C + HClO4 = H2O + Cl2 + CO2

C activated charcoal + HClO_4 perchloric acid ⟶ H_2O water + Cl_2 chlorine + CO_2 carbon dioxide

Balance the chemical equation algebraically: C + HClO_4 ⟶ H_2O + Cl_2 + CO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 HClO_4 ⟶ c_3 H_2O + c_4 Cl_2 + c_5 CO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Cl, H and O: C: | c_1 = c_5 Cl: | c_2 = 2 c_4 H: | c_2 = 2 c_3 O: | 4 c_2 = c_3 + 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7/2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 7/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 7 c_2 = 4 c_3 = 2 c_4 = 2 c_5 = 7 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 C + 4 HClO_4 ⟶ 2 H_2O + 2 Cl_2 + 7 CO_2

+ ⟶ + +

activated charcoal + perchloric acid ⟶ water + chlorine + carbon dioxide

Construct the equilibrium constant, K, expression for: C + HClO_4 ⟶ H_2O + Cl_2 + CO_2 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: 7 C + 4 HClO_4 ⟶ 2 H_2O + 2 Cl_2 + 7 CO_2 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 C | 7 | -7 HClO_4 | 4 | -4 H_2O | 2 | 2 Cl_2 | 2 | 2 CO_2 | 7 | 7 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 7 | -7 | ([C])^(-7) HClO_4 | 4 | -4 | ([HClO4])^(-4) H_2O | 2 | 2 | ([H2O])^2 Cl_2 | 2 | 2 | ([Cl2])^2 CO_2 | 7 | 7 | ([CO2])^7 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 = ([C])^(-7) ([HClO4])^(-4) ([H2O])^2 ([Cl2])^2 ([CO2])^7 = (([H2O])^2 ([Cl2])^2 ([CO2])^7)/(([C])^7 ([HClO4])^4)

Construct the rate of reaction expression for: C + HClO_4 ⟶ H_2O + Cl_2 + CO_2 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: 7 C + 4 HClO_4 ⟶ 2 H_2O + 2 Cl_2 + 7 CO_2 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 C | 7 | -7 HClO_4 | 4 | -4 H_2O | 2 | 2 Cl_2 | 2 | 2 CO_2 | 7 | 7 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 C | 7 | -7 | -1/7 (Δ[C])/(Δt) HClO_4 | 4 | -4 | -1/4 (Δ[HClO4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Cl_2 | 2 | 2 | 1/2 (Δ[Cl2])/(Δt) CO_2 | 7 | 7 | 1/7 (Δ[CO2])/(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 = -1/7 (Δ[C])/(Δt) = -1/4 (Δ[HClO4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[Cl2])/(Δt) = 1/7 (Δ[CO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | perchloric acid | water | chlorine | carbon dioxide formula | C | HClO_4 | H_2O | Cl_2 | CO_2 Hill formula | C | ClHO_4 | H_2O | Cl_2 | CO_2 name | activated charcoal | perchloric acid | water | chlorine | carbon dioxide IUPAC name | carbon | perchloric acid | water | molecular chlorine | carbon dioxide

| activated charcoal | perchloric acid | water | chlorine | carbon dioxide molar mass | 12.011 g/mol | 100.5 g/mol | 18.015 g/mol | 70.9 g/mol | 44.009 g/mol phase | solid (at STP) | liquid (at STP) | liquid (at STP) | gas (at STP) | gas (at STP) melting point | 3550 °C | -112 °C | 0 °C | -101 °C | -56.56 °C (at triple point) boiling point | 4027 °C | 90 °C | 99.9839 °C | -34 °C | -78.5 °C (at sublimation point) density | 2.26 g/cm^3 | 1.77 g/cm^3 | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 0.00184212 g/cm^3 (at 20 °C) solubility in water | insoluble | very soluble | | | surface tension | | | 0.0728 N/m | | dynamic viscosity | | 8×10^-4 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | | 1.491×10^-5 Pa s (at 25 °C) odor | | odorless | odorless | | odorless