CaCO3 + CH3COOH = H2O + CO2 + (CH3COO)2Ca

CaCO_3 calcium carbonate + CH_3CO_2H acetic acid ⟶ H_2O water + CO_2 carbon dioxide + (CH3COO)2Ca

Balance the chemical equation algebraically: CaCO_3 + CH_3CO_2H ⟶ H_2O + CO_2 + (CH3COO)2Ca Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCO_3 + c_2 CH_3CO_2H ⟶ c_3 H_2O + c_4 CO_2 + c_5 (CH3COO)2Ca Set the number of atoms in the reactants equal to the number of atoms in the products for C, Ca, O and H: C: | c_1 + 2 c_2 = c_4 + 4 c_5 Ca: | c_1 = c_5 O: | 3 c_1 + 2 c_2 = c_3 + 2 c_4 + 4 c_5 H: | 4 c_2 = 2 c_3 + 6 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 = 2 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CaCO_3 + 2 CH_3CO_2H ⟶ H_2O + CO_2 + (CH3COO)2Ca

+ ⟶ + + (CH3COO)2Ca

calcium carbonate + acetic acid ⟶ water + carbon dioxide + (CH3COO)2Ca

Construct the equilibrium constant, K, expression for: CaCO_3 + CH_3CO_2H ⟶ H_2O + CO_2 + (CH3COO)2Ca 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: CaCO_3 + 2 CH_3CO_2H ⟶ H_2O + CO_2 + (CH3COO)2Ca 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 CaCO_3 | 1 | -1 CH_3CO_2H | 2 | -2 H_2O | 1 | 1 CO_2 | 1 | 1 (CH3COO)2Ca | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CaCO_3 | 1 | -1 | ([CaCO3])^(-1) CH_3CO_2H | 2 | -2 | ([CH3CO2H])^(-2) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] (CH3COO)2Ca | 1 | 1 | [(CH3COO)2Ca] 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 = ([CaCO3])^(-1) ([CH3CO2H])^(-2) [H2O] [CO2] [(CH3COO)2Ca] = ([H2O] [CO2] [(CH3COO)2Ca])/([CaCO3] ([CH3CO2H])^2)

Construct the rate of reaction expression for: CaCO_3 + CH_3CO_2H ⟶ H_2O + CO_2 + (CH3COO)2Ca 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: CaCO_3 + 2 CH_3CO_2H ⟶ H_2O + CO_2 + (CH3COO)2Ca 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 CaCO_3 | 1 | -1 CH_3CO_2H | 2 | -2 H_2O | 1 | 1 CO_2 | 1 | 1 (CH3COO)2Ca | 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 CaCO_3 | 1 | -1 | -(Δ[CaCO3])/(Δt) CH_3CO_2H | 2 | -2 | -1/2 (Δ[CH3CO2H])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) (CH3COO)2Ca | 1 | 1 | (Δ[(CH3COO)2Ca])/(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[CaCO3])/(Δt) = -1/2 (Δ[CH3CO2H])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[(CH3COO)2Ca])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium carbonate | acetic acid | water | carbon dioxide | (CH3COO)2Ca formula | CaCO_3 | CH_3CO_2H | H_2O | CO_2 | (CH3COO)2Ca Hill formula | CCaO_3 | C_2H_4O_2 | H_2O | CO_2 | C4H6CaO4 name | calcium carbonate | acetic acid | water | carbon dioxide |