HCl + H2CO3 = H2O + Cl2 + C

HCl hydrogen chloride + H_2CO_3 carbonic acid ⟶ H_2O water + Cl_2 chlorine + C activated charcoal

Balance the chemical equation algebraically: HCl + H_2CO_3 ⟶ H_2O + Cl_2 + C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 H_2CO_3 ⟶ c_3 H_2O + c_4 Cl_2 + c_5 C Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, C and O: Cl: | c_1 = 2 c_4 H: | c_1 + 2 c_2 = 2 c_3 C: | c_2 = c_5 O: | 3 c_2 = c_3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 3 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HCl + H_2CO_3 ⟶ 3 H_2O + 2 Cl_2 + C

+ ⟶ + +

hydrogen chloride + carbonic acid ⟶ water + chlorine + activated charcoal

Construct the equilibrium constant, K, expression for: HCl + H_2CO_3 ⟶ H_2O + Cl_2 + C 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 HCl + H_2CO_3 ⟶ 3 H_2O + 2 Cl_2 + C 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 HCl | 4 | -4 H_2CO_3 | 1 | -1 H_2O | 3 | 3 Cl_2 | 2 | 2 C | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 4 | -4 | ([HCl])^(-4) H_2CO_3 | 1 | -1 | ([H2CO3])^(-1) H_2O | 3 | 3 | ([H2O])^3 Cl_2 | 2 | 2 | ([Cl2])^2 C | 1 | 1 | [C] 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 = ([HCl])^(-4) ([H2CO3])^(-1) ([H2O])^3 ([Cl2])^2 [C] = (([H2O])^3 ([Cl2])^2 [C])/(([HCl])^4 [H2CO3])

Construct the rate of reaction expression for: HCl + H_2CO_3 ⟶ H_2O + Cl_2 + C 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 HCl + H_2CO_3 ⟶ 3 H_2O + 2 Cl_2 + C 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 HCl | 4 | -4 H_2CO_3 | 1 | -1 H_2O | 3 | 3 Cl_2 | 2 | 2 C | 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 HCl | 4 | -4 | -1/4 (Δ[HCl])/(Δt) H_2CO_3 | 1 | -1 | -(Δ[H2CO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Cl_2 | 2 | 2 | 1/2 (Δ[Cl2])/(Δt) C | 1 | 1 | (Δ[C])/(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[HCl])/(Δt) = -(Δ[H2CO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[Cl2])/(Δt) = (Δ[C])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | carbonic acid | water | chlorine | activated charcoal formula | HCl | H_2CO_3 | H_2O | Cl_2 | C Hill formula | ClH | CH_2O_3 | H_2O | Cl_2 | C name | hydrogen chloride | carbonic acid | water | chlorine | activated charcoal IUPAC name | hydrogen chloride | carbonic acid | water | molecular chlorine | carbon