chemical equation algebraically: NaHCO_3 + C_3H_4O_4 ⟶ H_2O + CO_2 + CH_3COONa Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaHCO_3 + c_2 C_3H_4O_4 ⟶ c_3 H_2O + c_4 CO_2 + c_5 CH_3COONa Set the number of atoms in the reactants equal to the number of atoms in the products for C, H, Na and O: C: | c_1 + 3 c_2 = c_4 + 2 c_5 H: | c_1 + 4 c_2 = 2 c_3 + 3 c_5 Na: | c_1 = c_5 O: | 3 c_1 + 4 c_2 = c_3 + 2 c_4 + 2 c_5 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | NaHCO_3 + C_3H_4O_4 ⟶ H_2O + 2 CO_2 + CH_3COONa

+ C_3H_4O_4 ⟶ + +

sodium bicarbonate + malonyl ⟶ water + carbon dioxide + sodium acetate

Construct the equilibrium constant, K, expression for: NaHCO_3 + C_3H_4O_4 ⟶ H_2O + CO_2 + CH_3COONa 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: NaHCO_3 + C_3H_4O_4 ⟶ H_2O + 2 CO_2 + CH_3COONa 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 NaHCO_3 | 1 | -1 C_3H_4O_4 | 1 | -1 H_2O | 1 | 1 CO_2 | 2 | 2 CH_3COONa | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaHCO_3 | 1 | -1 | ([NaHCO3])^(-1) C_3H_4O_4 | 1 | -1 | ([C3H4O4])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 2 | 2 | ([CO2])^2 CH_3COONa | 1 | 1 | [CH3COONa] 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 = ([NaHCO3])^(-1) ([C3H4O4])^(-1) [H2O] ([CO2])^2 [CH3COONa] = ([H2O] ([CO2])^2 [CH3COONa])/([NaHCO3] [C3H4O4])

Construct the rate of reaction expression for: NaHCO_3 + C_3H_4O_4 ⟶ H_2O + CO_2 + CH_3COONa 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: NaHCO_3 + C_3H_4O_4 ⟶ H_2O + 2 CO_2 + CH_3COONa 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 NaHCO_3 | 1 | -1 C_3H_4O_4 | 1 | -1 H_2O | 1 | 1 CO_2 | 2 | 2 CH_3COONa | 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 NaHCO_3 | 1 | -1 | -(Δ[NaHCO3])/(Δt) C_3H_4O_4 | 1 | -1 | -(Δ[C3H4O4])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) CH_3COONa | 1 | 1 | (Δ[CH3COONa])/(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 = -(Δ[NaHCO3])/(Δt) = -(Δ[C3H4O4])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[CH3COONa])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium bicarbonate | malonyl | water | carbon dioxide | sodium acetate formula | NaHCO_3 | C_3H_4O_4 | H_2O | CO_2 | CH_3COONa Hill formula | CHNaO_3 | C_3H_4O_4 | H_2O | CO_2 | C_2H_3NaO_2 name | sodium bicarbonate | malonyl | water | carbon dioxide | sodium acetate IUPAC name | sodium hydrogen carbonate | | water | carbon dioxide | sodium acetate